I was planning to write an essay explaining the method of rationally resolving conflicts and always acting on a single idea with no outstanding criticisms. It would followup on my essay Epistemology Without Weights and the Mistake Objectivism and Critical Rationalism Both Made where I mentioned the method but didn't explain it.
I knew I'd already written a number of explanations on the topic, so I decided to reread them for preparation. While reading them I decided that the topic is hard and it'd be very hard to write a single essay which is good enough for someone to understand it. Maybe if they already had a lot of relevant background knowledge, like knowing Popper, Deutsch or TCS, one essay could work OK. But for an Objectivist audience, or most audiences, I think it'd be really hard.
So I had a different idea I think will work better: gather together multiple essays. This lets people learn about the subject from a bunch of different angles. I think this way will be the most helpful to someone who is interested in understanding this philosophy.
Each link below was chosen selectively. I reread all of them as well as other things that I decided not to include. It may look like a lot, but I don't think you should expect an important new idea in epistemology to be really easy and short to learn. I've put the links in the order I recommend reading them, and included some explanations below.
Instead of one perfect essay – which is impossible – I present instead some variations on a theme.
Update 2017: Buy my Yes or No Philosophy to learn a ton more about this stuff. It has over 6 hours of video and 75 pages of writing. See also this free essay giving a short argument for it.
Update Oct 2016: Read my new Rejecting Gradations of Certainty.
Popper's critical preferences idea is incorrect. It's similar to standard epistemology, but better, but still shares some incorrectness with rival epistemologies. My criticisms of it can be made of any other standard epistemology (including Objectivism) with minor modifications. I explained a related criticism of Objectivism in my prior essay.
Critical Preferences
Critical Preferences and Strong Arguments
The next one helps clarify a relevant epistemology point:
Corroboration
Regress problems are a major issue in epistemology. Understanding the method of rationally resolving conflicts between ideas to get a single idea with no outstanding criticism helps deal with regresses.
Regress Problems
Confused about anything? Maybe these summary pieces will help:
Conflict, Criticism, Learning, Reason
All Problems are Soluble
We Can Always Act on Non-Criticized Ideas
This next piece clarifies an important point:
Criticism is Contextual
Coercion is an important idea to understand. It comes from Taking Children Seriously (TCS), the Popperian educational and parenting philosophy by David Deutsch. TCS's concept of "coercion" is somewhat different than the dictionary, keep in mind that it's our own terminology. TCS also has a concept of a "common preference" (CP). A CP is any way of resolving a problem between people which they all prefer. It is not a compromise; it's only a CP if everyone fully prefers it. The idea of a CP is that it's a preference which everyone shares in common, rather than disagreeing.
CPs are the only way to solve problems. And any non-coercive solution is a CP. CPs turn out to be equivalent to non-coercion. One of my innovations is to understand that these concepts can be extended. It's not just about conflicts between people. It's really about conflicts between ideas, including ideas within the same mind. Thus coercion and CPs are both major ideas in epistemology.
TCS's "most distinctive feature is the idea that it is both possible and desirable to bring up children entirely without doing things to them against their will, or making them do things against their will, and that they are entitled to the same rights, respect and control over their lives as adults." In other words, achieving common preferences, rather than coercion, is possible and desirable.
Don't understand what I'm talking about? Don't worry. Explanations follow:
Taking Children Seriously
Coercion
The next essay explains the method of creating a single idea with no outstanding criticisms to solve problems and how that is always possible and avoids coercion.
Avoiding Coercion
Avoiding Coercion Clarification
This email clarifies some important points about two different types of problems (I call them "human" and "abstract"). It also provides some historical context by commenting on a 2001 David Deutsch email.
Human Problems and Abstract Problems
The next two help clarify a couple things:
Multiple Incompatible Unrefuted Conjectures
Handling Information Overload
Now that you know what coercion is, here's an early explanation of the topic:
Coercion and Critical Preferences
This is an earlier piece covering some of the same ideas in a different way:
Resolving Conflicts of Interest
These pieces have some general introductory overview about how I approach philosophy. They will help put things in context:
Think
Philosophy: What For?
Update: This new piece (July 2017) talks about equivocations and criticizes the evidential continuum: Don't Equivocate
Want to understand more?
Read these essays and dialogs. Read Fallible Ideas. Join my discussion group and actually ask questions.
Messages (241)
Why does no one actually want to learn enough to read through some links?
I explained some CR stuff, particularly about assumptions and foundations:
https://groups.google.com/forum/#!msg/fallible-ideas/r9KDPJUwg88/eRa1meO4AgAJ
https://docs.google.com/document/d/17chWJ2M0HlD47FFt1ZxsZr6Ogf6K-LW5-dGOfdxBxao/edit#
found via https://twitter.com/krazyander/status/1128203880695619585
> David Deutsch’s hard-to-vary (HTV) criteria [1] is offered as a solution to a problem faced by his falsificationist epistemology, and critical rationalism (CR) alike.
3 errors in the first sentence. Should be “criterion” and no comma. And DD’s falsificationist epistemology *is* CR, it’s not a separate thing. OK I'll now stop being picky and try to figure out what the point is.
> David has not given a satisfyingly unambiguous definition of his HTV principle
Yes, I wrote some things about that here:
http://curi.us/2124-critical-rationalism-epistemology-explanations
A basic issue is: hard to vary given what constraints?
> Being unable to vary something implies a constraint. So what is it that constrains a scientific theory? I will demonstrate that the constraint is empirical evidence, or past observations. We can only vary a theory so much before it becomes inconsistent with the evidence at hand (past observations).
They are constrained by *many types of criticism*, not by a single type. Contradicting evidence is one type of criticism. Another is internal contradiction.
Also, in general, whatever constrains non-scientific (non-empirical) theories can also be used with scientific theories.
> For example, we cannot easily change any aspect of Newton’s laws whilst still remaining consistent with past observation of the motion of objects, so Newton’s laws are HTV.
No, Newton’s laws are trivial to change in infinitely many ways if the only constraint is matching the evidence. E.g. take anything you have no data about and add a special case exception with an arbitrary conclusion in that case. E.g. that DD will x-fall if he jumps off a building, as discussed in FoR ch. 7.
> The induction implied by HTV is deduced as follows.
> 1) A HTV theory is one in which each of its concepts is constrained by some past observed phenomena.
> 2) When we reflect back on past observations to see how constrained our concepts are, it is the same as reflecting back to see how well confirmed our concepts are.
> 3) Therefore, every concept involved in a hard to vary theory must have support from past observations.
The CR view is that all non-refuted ideas have *equal evidential support*: that is, they are compatible with 100% of the data points that we accept. (The possibility of bad data is a detail I won’t go into here.) This is sometimes presented as all the non-refuted views having "no evidential support" by people who reject the concept of evidential support. The concept of evidential support isn't useful because it's about *degrees* of support, but there are (according to CR) only 2 categories here (no degrees): refuted by the evidence, or not.
So, after decisively rejecting some ideas (all the ones that contradict any evidence), you cannot differentiate *by using evidence* which of the infinitely many remaining ideas are better or worse.
Those ideas have to be differentiated by other means: by other types of criticism.
*I think the existence and use of other types of criticism is the basic thing the article is missing.*
See also: the links in the blog post above. There's a bunch of relevant stuff there like Rejecting Gradations of Certainty and Yes or No Philosophy.
Brett Hall's bad and kinda unfriendly reply to the same article that #12596 replies to:
https://docs.google.com/document/d/1jN2_5bkm8MVAinU1JfpZnkS40cLTHqU1qNe4ak-AmJU/edit
Expanding on #12596
We can't reject theories just by finding contradicting evidence. We can't gather evidence for everything. There are infinitely many things. And we don't want to test some things, e.g. DD doesn't want to jump off a building to see if he floats when jumping off that particular building at that particular time (which won't empirically prove anything about other buildings, other times, the results if he were wearing different clothes, the results if his hair was a bit longer, and so on).
We can supplement empirical criticism with logical criticism. Some ideas contain internal contradictions, e.g. they say DD will both fall and float at the same time. Nonsense! But we still need more tools to reject more ideas with.
The CR view, in short, is that we have critical discussions in which we point out what are *bad arguments* and why. We seek out errors and do our best to understand them. This isn't a perfect process. We make tentative judgments even though we can't be certain. We may be wrong, so we need an ongoing process of error correction so we can, over time, become less wrong.
There is a more standard, non-CR view which is different. It believes we can get more mileage out of data beyond merely looking at what does or does not contradict the data. It claims: we can prefer theories which better fit the data over ideas which fit the data less well and we can prefer theories with more evidential support over those with less. *This is induction.*
The basic problem with that standard view is there is no way to define which data supports which idea and how much. People have been trying to figure that out and have totally failed and CR (and some prior thinkers too) has given us arguments about why it'll never work. There's no way to define which data is relevant to which theory so that only some data supports a theory while some is irrelevant, and there's no way to define degree of fit between data and theory. (Actually there are ways to define such things, but they don't work. They don't have the desired properties. They lead to conclusions that no one wants or accepts.)
"hard to vary" as induction
#12596
Thanks for having a look at my argument. Here is a response.
You are right that logical consistency can also be considered a constraint on our theories, but that is of limited use in constraining claims about the world outside obviously invalid theories such as "plants require some sunlight, and no sun exposure". Maybe you have other sorts of constraints in mind?
As I argue, h2v also implies that for our theories to be "good", we require evidential support for our claims. This is a much stronger claim, and is necessary for achieving DD's goal of labeling myths and prophecies as "bad".
However, you seem to reject that this requirement for evidential support is sufficient. You give the example of a bad theory, x-falling, suggesting it satisfies my definition of h2v, because it "matches evidence". I disagree, because my definition is more than just "matching evidence". My definition says that every concept of a good theory must be constrained by past observations. The claim that people fall in general is well constrained by past observation. We can't vary our explanation to say that people don't fall, or that they fall faster, whilst remaining consistent with our observations.
However, that one particular individual is going to float on a certain date is not constrained by past observation. We can vary the date, or the name of the individual endlessly, whilst remaining consistent with past observation. We can't do the same for any concept involved in Newton's gravitation. Hence x-fall is e2v and Newton's gravitation is h2v.
To summarize. Just because a theory is consistent with the evidence at hand, doesn't mean all of its concepts are constrained by past observation. So I think the problem with your criticism is that you didn't get my definition of h2v correct.
#12624
Every empirical theory is constrained by every single piece of data we have. Every data point limits what the theory can say: nothing that logically contradicts that data point.
x-falling and regular falling both are logically consistent with all empirical evidence we have. They fit with (don't contradict) *every past observation*. They were both designed with the constraint in mind of not contradicting even a single past observation.
To make further progress, one must consider other constraints that aren't merely "does it logically contradict data?". That's too limited of a constraint to do enough. There are many other constraints – any type of critical argument is an attempt to constrain ideas, and people make all sorts of arguments – but I don't want to go into them immediately because I want to focus on one issue at a time.
> We can't vary our explanation to say that people don't fall, or that they fall faster, whilst remaining consistent with our observations.
Logically, we can. There is no logical contradiction in seeing objects fall in some circumstances and saying they won't in other circumstances. To stop such claims requires something more than empirical consistency.
I think you believe data is constraining in some greater way than requiring logical non-contradiction. That's the standard inductivist view which CR denies. The basic situation is that most people find that claim intuitive but no one has ever been able to figure out detailed arguments that work (and CR has, preemptively, a bunch of reasoning about why it won't work). It's roughly the same problem as defining what observations support what theories (and how much) – the idea there is to mean something more than "logical consistency" by "support" – but what?
(This is standard CR stuff, which DD and I both believe, which is not specific to the h2v issue. The h2v idea is meant to make sense within the context of these CR beliefs, not to stand on its own without these other CR claims. So we need to start with CR in general because that's where our first disagreement is. In other words, you're disagreeing with CR premises that DD had in mind when talking about h2v.)
#12625
I think this is important to highlight: "My definition says that EVERY concept of a good theory must be constrained by past observations."
So your example may be consistent with "every past observation", but when we examine your theory, we see at least one of its concepts is not constrained by past observation.
We have to be clear about the difference between:
1) every concept of a theory being constrained by past observation.
AND
2) A theory being consistent with every past observation.
They are not the same thing.
The "DD will float [in X circumstances]" aspect is constrained by every past observation: there is no past observation that it contradicts.
There is no observation that it contradicts. That is (2), but my definition is (1).
The "DD" and the "X" of "DD will float in X circumstances" are easy to vary concepts of your floater theory. We can swap out DD for any other name, and the theory still works. So the floater theory fails my definition.
Looking over my definition in the google docs, I can see why you would offer this criticism. I think I need to be careful where I say "We cannot easily vary any of these concepts without becoming inconsistent with the evidence at hand". I should clarify and add " or without adding some new easy-to-vary concept to the theory".
#12629 The constraint imposed by an observation (that we accept) is that any theory which *logically contradicts that observation* is rejected. This addresses (1), not just (2). The "DD will x-fall" theory (and just the specific part about him floating, too) as an empirical theory (one that makes some empirical claims) is constrained by every single past observation: at theory formation, and when considering changes to it, all of those constraints must be taken into account. That limits what empirical claims it makes just as much as every other empirical theory is limited by data.
Do you believe there is some other way that data points can constrain theories?
> " or without adding some new easy-to-vary concept to the theory".
That won't help with the problem of establishing that "DD will x-fall" *is* easy-to-vary. My point (which is also DD's position) is that that cannot be established in terms of just data constraints. That approach doesn't work. More than data is needed.
#12629
If we change Newton's inverse square law to an inverse cube law, our theory becomes falsified.
If we change DD to Kieren in the floater theory, the theory is still ok.
There is at least one element of the floater theory that can be easily varied without being falsified, so it fails my definition.
How do you account for this difference between the theories?
#12631 The topic under discussion was data constraints. You made claims relating to them. You're now bringing up other, non-data issues. Do you now agree that the x-falling theory is *fully constrained by the empirical data*, exactly the same as the Newtonian theory?
We need to resolve the current issue before switching.
My original revision of the google doc has "every concept of a hard-to-vary theory is required for explaining some past observations".
So my question to you is, what past observations is the "DD will float" part of you theory required for explaining?
#12632
I thought I was still talking about data constraints.
When I say falsified, I mean "inconsistent with past observations".
#12634
So varying newtons theory leads it to be inconsistent with out past observations that it is explaining, but varying your floater theory does not lead to such inconsistency.
The difference between h2v, and e2v.
> So my question to you is, what past observations is the "DD will float" part of you theory required for explaining?
None. That is not a data constraint. It's not about data ruling out or supporting anything. It's an abstract argument saying roughly that we shouldn't make purposeless claims. The constraint imposed by that argument is a philosophical, argument-based constraint. Do you think it's an inductive argument in some way?
FYI: the more general version of that argument is that every part of our ideas should have some *problem solving purpose*. Helping us understand our observations is one type of problem to solve. There are many other problems like what are the best thinking methods or how to live morally. This extension is important because CR is a universal epistemology: it deals with non-empirical ideas too.
#12636
I'm not sure if you have a special definition in mind when you talk about data constraints?
What I think of as data constraints is observations. My argument is about theories being constrained by *observations*.
> So varying newtons theory leads it to be inconsistent with out past observations that it is explaining, but varying your floater theory does not lead to such inconsistency.
1. There are infinitely many variations of Newton's laws which are *inconsistent* with past observations.
2. There are also infinitely many variations of Newton's laws which are *consistent* with past observations.
The same is true for the x-fall theory of physics:
3. There are infinitely many variations of x-fall theory which are *inconsistent* with past observations.
4. There are also infinitely many variations of x-fall theory which are *consistent* with past observations.
This is symmetric. It looked asymmetric because you picked examples from categories 1 and 4, but not 2 or 3.
> What I think of as data constraints is observations. My argument is about theories being constrained by *observations*.
I said what I meant by a data constraint: being constrained by *not contradicting* an observation.
You haven't said what you mean.
Very clearly stated :)
Can you give me an example of 2?
The x-fall theory is a variation of Newton's laws in category 2. That was what it was designed to be! It was chosen specifically for the purpose of illustrating that looking at what does and doesn't contradict past observations isn't constraining enough. There are infinitely many more like that which specify floating, instead of falling, in other circumstances (different people or objects, falling from different buildings, only applies to falling during arbitrary time ranges, etc). Another category 2 theory would be that gravity is only n% effective on living dinosaurs, for any real number n other than 100.
#12641
That is what I now expected. Originally I thought your x-fall theory was an example of an e2v theory that would fit my definition of h2v, but you actually provide it as an example of a variation of Newton's gravitation.
The fault is with me. I realize now that the recent changes to my google doc has left my definition open to this criticism. I should be able to fix this soon.
More clearly, my definition should say something like: Every concept of a hard-to-vary theory is required for explaining some past observations. We cannot easily vary any of these concepts whilst still being able to account for what we want to explain.
This is still a constraint by observations, but different to the one you have been arguing against.
#12642
Under this definition, your floater theory is rejected because you floating person is not required for explaining any past observations.
The way I link this to induction is through the requirement for every element of a theory to have some evidential support for it to be a "good" theory.
> More clearly, my definition should say something like: Every concept of a hard-to-vary theory is required for explaining some past observations. We cannot easily vary any of these concepts whilst still being able to account for what we want to explain.
This suggests a new and superior version of Newton's laws: it's like the old laws, except all claims about the future are replaced with "I don't know". This new version has gotten rid of an unnecessary part of the old laws. The future claims in the old laws were not useful for explaining any past observations, so we're better off without them. What do you think?
I see what you mean.
In this case, we would have two compatible theories with one of the theories saying more about the world than the other.
It's like me having one theory that says 'red helium balloons rise in the air', and another theory that says 'all helium balloons rise in the air'. Since the theories are compatible, I think the choice is yours.
If we want to predict as much as possible about the world, then we will be preferring the theory that says the most about the world.
I don't think theories which say "I don't know" about the future is a problem hard-to-vary was trying to address. I think that falls more with the "theories must be falsifiable" principle. Regardless, my focus is on the aspect of h2v that resembles induction.
Perhaps "required" is too strong, and it should be "Every concept of a hard-to-vary theory is involved in explaining..."
> If we want to predict as much as possible about the world, then we will be preferring the theory that says the most about the world.
Yes, preferring theories that say more (without being wrong) is a type of non-empirical constraint or criticism (we use it to argue against theories that say less).
> Since the theories are compatible, I think the choice is yours.
People want help making such choices, and it's a major role of epistemology to provide that help. It's not an arbitrary choice, some choices are better than others, so people want guidance about how to choose well. CR and h2v try to help with that. Induction also tries to help with it.
> I don't think theories which say "I don't know" about the future is a problem hard-to-vary was trying to address.
I can tell you, from discussions with DD (I've had thousands and also did extensive editing for BoI), that that is one of the problems h2v is meant to address (in DD's opinion). The way it addresses it is via non-empirical constraints on variation like preferring to say more (it's not that simple, but something kinda like that) and preferring more simple and elegant theories (which is not a simple thing to do or give the details of, but we do use ideas along those lines).
DD never meant h2v to be focused on empirical data. It's general purpose, but you interpreted it with a focus on empirical data. That's a common interpretation because of common non-CR ideas that most people hold which lead people to think that way.
Anyway, are you now willing to withdraw the claim that h2v is inductivist, or do you still have another way to try to argue that? (BTW I don't even think h2v is a perfect idea, I just don't think it's inductivist.)
I might grant you that h2v could really mean that a good theory is constrained by critisism in general, but then isn't it saying nothing more than "good theories have survived critisism".
I would suggest that the main critisism that h2v highlights is lack of evidential support for a particular claim.
I see this when DD talks about bad theories being barely connected with the "phenomena" they are trying to explain. All we know of a phenomena is our observations of it right? He points out how gods can be freely varied without the theory saying anything different about the phenomena.
Or when he says a h2v theory can't be changed whilst still being able to explain what it purports to explain. What it purports to explain is our observations right?
While DD might have something else in mind, all his examples seem to point out theories that are bad because they lack support for their claims.
DD is clear that h2v isn't an empirical matter when he writes, e.g.:
> That is what makes good explanations essential to science: it is only when a theory is a good explanation – hard to vary – that it even matters whether it is testable. Bad explanations are equally useless whether they are testable or not.
Here he presents h2v as an issue to worry about *prior to* whether a theory is empirical or testable at all.
> I might grant you that h2v could really mean that a good theory is constrained by critisism in general, but then isn't it saying nothing more than "good theories have survived critisism".
Roughly, yes, that's what it's saying. I tried to explain to DD, on multiple occasions, before BoI came out, that h2v isn't especially deep or important compared to other CR ideas (it's very deep and important compared to induction). It's one way, of many, to explain what knowledge is. DD chose to go ahead with presenting h2v as a crucial insight in the book anyway. I don't consider that a big problem. There is lots of room for leeway in how to attempt to explain ideas which are hard to explain to people successfully. It's good for a variety of approaches to be tried. His approach does have various upsides and lots of people have liked it.
h2v isn't wrong but IMO it also isn't superior to other ways of talking about knowledge: ideas that survive criticism, non-arbitrary ideas, ideas that are more constrained, ideas that solve problems, ideas that are adapted to a purpose, etc. (Or, more generally, information rather than ideas, since genes have adapted information which is knowledge but isn't really "ideas".) Or: knowledge is what you get from evolution (replication with variation and selection. the selection is in regards to some kinda goal, purpose, problem, set of criticisms, something like that. the variation can work a lot of different ways as long as it's not too bounded.)
Where people get stuck, I think, is more about empiricism than about which explanation of knowledge is presented (and anyway DD has presented other explanations of what knowledge is in his books, too). And BoI does have a section criticizing empiricism. DD, like Popper, tried to tell people to focus more on explanations and less on data, but it's a hard message to get across to people.
> All we know of a phenomena is our observations of it right?
No, most of our knowledge is not empirical, it's conceptual and explanatory. E.g. I know things about the inside of the sun even though I've never observed it.
> What it purports to explain is our observations right?
Most of our explanations and criticisms are more about *other explanations and criticisms* than about observations. We have explanations of explanations of explanations of explanations. We have a huge web of ideas which are interconnected in complex ways. People routinely take 2-10 ideas, and no observations, and make another idea. Originally, perhaps more of the ideas were related to observations or only a few levels removed from observations, but now tons of ideas are only distantly related to observations if at all. And ideas can and do gain autonomy from distant foundations even if they once had those foundations (this non-foundationalism is a CR idea which is discussed eg here https://groups.google.com/forum/#!msg/fallible-ideas/r9KDPJUwg88/eRa1meO4AgAJ ). And many ideas have always been pretty purely non-empirical, e.g. ideas about the *methods* of rational thinking or the *logic* of economics are not about explaining observations. The connection of moral values to observations has also long been doubted. And it's only via non-empirical ideas that we're able to interpret our observations in the first place, so everything depends on theory (see e.g. Popper's explanations that all observation is theory-laden).
Can you give me an example of how an accepted scientific theory is good because of non-arbitrary ideas, ideas that are more constrained, ideas that solve, etc, and not because its ideas are supported by past observation?
I've been presented these same principles before, but when I have insisted on asking "why" these principles work, I end up with a circular argument, or with hints of induction.
For example, people will complain about "arbitrary" elements of a theory, but if what they mean by arbitrary is "not connected to any past observations", then they make exactly the point I am trying to make.
Newton's theories are non-arbitrary b/c they don't have an arbitrary DD will sometimes float part.
Newton's theories are more constrained than "Stuff moves". They are designed under constraints like that they must provide a general mathematical law that doesn't depend on time, place, or other parochial details.
Newton's theories solve the problem of helping us understand motion. So e.g. "Joe is tall." would not be a viable replacement theory, even if true, because it's not addressing the problem.
Past observation is involved via argument: we sometimes make critical arguments that use observations. And we actually have arguments, which use certain observations from certain experiments, to conclude that Newton's laws are false. However, that critical argument only refutes Newton's laws for some purposes, e.g. the purpose of being a universally and exactly true theory of the physics of motion. It doesn't refute them as a good enough approximation in various ranges of circumstances (which is why it's fine for us to use them in this discussion).
In general, in critical discussions, we have *shared premises*. We agree on some things, either because we both share an idea or because we decide to accept those things for the purpose of the discussion. We then argue using those shared premises. In a different discussion, we can use different premises. No premises are absolute or unquestionable. However, at any given time, we can only discuss some things, not everything. We use ideas X, Y and Z to discuss W. Then later we critically consider X in terms of A, B and Z. And so on. Everything is improvable this way.
Things like non-arbitrary or h2v have more detailed versions of them. There's a lot more substance to them than the slogan. But no matter how much detail I gave, you could always desire more. We're only at the beginning of infinity. Our ignorance is infinite. There is infinite more stuff to learn. Our situation is always using ideas not because of any positive justification but merely because we don't know an error with them. We prefer ideas without known errors to ones with known errors. I don't know an error with my way of thinking about non-arbitrary, and I can often find discussion partners who understand enough of what I mean (and don't object to it) for us to make progress in discussion using it, so it works to discuss in terms of it.
Part of why these ideas usually aren't a big problem in discussion, even without giving more detail, is because I generally only use them in limited ways. If someone wants to suggest arbitrary exceptions to gravity, OK I'll say arbitrary stuff is bad. But people don't usually want to do that. They usually want to argue for something they believe in good faith like that that the many-worlds interpretation of quantum physics is false, and we end up arguing physics details, not calling each other's views arbitrary. I think h2v and non-arbitrary are useful for understanding epistemology and what knowledge is, and for dealing with certain types of abstract issues, but they are generally bad things to bring up when discussing some more specific topic and both people are being reasonable. Nevertheless I've written extensively about further details of epistemology, as have DD and Popper. Besides my websites and Popper reading recommendations, there's also well over 100,000 pages of forum archives where one can find many discussions elaborating on epistemology details. Some of the archives are downloadable at https://curi.us/ebooks
> Newton's theories are more constrained than "Stuff moves". They are designed under constraints like that they must provide a general mathematical law that doesn't depend on time, place, or other parochial details.
Why do we choose to let this constrain us though? Is it not related to the fact that in all our observations of motion, it has never depended on such parochial details. Isn't it a constraint because it is what we want to capture with our explanation?
Consider a theory that says people will float depending on how hard they clench their fist. It is arbitrary, but not so much if we happened to have a wealth of observations of this behavior.
If a theory is trying to explain some phenomena, then it is constrained by what observations we have in relation to that phenomena.
Let me put this to you. Any theory that says something new about the world puts forward a new general claim. This claim either:
1) is explained by other accepted theories, which in turn put forward their own general claims.
OR
2) is accepted as knowledge through induction.
So when you say that not all explanations are explaining just observations, but also sometimes other explanations, that is a instance of (1), but that doesn't mean the lower level explanation's claims aren't being rendered true via induction.
Newtons gravitation and his concept of force were not explained (deduced) from other explanations. Instead it was a new claim about the world (conjecture), rendered true from all of the vast phenomena it successfully explained. This is an application of (2).
> Past observation is involved via argument: we sometimes make critical arguments that use observations. And we actually have arguments, which use certain observations from certain experiments, to conclude that Newton's laws are false.
We also reference our lack of observations to reject theories, such as the existence of a particular god.
> Things like non-arbitrary or h2v have more detailed versions of them. There's a lot more substance to them than the slogan. But no matter how much detail I gave, you could always desire more.
I don't expect you to possess infinite levels of explanation. It has to start somewhere for us.
> I think h2v and non-arbitrary are useful for understanding epistemology and what knowledge is, and for dealing with certain types of abstract issues.
That's what I'm interested. A good theory of knowledge.
> Why do we choose to let this constrain us though?
We choose constraints when we guess they may serve a useful purpose, and we don't see anything wrong with them.
> It is arbitrary, but not so much if we happened to have a wealth of observations of this behavior.
What is addressed to solving a problem, and what isn't, depends on the current problem situation: what problems we have to solve, including problems related to ideas or to observations we want to understand better.
> Let me put this to you. Any theory that says something new about the world puts forward a new general claim.
No, some new ideas aren't general. "That dog is black", regarding a particular dog, is thought or said for a first time.
> but that doesn't mean the lower level explanation's claims aren't being rendered true via induction.
But induction can't and doesn't work, as explained by Popper and Deutsch. Have you read their arguments and come up with a refutation of their reasoning about why it doesn't work? When I asked you questions about it, e.g. to specify which observations support which ideas, you were not able to give any inductive solution. Your attempt at a solution was the *non-inductive* idea that ideas should be aimed to solve problems, including to help us understand observations.
> We also reference our lack of observations to reject theories, such as the existence of a particular god.
CRists reject god for not solving a problem, not for lack of observation. See DD's criterion for what exists.
> That's what I'm interested. A good theory of knowledge.
CR says knowledge is information which has been evolutionarily improved to better solve some problem(s). This makes it adapted, which means random variations are very likely to make it worse rather than better (regarding the problem(s) it aims to solve). Or, equivalently, conjectures which we don't know a refutation of.
> Newtons gravitation and his concept of force were not explained (deduced) from other explanations.
Explained does not mean "deduced" and *is not similar to deduction*. Where are you getting that?
> Instead it was a new claim about the world (conjecture), rendered true from all of the vast phenomena it successfully explained.
Things are tentatively accepted as true due to *lack of refutation* (lack of known error). The positive support approaches don't work when you try to work out the details. They have been refuted by CR.
> We choose constraints when we guess they may serve a useful purpose, and we don't see anything wrong with them.
We guess, and then we also try and falsify our guess right? roughly: the more failed falsification attempts the better.
>> It is arbitrary, but not so much if we happened to have a wealth of observations of this behavior.
> What is addressed to solving a problem, and what isn't, depends on the current problem situation: what problems we have to solve, including problems related to ideas or to observations we want to understand better.
The problem in this situation is to explain some phenomena, but as you say, there are infinite logically possible (many arbitrary) theories that could explain the same phenomena. So "it must solve a problem" is not a replacement for "every element of the theory must be involved in explaining some past observations".
> No, some new ideas aren't general. "That dog is black", regarding a particular dog, is thought or said for a first time.
Ok, we can include particular ideas too if you like. My point still stands.
> But induction can't and doesn't work, as explained by Popper and Deutsch. Have you read their arguments and come up with a refutation of their reasoning about why it doesn't work?
I have read their arguments against induction. I do not find them convincing. I agree with Hume, as do they, that you end up in a circle trying to justify induction rationally. As to the solution to this problem, my solution is closer to Hume's solution. I think induction is a part of our rationality. It is a part of our nature.
Just because induction cannot be justified doesn't mean it is wrong.
>When I asked you questions about it, e.g. to specify which observations support which ideas, you were not able to give any inductive solution.
The observations that support an idea are it's consequences that have been found to be true. It's the same as those consequences that we failed to falsify.
> CRists reject god for not solving a problem, not for lack of observation. See DD's criterion for what exists.
Where can I find this criterion for what exists?
Gods pulling the sun around the earth to explain the seasons does solve a problem. My theory that a particular dance will cure someone's disease also solves a problem.
> Explained does not mean "deduced" and *is not similar to deduction*. Where are you getting that?
With newtons laws I explain the motion of many simple machines. I infer their motion deductively from the laws. This is how I see them as similar.
> Things are tentatively accepted as true due to *lack of refutation* (lack of known error). The positive support approaches don't work when you try to work out the details. They have been refuted by CR.
Instances of failed falsification are instances of successful confirmations. Thinking better of a theory in general because you failed to falsify it in a number of instances is a form of induction.
> We guess, and then we also try and falsify our guess right?
Yes. Except I'd say we try to *criticize* our guesses. "Falsify" commonly refers only to empirical criticism, not all criticism. To avoid confusion, I use "criticize" or "refute" to refer to all types of criticisms, and "empirically falsify" for empirical criticism only.
> roughly: the more failed falsification attempts the better.
Very, very roughly, yes. But counting attempts is not actually a good way to judge. It runs into major problems.
> The problem in this situation is to explain some phenomena, but as you say, there are infinite logically possible (many arbitrary) theories that could explain the same phenomena. So "it must solve a problem" is not a replacement for "every element of the theory must be involved in explaining some past observations".
It wasn't a replacement, it was just a different criticism.
The claim "every element of the theory must be involved in explaining some past observations" is incorrect, both because of non-empirical theories and because it disallows any predictions about the future (which are not necessary for explaining the past).
> I have read their arguments against induction. I do not find them convincing.
Then quote an anti-induction CR argument – pick one of the ones you consider *best and most important – and point out an error in it.
> Where can I find this criterion for what exists?
The title of chapter 4 of DD's book *The Fabric of Reality* is "Criteria for Reality".
This question shows major lack of familiarity with DD's writing, which means you aren't in a good position to judge whether his anti-inductive arguments are correct. I suggest instead of trying to refute CR (as per the previous section) you focus more on learning what it says. E.g., before trying to refute an anti-induction CR argument, I think it'd be better to try to *state one in a way that a CR expert would agree with*, in order to test if your understanding of what CR says matches the understanding of the CR ppl or not. (Actually I'd recommend this as a good place to start anyway, with anyone, even if they were more familiar with the literature.)
> Gods pulling the sun around the earth to explain the seasons does solve a problem.
Yes but I already have other solutions to that problem, so I don't need God. God doesn't solve any open problem *I* have.
If you reject those solutions, God can *appear* to solve certain problems, but it doesn't really. Conjecturing some amount of arbitrary complexity to solve a problem with *less* complexity than that is only making things worse (overall), not solving anything. It's *increasing*, not decreasing, the amount of complexity in one's worldview that isn't explained well, isn't constrained well, isn't understood well, etc.
> With newtons laws I explain the motion of many simple machines. I infer their motion deductively from the laws. This is how I see them as similar.
That's a common misunderstanding of CR. Do you think you could state what CR means by explanation? And "newtons laws" is ambiguous about whether you mean just the mathematical formulas (which only predict) or also the explanations we know of that go with them.
> Instances of failed falsification are instances of successful confirmations. Thinking better of a theory in general because you failed to falsify it in a number of instances is a form of induction.
I agree that would be a form of induction. But CR *does not do that*. (Popper did consider doing something like that in his earlier work, which has led to confusion about this.)
I divide theories into exactly two categories: refuted and non-refuted. Theory X is better than theory Y if and only if theory X is in the category "non-refuted" and theory Y is in the category "refuted". There are no degrees of betterness, and failed falsifications do not make theories better (except maybe in some loose, informal, non-rigorous way – I'm just talking about what is technically correct, not about informal approximations).
kieren, I think you're interpretting h2v as inductive because of 2 things:
A) you are an inductivist. you think induction is true. [1]
B) you are trying to interpret h2v in a way that it's true
given A, you have to find a way to interpret h2v as induction or else it wouldn't be true (which would violate B).
I think DD would prefer that you claim h2v is false due to the lack of induction, rather than try to bring him into the inductivist camp. This would lead to discussing what I think is the right topic: *whether induction is correct*. You apparently disagree with DD/CR about that, so I think that's a better place to begin than whether h2v is inductive.
I think the best way to discuss that, right now, with you, is by you trying to understand (primarily) and criticize (secondarily) CR passages about induction. Quote a few paragraphs [2] and say both what you think it says and why it's false (not weak or non-best, but decisively and clearly wrong). Weaker criticisms could be discussed after we reach agreement about the decisive ones.
Or if you don't like that approach, you could suggest something else.
*Footnotes:*
[1] I think you believe/claim induction works, as opposed to CR which claims induction is impossible. CR says no one has ever learned the slightest thing by induction because induction *can't be done*. There is no set of steps a person can follow which is 1) induction and 2) possible. (This criticism of induction is not about whether induction is justified or rational.)
[2] For sources, please stick with DD's 2 books, the KP selections from http://fallibleideas.com/books#Popper and ET's writing. That's where the best CR arguments are.
> To avoid confusion, I use "criticize" or "refute" to refer to all types of criticisms, and "empirically falsify" for empirical criticism only.
Lets stick with how CR applies to scientific/empirical theories for now.
> It wasn't a replacement, it was just a different criticism.
Then it is an insufficient criticism for refuting my example.
> The claim "every element of the theory must be involved in explaining some past observations" is incorrect, both because of non-empirical theories and because it disallows any predictions about the future (which are not necessary for explaining the past).
My claim does not disallow predictions about the future. Because claims about the future may still be involved in explaining the past.
The same claims that account for some past observations may be predicting future observation too.
> Then quote an anti-induction CR argument – pick one of the ones you consider *best and most important – and point out an error in it.
DD seems to attack a form of inductivism that supposes that all knowledge comes from induction alone. My view is that induction is just one part of the picture.
So when DD says "inductivism purports to explain how science obtains predictions about experiences", he is attacking an idea of induction that I don't think anyone holds to. Deriving predictions is the role of deduction, not induction.
His other critisism is "The second fundamental misconception in inductivism is that scientific theories predict that ‘the future will resemble the past’, and that ‘the unseen resembles the seen’ and so on."
I'm not entirely sure what his getting at with this. He goes on to point out a number of counter-examples where the future is not like the past, etc. So I wonder if he is suggesting that induction requires the future to be like the past in all cases, and is refuting this with counter examples. I don't know anyone who holds this view of induction either.
> This question shows major lack of familiarity with DD's writing, which means you aren't in a good position to judge whether his anti-inductive arguments are correct.
I have read chapter 4 before, but I didn't remember it clearly. I've approached CR through Popper, DD, David Miller, and others. I'm still trying to get a better understanding of their views, but their are some fundamental problems that keeping surfacing for me.
> If you reject those solutions, God can *appear* to solve certain problems, but it doesn't really. Conjecturing some amount of arbitrary complexity to solve a problem with *less* complexity than that is only making things worse (overall), not solving anything. It's *increasing*, not decreasing, the amount of complexity in one's worldview that isn't explained well, isn't constrained well, isn't understood well, etc.
The god explains why the sun moves around. It solves the problem. Sure, the god now requires some explaining, but all explanations have unexplained elements. We never have a theory without any unexplained elements. We can explain one thing in terms of a new thing. We now have the problem of explaining that new thing. We continue this to infinity.
> That's a common misunderstanding of CR. Do you think you could state what CR means by explanation? And "newtons laws" is ambiguous about whether you mean just the mathematical formulas (which only predict) or also the explanations we know of that go with them.
The laws required for this sort of deduction would be in their mathematical form. So you disagree that we can deduce the motion of an object from such laws? Isn't it similar to a deduction from mathematical axioms?
> I agree that would be a form of induction. But CR *does not do that*. (Popper did consider doing something like that in his earlier work, which has led to confusion about this.)
> I divide theories into exactly two categories: refuted and non-refuted. Theory X is better than theory Y if and only if theory X is in the category "non-refuted" and theory Y is in the category "refuted". There are no degrees of betterness, and failed falsifications do not make theories better (except maybe in some loose, informal, non-rigorous way – I'm just talking about what is technically correct, not about informal approximations).
Say you have two similar medicinal options that are guessed to cure your pains; one has been tried 3 times (100% success), and another 100'000 times (99.9%) success. Do you choose the first option because it is not in your "non-refuted" category?
>> It wasn't a replacement, it was just a different criticism.
> Then it is an insufficient criticism for refuting my example.
I think this discussion is getting confused because it's mixing two things: debate and Q&A. I answered a question and then you said my answer was an insufficient criticism. It wasn't trying to be a criticism of your example, it was explaining something (which happened to be a criticism of something else) because you asked.
One of the major differences between debates and Q&A is that in debates focusing on *one topic at time*, and pursuing it to a conclusion, is important. Having a large number of short back and forths, instead of writing long things, is also more important in debate. There are other differences in how I reply depending on what we're doing.
I think you want to debate. That's fine. If you want to switch to Q&A, just ask, but let's try to keep to one at a time. I will make 2 more brief comments in hopes they're helpful. Then I will try to focus on one main debate point and I will try to keep it short.
> So you disagree that we can deduce the motion of an object from such laws?
No, I didn't say that. The topic I was discussing was whether explain = deduce. In CR literature, they are very different, so you'll misinterpret. I'm not denying you can deduce things, I'm saying deducing is a different thing than explaining.
> Say you have two similar medicinal options that are guessed to cure your pains; one has been tried 3 times (100% success), and another 100'000 times (99.9%) success. Do you choose the first option because it is not in your "non-refuted" category?
(Making reasonable assumptions to fill in the blanks for the scenario), I would criticize the first option for being high risk. If something works 99.9% of the time, that is not a refutation of the theory "I should use this." It would refute the theory "That medicine works 100% of the time.", which is a separate matter than whether I should take it.
---
# Debate
> DD seems to attack a form of inductivism that supposes that all knowledge comes from induction alone. My view is that induction is just one part of the picture.
OK, so the broad overview of your rebuttal to CR regarding induction is: *CR refutes many versions of induction (correctly?), but does not address the version of induction you believe.* Do I have your position right?
> It wasn't trying to be a criticism of your example, it was explaining something (which happened to be a criticism of something else) because you asked.
I misread you then. I thought you were offering an alternative account of why my example arbitrary theory is no good.
> I think you want to debate. That's fine. If you want to switch to Q&A, just ask, but let's try to keep to one at a time. I will make 2 more brief comments in hopes they're helpful. Then I will try to focus on one main debate point and I will try to keep it short.
Debate or Q&A, whichever it is, I'm happy with how thing's have gone so far; getting a lot out of this conversation. I'll try avoid opening up too many parallel conversations though.
> No, I didn't say that. The topic I was discussing was whether explain = deduce. In CR literature, they are very different, so you'll misinterpret. I'm not denying you can deduce things, I'm saying deducing is a different thing than explaining.
We say Newton's laws explain the motion of simple machines. We also say Newton's laws can be used to deduce the motion of simple machines.
I don't see why this is so nonsensical. An explanation (newton's laws) tells us what/how/why and from this we can deduce consequences (motion of simple machines).
> (Making reasonable assumptions to fill in the blanks for the scenario), I would criticize the first option for being high risk. If something works 99.9% of the time, that is not a refutation of the theory "I should use this." It would refute the theory "That medicine works 100% of the time.", which is a separate matter than whether I should take it.
Why is the first option higher risk than the second option?
Would you be ok with using option 2 if you failed to refute "I will use option 2 because it works more than 95% of the time"?
> # Debate
> OK, so the broad overview of your rebuttal to CR regarding induction is: *CR refutes many versions of induction (correctly?), but does not address the version of induction you believe.* Do I have your position right?
My rebuttal to DD's criticism of induction (as quoted from BoI) is that he has attacked a version of induction (or maybe just premises) that I don't see anyone holding. So yes, he has not addressed my view of induction.
> I'm happy with how thing's have gone so far; getting a lot out of this conversation.
Great.
> Why is the first option higher risk than the second option?
Because e.g. it has a lot of potential failure modes that people think are worth checking (testing) but which have not yet been checked, whereas with the second option there aren't a bunch of known risks in need of further investigation.
> My rebuttal to DD's criticism of induction (as quoted from BoI) is that he has attacked a version of induction (or maybe just premises) that I don't see anyone holding. So yes, he has not addressed my view of induction.
OK. So in order to address your view of induction – either with new material or by telling you how existing CR arguments address it – I'll need detailed information about your view.
So I have questions:
1) Do you think you have a view of induction with *no decisive refutations* that you know about?
I want to differentiate weaknesses (acceptable) with reasons something is actually *false* or *cannot work* (not acceptable). And I want to check whether you already know that your view is false, or not. Hopefully not, but a lot of people have kind of given up on finding something that is not refuted, and just try to choose which false view is less bad, so I want to ask.
For example, "That seems inelegant" would typically be a minor weakness that isn't a reason to give up on an idea. Whereas "That has an internal contradiction" or "That contradicts this observation" would generally be decisive refutations. (After a decisive refutation, variant ideas can still be considered. A refutation of X is sometimes totally irrelevant to X2 even if X and X2 are similar. Sometimes one can find a similar idea which isn't decisively refuted, but sometimes people fail to come up with such a variant (while also dealing with the constraints of choosing a variant which is not decisively refuted by a long list of other well known and standard criticisms, because we don't want to avoid one refutation by walking right into another. The point is to come up with a variant with no known decisive refutations, which sometimes is easy and sometimes hard).)
2) Is your view of induction *written down* in detail?
I'd like to be able to read and review the explanations, including details, that I'd need in order to understand the view, analyze it, agree or disagree, refute it, etc. The writing should be reasonably unambiguous, consistent with itself, cover the key issues in the field, and be complete enough that I don't keep getting told new information that wasn't included after I try to reply.
If it's written down, I'll want to know where. If not, how should I or CR respond to it?
I would expect any sources you refer me to would be things that you have read in full, and *take full responsibility for any errors in*. If you want to use a source which has an error you want to disown, there would need to exist a meta-source which says e.g. "Chapter 3 of book B, except disregard claim C. The argument stands with claim C omitted." Or a replacement claim could be given, or something else. The point is sources should either be error free (as far as you know, so any criticism would be important information) or else the errors should be documented and the workarounds/replacements/alternatives also documented (so then the pairing of the original source, plus the extra information about the error and its solution – that pairing as a whole – doesn't have a known error.)
FYI, I am familiar with the inductivist literature in general (many traditions of it, not just a couple), and have discussed with hundreds of inductivists. And FYI, in my experience, both the literature and the people today routinely hold the very same ideas that CR criticizes. If you know of other viewpoints, great. In the alternative, it may be that CR has criticized the viewpoints you advocate but you don't understand how the criticisms or how they apply. Also, if you refer to some standard literature or ideas, there is a good chance that I'll already be familiar with them, which will make conversation easier.
#12673
> Because e.g. it has a lot of potential failure modes that people think are worth checking (testing) but which have not yet been checked, whereas with the second option there aren't a bunch of known risks in need of further investigation.
There are infinite potential ways in which either option could fail. The only difference between each option is that one has been tested more than the other and it has a known failure case. Despite this known failure, you still choose this option. All else being equal, it seems you preference theories that have survived a greater number of tests. How do you account for this?
> 1) Do you think you have a view of induction with *no decisive refutations* that you know about?
Yes.
> 2) Is your view of induction *written down* in detail?
My view of induction is pretty well summed up by what you find in a dictionary, on wikipedia, or in stanfords philosophy encyclopedia.
“In a good inductive argument, the truth of the premises provides some degree of support for the truth of the conclusion, where this degree-of-support might be measured via some numerical scale.”
I’ve found Peirce’s account of the logic of the scientific method compelling. He provides a detailed account of induction that I am willing to defend for the most part. Relevant writings by him are provided below. Of the first article, the last two sections are most relevant. You could skim everything leading up to that.
The Probability of Induction
Deduction, Induction, and Hypothesis
I won’t pretend that I have a complete understanding of the depths of Peirce’s argument and I certainly have found some of his remarks questionable (e.g. reality is where the final opinion will be led after sufficient investigation), but nothing major enough for me to abandon induction. Peirce believes induction is justified logically, but I am more sympathetic to the view that it is an evolved faculty of reasoning.
> How do you account for this?
When it comes to medical risk, I generally prefer the option where we tested everything we think we should test, as opposed to the new drug which is still undergoing tests we think are important. It's not the number of tests but the question: is there a risk I want tested before I take it (in order to lower my risk) which has not yet been tested? In other words, one drug has known potential risks/dangers that are untested (those constitute a criticism of taking it when there's a better option), the other doesn't.
> “In a good inductive argument, the truth of the premises provides some degree of support for the truth of the conclusion, where this degree-of-support might be measured via some numerical scale.”
OK, and where can I read, in detail (with a formula?), which (observational) premises support which conclusions in what degree? Is there a particular thing Peirce wrote which answers this? I want general principles for this which can be used to evaluate anything (rather than the answers being made up on a case by case basis), plus a worked example.
FYI this is the kind of viewpoint that CR criticized at length. That's a really standard belief.
#12683
> When it comes to medical risk, I generally prefer the option where we tested everything we think we should test, as opposed to the new drug which is still undergoing tests we think are important. It's not the number of tests but the question: is there a risk I want tested before I take it (in order to lower my risk) which has not yet been tested? In other words, one drug has known potential risks/dangers that are untested (those constitute a criticism of taking it when there's a better option), the other doesn't.
Endless possible complications could arise when using a new type of medicine. We can’t always assume we know the main modes of failure (where do you think these come from anyway?). What we can assume is that we have a random sample of the effects that this medication has had on others who tried it. Isn’t a greater sample size much more preferable here?
> OK, and where can I read, in detail (with a formula?), which (observational) premises support which conclusions in what degree? Is there a particular thing Peirce wrote which answers this? I want general principles for this which can be used to evaluate anything (rather than the answers being made up on a case by case basis), plus a worked example.
Given a general claim about the world such as “all grass is green”, we can deduce a number of particular claims such as “my lawn is green” and “the grass at parliament house is green”. If we take a random sample of these particular claims and note the proportion that are true, then this is what gives us our proportionate support for the general claim. We tend to assume the constancy of the character we are studying unless we have knowledge that says otherwise.
Relevant writing of Peirce would be the following.
The Order of Nature
> FYI this is the kind of viewpoint that CR criticized at length. That's a really standard belief.
I’d like you to elaborate on DD’s BoI quotes that I provided, because I don’t see how they can be understood as refuting the standard belief.
> We can’t always assume we know the main modes of failure (where do you think these come from anyway?).
I didn't assume that. I said if you know some important failure modes, and tested one medicine for them but not the other, then you have a big risk difference.
> Given a general claim about the world such as “all grass is green”, we can deduce a number of particular claims such as “my lawn is green” and “the grass at parliament house is green”. If we take a random sample of these particular claims and note the proportion that are true, then this is what gives us our proportionate support for the general claim. We tend to assume the constancy of the character we are studying unless we have knowledge that says otherwise.
Then "all grass is green unless it's on mars" will have exactly equal support, right? You aren't dealing with the problem of exceptions or variants.
And there is no way to do the random sampling you suggest. How do you pick randomly from an infinite set?
And won't the correct proportion normally be 100%? If it's 99% then that means we found 1 or more counter examples, so the universal claim is *false*, which is totally different than 99% true. You seem to want to say that false ideas have a lot of support? I think that's bad.
You have not given an example where e.g. the amount of support lets us choose to prefer one idea over another. You gave an example where the amount of support is irrelevant because a claim like "all X are Y" is decisively refuted by one counter example.
Further, I don't want you to write ad hoc explanations of induction. The request was for you to provide writing which already covers this. You did give one link but no relevant quotes from the link and the link only has the word "support" one time (and used in a different sense). The link begins by talking about religion for some reason, which also isn't related to the specific issue we're talking about.
> I’d like you to elaborate on DD’s BoI quotes that I provided, because I don’t see how they can be understood as refuting the standard belief.
I will be happy to explain how they refute induction *after* you specify what you think induction is. I can't refute something unspecified when you've already tried to deny induction is what CR claims it to be. So we have to do the one thing before the other.
https://en.wikisource.org/wiki/Popular_Science_Monthly/Volume_13/June_1878/Illustrations_of_the_Logic_of_Science_V
> It is easy to see that the number of accidental agreements of this sort would be quite endless. But suppose that, instead of considering a character because of its prevalence in the sample, we designate a character before taking the sample, selecting it for its importance, obviousness, or other point of interest.
This is theory-before-observation, which is agreeing with CR and disagreeing with a large part of the tradition of inductive thought.
And also it doesn't work well because you can come up with "everyone falls when they jump off buildings, except..." in advance and then check a sample of observations. Since the exceptions involve an infinitesimal part of the general case, the probability of randomly running into them is infinitesimal. So we'll get "accidental agreement" between data and between theories with exceptions. This is why CR doesn't advocate *random* testing. It advocates testing key issues that differentiate between theories.
> selecting it for its importance, obviousness, or other point of interest.
How can you know what is important, obvious, or interesting?
Isn't that presupposing you're an intelligent person capable of thinking about such things, *before* you can do induction?
But one of the problems epistemology is trying to address – and the inductive tradition of thought claims to address – is *how can we think*? How can we know what is important, obvious, interesting, or whatever else? Induction is suppose to come *before* that issue, not after. If you put induction after, you need something else before to explain how intelligent thought works. So you'll have to accept CR or come up with some other alternative. But you can't explain how people think and learn using induction *and*, at the same time, make using general purpose intelligent thought be one of the steps used in induction.
CR tells us how knowledge can be created from non-knowledge. Induction claimed to too, but this version of induction doesn't appear to be trying to address that basic epistemological problem.
#12693
>I didn't assume that. I said if you know some important failure modes, and tested one medicine for them but not the other, then you have a big risk difference.
And if we didn’t know any important failure modes, does the difference in the amount of testing make no difference?
>Then "all grass is green unless it's on mars" will have exactly equal support, right? You aren't dealing with the problem of exceptions or variants.
Sure, if we wanted to test one of your theory+exception type hypotheses we could do so in the same way, and we would very likely find identical levels of support (so long as your exceptional cases are exceptional and not commonplace). This corresponds to the fact that the theory and the theory+exception hypotheses would both lead us right in a very similar proportion of cases, although as you add more exceptions, the less support for these theories overlap.
So this isn’t a problem for induction, but rather a question of how to differentiate good and bad hypotheses, in particular, how to differentiate plausible and implausible hypotheses. We find induction has a role in answering this question. Take for example the floater theory of gravity where DD floats in some special circumstance. We don't have any support for the claim that the principles of motion are dependent on an individuals name, date of birth, position, etc. Instead we have strong support of the opposite, that the principles of motion are independent of such qualities. This is the deductive application of a general rule whose truth has been inferred inductively.
Perhaps there is some not yet observed exceptional case in the universe, with a character unlike anything we have seen before, but to prefer a theory in its favour for no reason whilst ignoring knowledge that speaks against the case is irrational.
>And there is no way to do the random sampling you suggest. How do you pick randomly from an infinite set?
The ideal case is a random sample, free from bias. However, we are limited to what the universe provides us. We can do the best we can, but if the universe is in such a way that we are unable to get a representative sample of some phenomena, then that phenomena is outside the limits of our knowledge. A quote from that article I sent you: “But, though there exists a cause for every event, and that of a kind which is capable of being discovered, yet if there be nothing to guide us to the discovery; if we have to hunt among all the events in the world without any scent; if, for instance, the sex of a child might equally be supposed to depend on the configuration of the planets, on what was going on at the antipodes, or on anything else—then the discovery would have no chance of ever getting made”.
>And won't the correct proportion normally be 100%? If it's 99% then that means we found 1 or more counter examples, so the universal claim is *false*, which is totally different than 99% true. You seem to want to say that false ideas have a lot of support? I think that's bad.
A 99% supported theory is roughly speaking “true”,but precisely speaking “false but strongly supported”. A theory that works in most cases is still incredibly useful, and it would be wrong to just lump it in with the rest of our “false” theories. We may call such a theory “true” when it is expedient to do so.
>You have not given an example where e.g. the amount of support lets us choose to prefer one idea over another. You gave an example where the amount of support is irrelevant because a claim like "all X are Y" is decisively refuted by one counter example.
I think the medicine example is what you're asking for. Even in the case where a theory is refuted it can still be extremely useful to us. We might even later find out that our refutation was wrong. Some theories can be weakly disconfirmed in the same way they can be weakly confirmed.
>Further, I don't want you to write ad hoc explanations of induction. The request was for you to provide writing which already covers this. You did give one link but no relevant quotes from the link and the link only has the word "support" one time (and used in a different sense). The link begins by talking about religion for some reason, which also isn't related to the specific issue we're talking about.
My explanation of induction was not ad hoc. It was generalized, and I provided an example at your request. I’ve given three links by the way. They are separate articles.
Peirce gives us an overview of induction in ‘Deduction, Induction, and Hypothesis’:
“Induction is where we generalize from a number of cases of which something is true, and infer that the same thing is true of a whole class. Or, where we find a certain thing to be true of a certain proportion of cases and infer that it is true of the same proportion of the whole class.”
And in his concluding remarks in ‘The Probability of Induction’:
“When we draw a deductive or analytic conclusion, our rule of inference is that facts of a certain general character are either invariably or in a certain proportion of cases accompanied by facts of another general character. Then our premise being a fact of the former class, we infer with certainty or with the appropriate degree of probability the existence of a fact of the second class. But the rule for synthetic inference is of a different kind. When we sample a bag of beans we do not in the least assume that the fact of some beans being purple involves the necessity or even the probability of other beans being so. On the contrary, the conceptualistic method of treating probabilities, which really amounts simply to the deductive treatment of them, when rightly carried out leads to the result that a synthetic inference has just an even chance in its favor, or in other words is absolutely worthless. The color of one bean is entirely independent of that of another. But synthetic inference is founded upon a classification of facts, not according to their characters, but according to the manner of obtaining them. Its rule is, that a number of facts obtained in a given way will in general more or less resemble other facts obtained in the same way; or, experiences whose conditions are the same will have the same general characters.
In the former case, we know that premises precisely similar in form to those of the given ones will yield true conclusions, just once in a calculable number of times. In the latter case, we only know that premises obtained under circumstances similar to the given ones (though perhaps themselves very different) will yield true conclusions, at least once in a calculable number of times. We may express this by saying that in the case of analytic inference we know the probability of our conclusion (if the premises are true), but in the case of synthetic inferences we only know the degree of trustworthiness of our proceeding. As all knowledge comes from synthetic inference, we must equally infer that all human certainty consists merely in our knowing that the processes by which our knowledge has been derived are such as must generally have led to true conclusions.”
I’m not sure how familiar you are with Peirce’s works, so I can only guess how useful these quotes will be independent of their logical development.
> And if we didn’t know any important failure modes, does the difference in the amount of testing make no difference?
Depends. You didn't give a detailed scenario so I made reasonable assumptions. If you want to go into details and try to make it a trickier scenario, you'd need a much more detailed scenario that gives way more info including dozens of scientific papers covering the actual issues. Then one could consider what the explanations and criticisms involved are. I thought the point was to see how a CR perspective works in a simple, easy scenario, but now you seem interested in changing to a more difficult scenario.
> So this isn’t a problem for induction
In the history of philosophy, that is a problem for induction. Most inductivists today think induction does solve that problem of rejecting junk theories with arbitrary exceptions.
If you want induction only for some limited purposes, you should specify exactly what it does and doesn't do, and also what the overall epistemology as a whole is and what other components it has besides induction and what they do. All of that is stuff that ought to already be written down, not stated ad hoc.
> We can do the best we can, but if the universe is in such a way that we are unable to get a representative sample of some phenomena, then that phenomena is outside the limits of our knowledge.
How do you know what is a representative sample? By thinking in some way. So your view of induction *presupposes intelligent thinking*, rather than explaining how thinking works.
If you're going to do that, what you should do next is consider *what comes before induction*. How does the thinking prior to induction work and what is it capable of? And then, what is left over for induction to accomplish, which can't be accomplished by this prior stuff? If the prior stuff is or includes CR, then nothing is left over because CR is universal (it covers *all* thinking).
---
We need to focus. You're giving quotes making new claims instead of following up to a conclusion regarding the prior claims. You said:
>> “In a good inductive argument, the truth of the premises provides some degree of support for the truth of the conclusion, where this degree-of-support might be measured via some numerical scale.”
I asked:
> OK, and where can I read, in detail (with a formula?), which (observational) premises support which conclusions in what degree? Is there a particular thing Peirce wrote which answers this? I want general principles for this which can be used to evaluate anything (rather than the answers being made up on a case by case basis), plus a worked example.
I understand your answer to be: Ignore all non-empirical thinking. Consider the infinite set of empirical implications of a theory. Test a random sample of them and see what percentage of the time it's correct. Call that percentage its "inductive support". Prefer theories with a higher percentage.
This does not address how to tiebreak between theories that both score 100%. That's a serious problem because there are infinitely many theories that score 100%. So you think you're doing a good job of differentiating theories by assigning different scores, but looking only at the theories with the max score you still have infinitely many left. So your approach results in a massive tie that it doesn't help with. CR does help with that tie.
It also does not correspond to the actual facts of science, where people design tests to differentiate theories instead of testing randomly. You've also, contrary to scientific practice, advocated for the high value of theories with known counter examples. Wouldn't it be better to find a variant theory without a known counter example? Why not do that? Why stick with something we know is false when there are infinitely many alternatives that we don't know to be false, and it's trivial to state some of them? For example, if you know of a counter example of "All X are Y" you can consider the variant theory "All X are Y except for Z." This has the advantage of not being known to be false, so isn't it superior? Yet your inductive system is focused on offering varying degrees of support *for refuted theories*, but all the non-refuted theories get the identical score and aren't differentiated.
And there's the problem that you can't random sample infinite sets, and also the problem that even if you had a sample of things to test, you wouldn't be able to test most of the things in the sample (b/c e.g. many of them would involve doing tests in other galaxies). So you want us to do an approximately random sample of only tests which are reasonably convenient/accessible. You have not provided details for how to do this. I want a *set of steps I could follow to perform an induction* (walk me through doing one to show me that it's possible to do one), but you have not provided the steps for how to approximate a random sample of only conveniently testable things and make it representative enough.
You've also attempted to introduce a rule that theories aren't compared with data from before the theory was formed. Something like that. I don't think you really want that rule to be upheld strictly thought, and it isn't how science works. And there are easy workarounds, e.g. form *all logically possible theories* right now and then test all of them at once going forward. We shouldn't be limited to only testing one or two theories at a time.
You also seem to *not treat induction as a starting point of thinking*. In that case, shouldn't we start at the start of your epistemology? If it doesn't start with induction, what does it start with? What are all the things that are prior to induction? You also regard induction as incomplete because it doesn't address non-empirical matters, so what else do you have in your epistemology to cover those? You're limiting induction more than many inductivists do, so you need replacements to cover the stuff you don't think induction does. (And then we could consider things like whether the replacements include the whole of CR in them, or are otherwise complete without ever adding induction into the picture.)
kieren, all you really said is: prefer theories where counter-examples are rarer to ones where counter-examples are more common. This is pointless because it's better to use theories with no known counter examples. It also can't be done without using premises which go beyond the traditional premises of induction. Adding additional premises to your theory of induction is an important change that merits carefully listing all of them and analyzing them.
Also you said basically to logically derive predictions from theories. You can do that from "All grass is green" but you can't do it from e.g. "Most grass is green". You can't derive any particular predicted observations from that claim. So are you *only* dealing with empirical universal laws? If so, that's pretty limited. And it clarifies the issue that it's desirable and easy to use ones with *no* counter examples, so there's no purpose to your system of differentiating between ones with different frequencies of being wrong.
But you seem to be ignoring me.
#12700
Thanks for the continued discussion. I’ll try focus on what I think are your main criticisms and avoid opening up too many parallel conversations. If you would prefer me to prioritize other criticisms then let me know, but let's not try and talk about too many things at the same time.
>If you want to go into details and try to make it a trickier scenario, you'd need a much more detailed scenario that gives way more info including dozens of scientific papers covering the actual issues.
I was trying to keep it simple. I think you have complicated things by introducing “known important failure modes”. Don’t do that. Assume the only difference between the theories is that one has been tested far more than the other. The testing is random, and not biased towards any sort of failure modes, etc. I want to know if the size of the sample matters for you. To do so you need to consider it independently of other factors.
>In the history of philosophy, that is a problem for induction. Most inductivists today think induction does solve that problem of rejecting junk theories with arbitrary exceptions.
The history of induction looks pretty murky for me with a lot of different interpretations. I think Peirce has categorized our inferences best and gives the best account of the logic of induction.
The scientific method for Peirce looks like this.
Hypothesis: “where we find some very curious circumstance, which would be explained by the supposition that it was a case of a certain general rule, and thereupon adopt that supposition.”
Deduction: where we derive particular instances (consequences/predictions) from our hypothesis.
Induction: “where we generalize from a number of cases of which something is true, and infer that the same thing is true of a whole class.”
This is why I say your theory+exception type theories are not a problem for induction, because they are ruled out at the hypothesis stage instead. However, I do believe induction has its role in ruling out these sorts of theories as I demonstrated in my previous response.
> This does not address how to tiebreak between theories that both score 100%. That's a serious problem because there are infinitely many theories that score 100%. So you think you're doing a good job of differentiating theories by assigning different scores, but looking only at the theories with the max score you still have infinitely many left. So your approach results in a massive tie that it doesn't help with. CR does help with that tie.
The majority of these infinite logically possible theories make claims that have no support. In fact, there is strong support in opposition to the class of claims made by these theories. If you want to pose the theory that says my wallet will be transported to the moon in the next second then you are claiming a character for physical objects that has absolutely zero support. That not a single physical object has ever had this sort of character is too much to be overcome by such theories.
Our existing theories and observations tell us which theories are most plausible. These are the ones that we preference and choose to expend resources testing. If we want to trace back to our most fundamental measures of plausibility we end up with our natural reactions and innate ideas.
> It also does not correspond to the actual facts of science, where people design tests to differentiate theories instead of testing randomly.
Testing randomly is very important in science, especially when coming up with a confidence interval/level for the reporting of results. I think of testing randomly as sampling without bias. If you have no reason to think your sample is biased in any particular way, then you are standing on good ground. As I said before, We tend to assume the constancy of the character we are studying unless we have knowledge that says otherwise.
Reading at least the last two sections of The Probability of Induction would give you a good idea of Peirce's account of induction.
Are you familiar with any of Peirce's work?
>kieren, all you really said is: prefer theories where counter-examples are rarer to ones where counter-examples are more common. This is pointless because it's better to use theories with no known counter examples.
Why do you prefer the use of theories with no known counter examples? Are they more likely to work than a theory that has a counter example?
>Also you said basically to logically derive predictions from theories. You can do that from "All grass is green" but you can't do it from e.g. "Most grass is green". You can't derive any particular predicted observations from that claim.
That's because your theory doesn't imply any particular predicted observations, but it does imply that in any random sample of grass, the majority of it will be green, most of the time. We might find that your rule leads us right in 90% of cases.
> Why do you prefer the use of theories with no known counter examples? Are they more likely to work than a theory that has a counter example?
To begin with, consider a variant theory which takes the original theory and adds exceptions for all known counter-examples. This is more likely to be correct (setting aside the issue that the difference is infinitesimal) because it's equally likely to be correct in all the other cases, plus it's correct instead of incorrect regarding the counter examples. The point is that we always have easy access to a theory that is *strictly better* (in terms of matching our observations), so there's no reason to ever use a theory with any known counter examples if our goal is empirical correctness (which is a goal you've been advocating).
Now that I've clarified, as you asked me to, please reply again to what I was saying.
> That's because your theory ["Most grass is green"] doesn't imply any particular predicted observations,
I know and said that. You're repeating what I said back to me. I don't know why. I brought it up in order to ask you a question, which you haven't answered.
> but it does imply that in any random sample of grass, the majority of it will be green, most of the time.
That is vague and basically meaningless/has-no-content. There is no set of observations we could make which would refute that alleged implication. The "most of the time" is a hedge that means it could fail to happen an unlimited number of times. Logical implications require extreme preciseness. If you don't want to be precise, don't make claims about logic.
> Induction: “where we generalize from a number of cases of which something is true, and infer that the same thing is true of a whole class.”
Infer that it’s true of *which* whole class?
This is standard induction which fails to deal with standard CR reasoning.
**I particularly want an answer to this point.** Going forward (after this comment and the next one about Peirce), I plan to (actually!) reply to *only one thing at a time*, rather than continuing to write long explanations. If you want more long explanations, you can read and comment on CR materials, and focus on learning, and then I would expect to write more of them. But they’re making it difficult to resolve the points being debated.
> This is why I say your theory+exception type theories are not a problem for induction, because they are ruled out at the hypothesis stage instead.
Then you need to give the full details of this prior stage, including a full specification of all things it rules out and why (or give the methods of determining what is ruled out). Further, since this stage is *prior to induction*, it must be governed by a *non inductivist epistemology*. So that’s a very notable concession coming from an inductivist. It concedes that there is a way of thinking which is effective at least for some important things, which goes well beyond deductive logic, and which doesn’t involve induction. What are the limits of this epistemology and why do you advocate multiple epistemologies instead of just one? (An epistemology is a set of ideas saying how thinking/reasoning/learning work, which governs what conclusions are considered and accepted. Your epistemology as a whole has a sub-epistemology nested in its first stage. My belief is that this epistemology is either equivalent to CR or won’t work. Does there exist a text which is aware that it is trying to specify a pre-inductivist epistemology, for use in this stage of thinking that comes before induction, and which then explains in detail some CR rival?)
> The majority of these infinite logically possible theories make claims that have no support. In fact, there is strong support in opposition to the class of claims made by these theories. If you want to pose the theory that says my wallet will be transported to the moon in the next second then you are claiming a character for physical objects that has absolutely zero support. That not a single physical object has ever had this sort of character is too much to be overcome by such theories.
This is part of a pattern where you (and most inductivists do this) start making common sense arguments. That is impermissible in a discussion of first principles, of how the beginnings of thought/reasoning work. The first problem of epistemology is to understand how reason works, which, to avoid circularity, must be done without using reasonable thinking as a tool (you can’t presuppose the thing you’re explaining).
And so far you haven’t established any correct meaning of “support”, but now you’re using it in the standard way instead of continuing the part of the discussion where you try to detail and defend “support”. My #12700 gave several arguments regarding your approach to empirical support which you haven’t answered. In the meantime, while you haven’t answered all criticisms of support, please stop using your concept of support as a premise. It’s not productive to make arguments based on premises which are in dispute (that’s called begging the question).
You’re also trying to introduce a new evaluation procedure (without stopping and saying you’re going to do so, naming it, or otherwise giving it appropriate attention, just tossing it in without details) whereby some arguments, instead of being evaluated by proportion of empirical, logical implications that test correctly, are instead evaluated in some other way. This other way has not been specified in detail but seems to involve splitting ideas into parts (which ideas are split into which set of parts?), evaluating the incomplete parts separately, and then somehow combining the evaluations to reach an overall conclusion. You did mention this previously but didn’t give details then either. It’s all problematic and, I fear, ad hoc (rather than something that someone had worked out, thought was correct *after* he finished figuring out the details, and then published). I think the actual thing going on here is an epistemology prior to induction which must be used to do this claim splitting *according to creative and intelligent thought* (rather than according to predefined rules, math, non-AGI computer code, or any logical procedure). That prior epistemology is either CR or an unspecified rival to CR that doesn’t use induction.
> Testing randomly is very important in science
No tests are purely random. All tests are either 1) not random (those tests are very important, which was my point, because the view you were presenting only involved random testing); or 2) partially random, with the random and non-random aspects chosen by design (not chosen randomly. it’s always intelligent reasoning that’s guiding things, not random data). I was not denying the value of partially random tests *in addition to* non-random tests. I don’t think you’ve carefully considered in what ways partially random tests are and are not random, nor have you found any inductivist writer who has done so and explained it for you. Instead, you have a vague idea of random tests which isn’t logically rigorous and involves ideas like “If you have no reason to think your sample is biased in any particular way” which is presupposing some other non-inductivist epistemology (which governs reasoning and judging what we do and do not have reason for) prior to your treatment of induction. (It has to be prior to avoid circularity.) Also, random is a different thing than representative or unbiased.
> I was trying to keep it simple. I think you have complicated things by introducing “known important failure modes”. Don’t do that. Assume the only difference between the theories is that one has been tested far more than the other. The testing is random, and not biased towards any sort of failure modes, etc. I want to know if the size of the sample matters for you. To do so you need to consider it independently of other factors.
If you completely set aside all concepts and explanations, and you have only data, then *you know nothing.* Sample size *alone* doesn’t tell you anything. You have to e.g. check for systematic bias in the sample, which requires understanding what is being sampled and how (e.g. you need to check whether the judgments of success or failure are made in a reasonable way or not). What you’re talking about is the *explanationless science* that DD criticizes in BoI.
You assert things like that the testing is random and unbiased, but there is no way to know that without bringing in other factors like explanations. And what you actually mean is the testing is random in some ways but not others (rather than observing random things, you’re trying to observe whether a medicine works), and the reasoning for what to do randomly and nonrandomly, and how and why, is important. Sample size does matter in some ways, but not independently of other factors, you can’t get anywhere with no other factors involved.
Sample size, like observations in general, only matters *when there is an explanation/argument saying why it matters in this case*. It can’t be divorced from reasoning and still matter. Reasoning is necessary.
Peirce
Since you’ve insisted again, I’ll say more about Peirce, even though it’s opening more topics:
> Are you familiar with any of Peirce's work?
I haven't read much Peirce (Popper did – Peirce is one of the thinkers that Popper was addressing with CR, it’s not something CR overlooked), but I'm familiar with the ideas he's talking about. E.g. the first sentence of the link contains several standard inductivist errors:
https://en.wikisource.org/wiki/Popular_Science_Monthly/Volume_12/April_1878/Illustrations_of_the_Logic_of_Science_IV
> WE have found that every argument derives its force from the general truth of the class of inferences to which it belongs; and that probability is the proportion of arguments carrying truth with them among those of any *genus*.
One of the crucial errors, which relates to what we've been talking about, is that every argument belongs to *infinitely many classes of inferences*, not one class. Failure to consider and deal with infinite sets/classes/etc is one of the typical themes of inductivist reasoning. I saw this immediately and I’m not saying anything original here. Peirce is walking right into CR arguments, rather than saying something they don’t apply to. (In his defense, he predates CR. But you’re trying to bring up his beliefs as something you think is correct today.)
Also, to discuss the “proportion of arguments” that are true from an infinite set requires defining a measure on that set (not all inference classes contain infinitely many arguments, but infinitely many of them do). Peirce doesn’t address that. After defining that measure, he would then need to address the fact that we can’t actually do that measurement, so we’d need an effective way to approximate it (and arguments/analysis to show that it is effective), which he doesn’t provide. This stuff is problematic even in finite cases because even if you have a list of every argument in the class you still may not know which arguments are true.
(Here is a semi-new issue which is different than most other inductivists.) His argument is actually similar to a circular argument because it says to judge the truth of arguments by the the truth of other arguments in the class. He has you judge arg1 based on the evaluations of arg2, arg3, arg4, arg5, etc. But the evaluation of arg2 depends on the evaluation of arg1. The evaluation of every argument in the class depends on the evaluation of every other argument in the class, so how can you evaluate any of them?
If you believe Peirce correctly answers any of this, please give exact quotes as direct replies to specific arguments that I made.
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I’ll give 2 quotes from LScD for examples of Popper speaking about Peirce (bold added):
> I now turn to the last group of epistemologists—those who do not pledge themselves in advance to any philosophical method, and who make use, in epistemology, of the analysis of scientific problems, theories, and procedures, and, most important, of scientific discussions. This group can claim, among its ancestors, almost all the great philosophers of the West. (It can claim even the ancestry of Berkeley despite the fact that he was, in an important sense, an enemy of the very idea of rational scientific knowledge, and that he feared its advance.) Its most important representatives during the last two hundred years were Kant, Whewell, Mill, **Peirce**, Duhem, Poincaré, Meyerson, Russell, and—at least in some of his phases—Whitehead. Most of those who belong to this group would agree that scientific knowledge is the result of the growth of common-sense knowledge. But all of them discovered that scientific knowledge can be more easily studied than common-sense knowledge. For it is common-sense knowledge writ large, as it were. Its very problems are enlargements of the problems of common-sense knowledge. For example, it replaces the Humean problem of 'reasonable belief' by the problem of the reasons for accepting or rejecting scientific theories. And since we possess many detailed reports of the discussions pertaining to the problem whether a theory such as Newton's or Maxwell's or Einstein's should be accepted or rejected, we may look at these discussions as if through a microscope that allows us to study in detail, and objectively, some of the more important problems of 'reasonable belief'.
and
> 4. I do not think that this paradox can be solved within the frame-work of the subjective theory, for the following reason.
>
> The *fundamental postulate of the subjective theory* is the postulate that degrees of the rationality of beliefs in the light of evidence exhibit a *linear order*: that they can be measured, like degrees of temperature, on a one-dimensional scale. But from **Peirce** to Good, all attempts to solve the problem of the weight of evidence within the framework of the subjective theory proceed by introducing, in addition to probability, *another measure of the rationality of belief in the light of evidence*. Whether this new measure is called 'another dimension of probability', or 'degree of reliability in the light of the evidence', or 'weight of evidence' is quite irrelevant. What is relevant is the (implicit) admission that it is not possible to attribute linear order to degrees of the rationality of beliefs in the light of the evidence: that there may be *more than one way in which evidence may affect the rationality of a belief*. This admission is sufficient to overthrow the fundamental postulate on which the subjective theory is based.
>
> Thus the naïve belief that there really are intrinsically different kinds of entities, some to be called, perhaps, 'degree of the rationality of belief' and others 'degree of reliability' or of 'evidential support', is no more able to rescue the subjective theory than the equally naïve belief that these various measures 'explicate' different '*explicanda*'; for the claim that there exists an '*explicandum*' here—such as 'degree of rational belief—capable of 'explication' in terms of probability stands or falls with what I have called the 'fundamental postulate'.
Peirce’s name also appears in other books, e.g. *on 90 separate pages* in The philosophy of Karl Popper. Edited by Paul Arthur Schilpp. In that book, Popper explains some of his disagreements with Peirce. Peirce also comes up in C&R, OK and elsewhere.
I’m not asking you to understand or respond to these passages (quoted or not). I want you to know that CR already took into account Peirce. (And if CR did so incorrectly, some fan of Peirce, who is also familiar with Popper, ought to have written something pointing out CR’s errors.) Your view of the state of the debate, in which CR argues against other types of induction but not Peirce’s, is incorrect.
> To begin with, consider a variant theory which takes the original theory and adds exceptions for all known counter-examples. This is more likely to be correct (setting aside the issue that the difference is infinitesimal) because it's equally likely to be correct in all the other cases, plus it's correct instead of incorrect regarding the counter examples. The point is that we always have easy access to a theory that is *strictly better* (in terms of matching our observations), so there's no reason to ever use a theory with any known counter examples if our goal is empirical correctness (which is a goal you've been advocating).
This is not true. If your corrected theory is only corrected in those predictions that we got wrong, then it can do no better or worse than the original theory on new predictions. If you change it in more ways than this, then either theory could outperform the other.
> Now that I've clarified, as you asked me to, please reply again to what I was saying.
To perform an induction I assume we have a hypothesis to test. A hypothesis that allows us to deduce predictions about the world.
> That is vague and basically meaningless/has-no-content. There is no set of observations we could make which would refute that alleged implication. The "most of the time" is a hedge that means it could fail to happen an unlimited number of times. Logical implications require extreme preciseness. If you don't want to be precise, don't make claims about logic.
Then you have provided a theory whose implications are vague and of little use to us. If we can't gather support for your theory through induction, then it doesn't get it.
> I’m not asking you to understand or respond to these passages (quoted or not). I want you to know that CR already took into account Peirce. (And if CR did so incorrectly, some fan of Peirce, who is also familiar with Popper, ought to have written something pointing out CR’s errors.) Your view of the state of the debate, in which CR argues against other types of induction but not Peirce’s, is incorrect.
The section of Popper you quoted is part of his argument against the subjective theory of probability. He ends up claiming that the objective theory of probability is superior:
>>5. All these difficulties disappear as soon as we interpret our probabilities objectively.
Peirce does the exact same thing in the article I linked you "The Probability of Induction". He argues against the subjective theory and in favour of the objective theory. Summarised by Stanford Encyclopedia of Philosophy:
>>Peirce vigorously attacked the subjectivist view of de Morgan and others to the effect that probability is merely a measure of our level of confidence or strength of belief. He allowed that the logarithm of the odds of an event might be used to assess the degree of rational belief that should be accorded to an event, but only provided that the odds of the event were determined by the objective relative frequency of the event. In other words, Peirce suggested that any justifiable use of subjectivism in connection with probability theory must ultimately rest on quantities obtained by means of an objectivist understanding of probability.
If you are suggesting that Popper has attempted to refute Peirce here, then I think you have misread Popper, or perhaps Popper misread Peirce.
Popper and Peirce actually seem to agree for the most part. Peirce anticipated Popper with his ideas of fallibilism, propensity probability, critical tests, etc. Their accounts of science are quite similar too where they both highlight steps of hypothesis and deduction. However, Peirce allows for positive support through induction as well. In the end Popper admitted "whiffs" of induction in his attempts to provide a working theory of corroboration/verisimilitude, so maybe their theories are similar here too.
I'll reply to your other comment tomorrow.
> If you are suggesting that Popper has attempted to refute Peirce here, then I think you have misread Popper, or perhaps Popper misread Peirce.
I stated why I gave those quotes and references. That was not the reason I stated.
> In the end Popper admitted "whiffs" of induction in his attempts to provide a working theory of corroboration/verisimilitude
Not in the end but *in the beginning*, in his early work, which he then improved on (and then DD and I improved on it further). Popper provided a complete epistemology even if you ignore corroboration.
> I'll reply to your other comment tomorrow.
ok
> Infer that it’s true of *which* whole class?
The class of things is fixed by the hypothesis. In order to perform our induction we require a hypothesis that we can derive particular claims from. It’s the same requirement for falsifying a hypothesis. I’m happy to accept the description of our hypotheses as “creative guesses”.
> Then you need to give the full details of this prior stage, including a full specification of all things it rules out and why (or give the methods of determining what is ruled out). Further, since this stage is *prior to induction*, it must be governed by a *non inductivist epistemology*. So that’s a very notable concession coming from an inductivist. It concedes that there is a way of thinking which is effective at least for some important things, which goes well beyond deductive logic, and which doesn’t involve induction.
As I said before, there are three stages in Peirce’s scientific method corresponding to his three types of inference; hypothesis (abduction), deduction, and induction. When did I ever say the scientific method is entirely inductive?
You are asking for a full specification of all the rules involved in the hypothesis stage, but we are supposed to be discussing induction instead.
You can think of my view as similar to Popper where we both accept abductive (hypothesis) and deductive reasoning. The difference is that I do not reject inductive reasoning.
> This is part of a pattern where you (and most inductivists do this) start making common sense arguments. That is impermissible in a discussion of first principles, of how the beginnings of thought/reasoning work. The first problem of epistemology is to understand how reason works, which, to avoid circularity, must be done without using reasonable thinking as a tool (you can’t presuppose the thing you’re explaining).
I’ll try to provide more details on what I mean by support. Every successful prediction made by a theory counts as a reason in its favour. Unsuccessful predictions count as reasons against it. Reasons compel our beliefs and action. The ratio of favourable to unfavourable cases can be considered as the chance of the theory being true. Peirce says:
>>Probability and chance undoubtedly belong primarily to consequences, and are relative to premises; but we may, nevertheless, speak of the chance of an event absolutely, meaning by that the chance of the combination of all arguments in reference to it which exist for us in the given state of our knowledge. Taken in this sense it is incontestable that the chance of an event has an intimate connection with the degree of our belief in it. Belief is certainly something more than a mere feeling; yet there is a feeling of believing, and this feeling does and ought to vary with the chance of the thing believed, as deduced from all the arguments. Any quantity which varies with the chance might, therefore, it would seem, serve as a thermometer for the proper intensity of belief. Among all such quantities there is one which is peculiarly appropriate. When there is a very great chance, the feeling of belief ought to be very intense. Absolute certainty, or an infinite chance, can never be attained by mortals, and this may be represented appropriately by an infinite belief. As the chance diminishes the feeling of believing should diminish, until an even chance is reached, where it should completely vanish and not incline either toward or away from the proposition. When the chance becomes less, then a contrary belief should spring up and should increase in intensity as the chance diminishes, and as the chance almost vanishes (which it can never quite do) the contrary belief should tend toward an infinite intensity. Now, there is one quantity which, more simply than any other, fulfills these conditions; it is the logarithm of the chance. But there is another consideration which must, if admitted, fix us to this choice for our thermometer. It is that our belief ought to be proportional to the weight of evidence, in this sense, that two arguments which are entirely independent, neither weakening nor strengthening each other, ought, when they concur, to produce a belief equal to the sum of the intensities of belief which either would produce separately. Now, we have seen that the chances of independent concurrent arguments are to be multiplied together to get the chance of their combination, and therefore the quantities which best express the intensities of belief should be such that they are to be added when the chances are multiplied in order to produce the quantity which corresponds to the combined chance. Now, the logarithm is the only quantity which fulfills this condition. There is a general law of sensibility, called Fechner's psychophysical law. It is that the intensity of any sensation is proportional to the logarithm of the external force which produces it. It is entirely in harmony with this law that the feeling of belief should be as the logarithm of the chance, this latter being the expression of the state of facts which produces the belief.
Peirce says the rule of induction is “that a number of facts obtained in a given way will in general more or less resemble other facts obtained in the same way”. The ways of collecting these facts that can be found to support our theory is fixed by our hypothesis. If we take a random sample of these facts and find that our theory is correct in 99% of cases, then depending on the sample size and our allowed confidence interval, we can determine how trustworthy our induction is (confidence level).
If we intentionally limited our testing (collecting of facts in a particular way) of products to those who were produced in one particular factory, then we lose confidence in our induction when inferring the same proportion of success in a different factory. However, we do not lose all confidence in our inference, because even an approximately random sample will often give us good results. If we intentionally limited ourselves to those facts that we know will confirm our theory, then we lose all confidence in our induction because it was manufactured to be a certain way. This is why a random sample is important for our induction.
> If you completely set aside all concepts and explanations, and you have only data, then *you know nothing.* Sample size *alone* doesn’t tell you anything.
I didn’t ask you to set aside all concepts and explanations. I wanted you to set aside all the *differences* between the two medical theories, except for the difference in their sample size.
If someone asks you to choose between two different things, informing you of their differences, then you should not answer the question by first assuming other differences between the things and then basing you answer on these other differences instead. If you can’t make a decision based on sample size alone, then just say so.
> Popper admitted "whiffs" of induction
At the time that you wrote this, did you know a source where Popper said this *exact* quote? If so, please share. If not, you shouldn't present it as a quote from Popper.
> To perform an induction I assume we have a hypothesis to test. A hypothesis that allows us to deduce predictions about the world.
So your idea of induction doesn't deal with "Most grass is green."? So you have something else, something non-inductive, to deal with it? What?
>>>> all you really said is: prefer theories where counter-examples are rarer to ones where counter-examples are more common. This is pointless because it's better to use theories with no known counter examples. It also can't be done without using premises which go beyond the traditional premises of induction. Adding additional premises to your theory of induction is an important change that merits carefully listing all of them and analyzing them.
>> To begin with, consider a variant theory which takes the original theory and adds exceptions for all known counter-examples. This is more likely to be correct (setting aside the issue that the difference is infinitesimal) because it's equally likely to be correct in all the other cases, plus it's correct instead of incorrect regarding the counter examples. The point is that we always have easy access to a theory that is *strictly better* (in terms of matching our observations), so there's no reason to ever use a theory with any known counter examples if our goal is empirical correctness (which is a goal you've been advocating).
> This is not true. If your corrected theory is only corrected in those predictions that we got wrong, then it can do no better or worse than the original theory on new predictions. If you change it in more ways than this, then either theory could outperform the other.
We do a science experiment, E, with controlled circumstances and get a result, R2. E is also done by several other labs with the same result, and no one has any criticism of the result. We accept the result. R2 refutes a theory, T1, which predicted R1. So we form a variant theory, T2, which has the same claims as T1 except that, in the case of E being done again, it predicts R2 not R1. What's the (directly relevant to the quoted context) problem?
> At the time that you wrote this, did you know a source where Popper said this *exact* quote? If so, please share. If not, you shouldn't present it as a quote from Popper.
Yes, it's in "The Philosophy of Karl Popper Vol 2", in chapter "replies to my critics".
> So your idea of induction doesn't deal with "Most grass is green."? So you have something else, something non-inductive, to deal with it? What?
If my requirement is for our hypotheses to imply particular claim, and if your "most grass is green" does not meet this requirement, then it does not move onto the inductive stage. How do you deal with this theory in CR?
>> This is not true. If your corrected theory is only corrected in those predictions that we got wrong, then it can do no better or worse than the original theory on new predictions. If you change it in more ways than this, then either theory could outperform the other.
> We do a science experiment, E, with controlled circumstances and get a result, R2. E is also done by several other labs with the same result, and no one has any criticism of the result. We accept the result. R2 refutes a theory, T1, which predicted R1. So we form a variant theory, T2, which has the same claims as T1 except that, in the case of E being done again, it predicts R2 not R1. What's the (directly relevant to the quoted context) problem?
You are claiming T2 is "more likely to be correct" because its claims have been adjusted for what was correct in the past. When it comes to future repeats of experiment E, what's to stop T1 from being correct and not T2?
Your claim that T2 is more likely to be correct because of its success in the past is an inductive argument.
There is only a problem here if you reject induction.
>> At the time that you wrote this, did you know a source where Popper said this *exact* quote? If so, please share. If not, you shouldn't present it as a quote from Popper.
> Yes, it's in "The Philosophy of Karl Popper Vol 2", in chapter "replies to my critics".
I checked that book, and others, before posting. You have misquoted it. I imagine you'll find this pedantic, but I think *exact* quotes are important to discussion, I think it really matters. It's especially problematic to do things like doubling down on the *exactness* of a misquote. It's worrying to compound error in a case where you ought to be changing your mind. Whether you agree with the general attitude or not, please, in this discussion, just don't use quotes unless you're fully confident that they're exact. FYI my attitude to quotes is the standard one at this forum; my opinion that quoting matters has been developed over the years in which I and others believe it did matter to many discussions.
> If my requirement is for our hypotheses to imply particular claim, and if your "most grass is green" does not meet this requirement, then it does not move onto the inductive stage. How do you deal with this theory in CR?
You haven't answered how you deal with it. It doesn't move on to the inductive stage, but how do you evaluate the idea, what do you do with it? Do you just ignore/reject all ideas that you can't deal with inductively?
CR deals with this theory the same way it deals with everything else: by conjectures and refutations. You come up with various ideas – that's not the important part, and this idea is fine – and then you use critical discussion to try to find flaws in the ideas. When you have a criticism of a flaw in the idea, you use it to improve your knowledge, either by changing the idea to a better idea (that doesn't have that flaw) or by rejecting the idea.
The CR method works just as well with empirical and non-empirical matters. (And as DD pointed out in FoR, even when we can do empirical tests, we deal with the majority of ideas without doing them.) Some criticisms mention observations and some don't, that's all. Using observations is a useful type of criticism and worth some study, but it's not different at the most fundamental level.
I had thought that you were familiar enough with CR to know this.
> You are claiming T2 is "more likely to be correct" because its claims have been adjusted for what was correct in the past. When it comes to future repeats of experiment E, what's to stop T1 from being correct and not T2?
I don't disconnect the future and the past. I connect them (in some cases and not others – as a matter of logic, the future always resembles the past in some ways while differing in other ways) by non-inductivist means. But my view (CR) is another matter. That's a topic change.
I was trying to make a point within your framework, using your premises, not using CR premises. Don't you think that T2 is the better theory than T1, by your own standards and in your view? Or do you want to deny that (on what grounds that you believe)? I was trying to make sense of how you compare theories, both to get information about it and to point out problems.
Quoting
Dagny, FYI: Years ago I quit my role as contributor to a CR group blog because the owner misquoted me and then also refused to fix it. I couldn't associate with a website which insisted on spreading misinformation about my statements or beliefs.
I quoted one word with scare quotes to emphasize it "whiffs". The exact quote only differs by a single letter "In spite of this, there may be a 'whiff' of inductivism here".
I think you have overreacted somewhat.
#12741 When I asked you about whether it was an *exact* quote, you said it was and gave a source. At that time you had the opportunity to say that I had misunderstood you and that it wasn't a quote at all. You did not take that opportunity. You did not say that you used quote marks in the role of italics (emphasis) or as scare quotes (which are different than emphasis). You said that "Yes" it was an exact quote, but now you have changed your story and contradicted yourself in order to deny error.
You are in the wrong here but seem unable to admit it, and have also added an accusation against me. Being correct matters. You made a mistake. I'm perfectly happy to forgive a mistake, but not to accept a refusal to admit error in an especially clear case. The original mistake is, in my opinion, large enough to correct, but not very large. The second mistake (saying it was an exact quote after I asked) was larger but still not too awful. However, refusing to correct an error is, itself, a large and serious mistake, and totally contrary to the spirit of CR. If you can make no concession here, I will have to judge that you aren't worth talking to, because I would not be able to expect to persuade you of anything about epistemology, because that discussion/debate will be less clearcut/decisive than this.
PS Besides changing the inflection, you also removed Popper's scare quotes, so it was a misquote in two ways.
The truth is that I was trying to emphasize the word. So often I see it quoted with scare quotes (as Popper did himself) that I did the same, without really thinking it through.
When you asked for the *exact quote* I misunderstood you. I thought you wanted to know whether I had any source for this claim. Hence why I replied with the source. I didn't realize you were really taking issue with the fact that I misquoted a *single word!* by *one character!*.
Surely you can understand the possibility for misunderstanding here.
#12744 Saying it was a misunderstanding is another story change (it changes every time you comment) and is, in any case, compatible with you having made a mistake. Your comment is ambiguous and doesn't directly address the points in my previous comment. But it's somewhat clear, overall, that you refuse to concede that you made a mistake.
> Surely you can understand the possibility for misunderstanding here.
This comment implies, using social hints, that I'm being unreasonable. Some of the previous text hints, even less overtly, that I'm being unreasonable. That's your second time trying to attack me as a strategy to avoid correcting your own errors. That's typical irrational psychology.
Bye.
I don't mean to offend you with my use of language.
I'm happy to clarify that Popper used the word "whiff" and not "whiffs", but I'm not going to admit to your accusation that I was doubling down on misquoting Popper. If I was trying to quote Popper exactly, I would have looked up the text and given the full quote in the first place.
As I said, I misunderstood you as claiming that I was without a source. Instead you were just trying to point out that Popper said "whiff", not "whiffs". I incorrectly assumed you had a much bigger issue with what I had said.
> The class of things is fixed by the hypothesis.
OK, I think I understand. I thought induction had a starring role in your epistemology, but now I think it has only a secondary role. And I have no objection to you using deductive logic (narrowly and strictly considered) in any stage. But the hypothesis formation stage needs discussing before induction because your induction depends on it. I think it’s a positive and productive development that we’ve figured this out.
> I’m happy to accept the description of our hypotheses as “creative guesses”.
I don’t know what that means in adequate detail and it’s not a quote from earlier in this discussion. Do you believe that the hypothesis formation stage:
1. Is prior to induction.
2. Is non-inductive.
3. Is required for induction. You can’t do induction separately without any hypothesis formation.
4. Involves intelligent, creative reasoning, including both guesses *and* criticism.
? Short or yes/no answers are fine. I’m expecting “yes” to the first 3, but I want to be clear and check.
> I didn’t ask you to set aside all concepts and explanations. I wanted you to set aside all the *differences* between the two medical theories, except for the difference in their sample size.
Even if (contrary to logic, but for the sake of argument) the explanations and context for both medicines were identical (so sample size is the *only* difference), I would *still* need to know what those explanations and context were in order to evaluate whether (and in what ways) the sample size difference matters.
> If you can’t make a decision based on sample size alone, then just say so.
I did:
>> Sample size *alone* doesn’t tell you anything.
(PS: Please don’t use quotes again unless it’s a literal, exact quote.)
(PPS: I thought better of my one thing at a time discussion policy and replied to two separate things. I’ll try this policy: at most: one question, criticism or argument, and one short answer. That leaves room for half the discussion where you answer me, and half where I answer you. I think a larger number of shorter messages will be more effective, for the same word count, than a smaller number of longer messages. I’ll aim for shorter than this next time.)
> Do you believe that the hypothesis formation stage:
> 1. Is prior to induction.
> 2. Is non-inductive.
> 3. Is required for induction. You can’t do induction separately without any hypothesis formation.
If the conclusion of an induction is the rational support/justification of a hypothesis, then yes we do require a hypothesis prior to our induction, and we cannot perform an induction without a hypothesis to test.
The hypothesis stage is non-inductive in the sense that it is not induction. Hypothetical inference often involves the conclusion of a new kind of fact, different to what can be found in its premises. This is unlike induction where the conclusion is usually support for a generalisation of its premises. However, as we trial solutions to a problem in our mind we will often rule them out (deductively) due to their contradictions with already accepted prior knowledge. If the reason this prior knowledge is accepted is due to support via induction, then induction does have an (indirect) role in the hypothesis formation stage.
> 4. Involves intelligent, creative reasoning, including both guesses *and* criticism.
Yes, I think this is a fine way of describing it.
> Even if (contrary to logic, but for the sake of argument) the explanations and context for both medicines were identical (so sample size is the *only* difference), I would *still* need to know what those explanations and context were in order to evaluate whether (and in what ways) the sample size difference matters.
Maybe I will try one last attempt at asking this question. Imagine the doctor offers you the red pill or the blue pill. He doesn’t know why they work, but he suspects in time they will come to understand. All he knows is that on a random sample of the population, the blue pill has worked 100% of the time (sample of 3 people), and the red pill has worked 99% of the time (sample of 100’000) people. He is willing to let you try one, and not the other. Assuming your condition is life threatening, which option would you pick?
I'm interpreting #12770 as saying yes to the 4 points listed in #12750 And yeah, no problem about prior knowledge, regardless of source, being used in stage 1.
> we cannot perform an induction without a hypothesis to test.
From prior discussion, I understand the induction step to rely on certain limits on the hypothesis creation step. Not just any hypothesis can be created, only certain ones. There are some rules or restrictions because the induction step is unable to deal with certain ideas and they must be ruled out earlier. When I asked how induction dealt with some ideas, I found out they would have been dealt with previously. Can you give details of the goals and rules of the hypothesis stage? What is done in it and what is not done?
> Assuming your condition is life threatening, which option would you pick?
I'd read the literature. Even non-technical literature (magazine article, advice webpage, doctor's office info sheet, or instead of reading the doc could explain it to me) giving a basic overview of the choices and the upsides and downsides of each one would be so much better than nothing. Doctors always either tell me what to do or give me some info about my choices.
If you modified the scenario enough that I must decide immediately, I have brain damage and can't think much, I don't even know what part of my body needs the medicine, etc., then I would ask the doctor to decide for me (or, better, my trusted critical rationalist proxy who could read the literature). If I can't have info to make an informed decision myself, then the doctor (or my proxy) should use his expert judgment.
> Can you give details of the goals and rules of the hypothesis stage? What is done in it and what is not done?
I think as a simplification for our discussion we can consider hypothesis as beginning with a random guess at what is true.
Once we have a guess, we then consider if it is worth taking seriously. We look at what our guess says about the world, and then we compare against what our existing theories (background knowledge) says about the world. If we find our guess can be deduced from our existing knowledge, then we may not even need to move onto the testing (inductive) stage.
We may only find our guess gets partial support, or is rendered only probable, but not necessary, by our existing knowledge. In this case, if we find the benefits provided by our guess (if it were to turn out true) worth our time, we may move onto the testing stage. Testing would focus on the new general claims provided by the theory; the claims whose grounds are most shaky.
If we find that our guess is in contradiction or poorly supported by our background theories, then we may cast it aside without any further consideration.
In regards to my medical example. Would you consider the use of statistical confidence intervals/levels found from a random sampling of the drugs use on the population as input into your decision?
> We may only find our guess gets partial support, or is rendered only probable, but not necessary, by our existing knowledge.
You're saying that ideas support ideas? How? Which ideas support which other ideas, and how much? Is there a formula or any clear guidelines, or is this done by intuition and "I know it when I see it"
This gets into many of the same issues I brought up previously. Your answer before was to filter out most ideas at an earlier step, but now we're at the earliest step so you'll have to deal with infinite classes of possible ideas.
> Would you consider the use of statistical confidence intervals/levels found from a random sampling of the drugs use on the population as input into your decision?
Anything is input, but that input is not useful with literally zero context. Statistics and numbers don't mean anything with no context in which to interpret them.
The support by other theories is deductive. Say I guess that 'All marsupials have eyes'. We might have existing knowledge that 'All small animals have eyes'. The deduction looks like this.
1) All small animals have eyes
2) Marsupials are small animals
3) Therefore, all marsupials have eyes.
If the the existing knowledge was only probable 'most families of small animals have eyes', then our deduction only lets us conclude that 'animals under the marsupial family most likely have eyes'. Here it is deduced from our existing knowledge that we have more than an even chance of being right.
>Anything is input, but that input is not useful with literally zero context.
The context is the large random sample of tests of this drug.
I think we use many drugs today with little knowledge of how they work. Knowledge of their success in a vast number of use cases does a lot to overcome this uncertainty.
#12798
You're maybe using the word "supports" here to mean something like "is a premise of". That is different than how the term is used in induction. Let's not reuse the same term with a different meaning. That will be confusing. Can we call it something else, e.g. logical implication? Or is it somehow different than logical implication?
I take it that "Therefore all small animals have eyes or (Stalin was God and Mao was his prophet)." is equally (100%) "supported", the same as (3). Right? (The parentheses are to clarify order of operations.)
How would deduction lead to something being 30% "supported"?
If a premise is "There is a 30% chance that X is true" then the implication "2+2=5 or there is a 30% chance that X is true" is 100% implied ("supported"), right? Given the truth of the premises (and given, as always, the truth of our view of deduction, and that we didn't make an analysis error) it's true, just like with any other syllogism.
You are using the word "probable" but you aren't referring to physical probability of events, e.g. dice rolls. Are you using it metaphorically, imprecisely, or what? Where are the details of its meaning? (It would help if you introduced as few additional, complex topics as you can.)
If something is the conclusion of multiple syllogisms, is it more "supported", or the same? Does something just have to be the conclusion of one syllogism to get 100% support? What if the negation of something is the conclusion of a syllogism, does that matter?
Which system of deductive logic is used for this? (And does it cover the issue of probability that you brought up?)
*But I shouldn't have to be asking these questions. Where is this written down?* Can you answer me using quotes instead of by writing ad hoc material? These strike me as basic questions. If the system you're advocating has been developed by anyone, I would expect them to be clearly addressed. Do you think that's unreasonable? Did Peirce answer all these questions? Previously you indicated you weren't advocating a new view, but maybe you'll want to revise that claim now, idk.
> The context is the large random sample of tests of this drug.
That is not an adequate specification of the context. You are leaving out e.g. what the drugs do, how, and the differences in design between the two drugs being considered. You are leaving out even a condensed summary of such matters as would routinely be provided to a patient IRL.
> I think we use many drugs today with little knowledge of how they work. Knowledge of their success in a vast number of use cases does a lot to overcome this uncertainty.
Little or limited knowledge is categorically different than *zero* knowledge. You're dramatically changing the topic. What's going on?
>You're maybe using the word "supports" here to mean something like "is a premise of". That is different than how the term is used in induction. Let's not reuse the same term with a different meaning. That will be confusing. Can we call it something else, e.g. logical implication? Or is it somehow different than logical implication?
>I take it that "Therefore all small animals have eyes or (Stalin was God and Mao was his prophet)." is equally (100%) "supported", the same as (3). Right? (The parentheses are to clarify order of operations.)
>How would deduction lead to something being 30% "supported"?
You are right, we can call it a logical or deductive implication.
Stalin being a god is not a logical deduction from 'all small animals have eyes'.
What I mean by probable support is that the claim is true often enough or in some given proportion of cases. So if I am to make sense of your "30% supported", then it could only mean that the theory is true in 30% of cases.
Peirce gives his own example in "Deduction, Induction, and Hypothesis":
>>If, from a bag of beans of which we know that 2/3 are white, we take one at random, it is a deductive inference that this bean is probably white, the probability being 2/3. We have, in effect, the following syllogism:
Rule.—The beans in this bag are white.
Case.—This bean has been drawn in such a way that in the long run the relative number of white beans so drawn would be equal to the relative number in the bag.
Result.—This bean has been drawn in such a way that in the long run it would turn out white 2/3 of the time.
>"There is a 30% chance that X is true" then the implication "2+2=5 or there is a 30% chance that X is true"
Sure.
>If something is the conclusion of multiple syllogisms, is it more "supported", or the same? Does something just have to be the conclusion of one syllogism to get 100% support? What if the negation of something is the conclusion of a syllogism, does that matter??
If our claim can be deduced from more than one of our existing theories then it can gain more support. For example, I might claim that 'lemon and honey can cure a sore throat'. If we already know that lemon cures a sore throat in 80% of cases and honey in 40% of cases, then we can use probability laws to determine that our new claim will lead us right in 88% of cases. Our everyday reasoning is of a more qualitative sort than this, but the form is the same.
If our new claim is negated by existing knowledge, then we have reasons to think it is false, or that it won't be true. If the negation is strong enough (we might prove the null hypothesis), then we will likely stop investigating our new claim.
I can't point to precise quotes to answer each of your particular questions because I'm not sure if Peirce has given explicit answers to each of them. Your questions are ones I haven't seen people asking before, but I can derive answers from my understanding of Peirce's work (mostly from the three articles I have linked so far).
>Little or limited knowledge is categorically different than *zero* knowledge. You're dramatically changing the topic. What's going on?
Even with *zero* knowledge of how some drugs work, we still use them. We know they will work because they have worked well in the past, not because we have an understanding of how the particular chemical reactions play out. Such an understanding can often come later.
> Stalin being a god is not a logical deduction from 'all small animals have eyes'.
You're denying that X implies (X or Y)? That is part of every standard deductive logic system. Are you familiar with deductive logic? I reiterate:
>>> Which system of deductive logic is used for this?
---
> Even with *zero* knowledge of how some drugs work, we still use them.
Name one.
Sure, X implies X or Y. What is your point?
> Name one.
https://en.wikipedia.org/wiki/Category:Drugs_with_unknown_mechanisms_of_action
>>> Stalin being a god is not a logical deduction from 'all small animals have eyes'.
>> You're denying that X implies (X or Y)?
> Sure, X implies X or Y. What is your point?
I made a statement of the X implies X or Y variety. You then took issue with it, as quoted, again.
The statement was "Therefore all small animals have eyes or (Stalin was God and Mao was his prophet)."
And then you were objecting. Why? My point is my statement was correct and your objection was incorrect.
Also, again,
>>>>> Which system of deductive logic is used for this?
*Specify* which deductive system your epistemology uses.
---
>> Name one.
> https://en.wikipedia.org/wiki/Category:Drugs_with_unknown_mechanisms_of_action
Name *one* (that you are knowledgeable and confident about).
Kieren's list from #12818 includes:
https://en.wikipedia.org/wiki/Ketamine
> Ketamine is an NMDA receptor antagonist, but it may also have other actions.
Knowing that something has a mechanism of action where it inhibits a particular type of receptor is not even close to *zero* knowledge of how it works.
Sorry, I misread you. That is why I objected against 'X implies Y'. I accept 'X implies (X or Y)'.
I don't have any special system in mind when I am talking about deduction. I believe I'm just using generic brand Modus ponens/tollens. What system of deduction do you use?
> Name *one* (that you are knowledgeable and confident about).
Beta blockers are often taken to help with blood pressure problems. I know someone with Long QT syndrome who takes these drugs because they have been shown to substantially reduce mortality rates in long QT patients. His doctor cannot tell him why it works, only that the evidence suggests it has such and such beneficial effects, most of the time.
> I don't have any special system in mind when I am talking about deduction. I believe I'm just using generic brand Modus ponens/tollens. What system of deduction do you use?
You don't need a special system, you need any specific system, that way you can judge what is a correct deduction. Specifying a system also lets you examine it to see what it can do and what its limits are, e.g. you can look at a list of everything within the system and see if probability is involved in any way or not. I see that you have not considered the specific rules of deduction despite their large role in your epistemology. Now let's look at one of your claims related to deduction:
> What I mean by probable support is that the claim is true often enough or in some given proportion of cases. So if I am to make sense of your "30% supported", then it could only mean that the theory is true in 30% of cases.
If X happens in situation Y in 30% of cases then the claim "X always happens in situation Y" is not 30% supported, it's *false*. And the claim "X happens in situation Y in 30% of cases" is not 30% supported, it's *true*.
So how does this "30% logically implied/supported" idea work, in terms of details of deductive logic or even at all?
> Beta blockers
OK, I Googled them, went to the first website that came up, and read the first body paragraph. It says:
https://www.mayoclinic.org/diseases-conditions/high-blood-pressure/in-depth/beta-blockers/art-20044522
> Beta blockers, also known as beta-adrenergic blocking agents, are medications that reduce your blood pressure. Beta blockers work by blocking the effects of the hormone epinephrine, also known as adrenaline.
Do you believe that that paragraph contains *zero* knowledge about how beta blockers work, or more than *zero*?
> So how does this "30% logically implied/supported" idea work, in terms of details of deductive logic or even at all?
Take my earlier example 'marsupials have eyes'. If we know that marsupials are a type of small animal, and that 90% of small animal types have eyes, then we know that posing such new theories would lead us right in 90% of cases. This is what I would call probable support from our existing knowledge.
> Do you believe that that paragraph contains *zero* knowledge about how beta blockers work, or more than *zero*?
Beta blockers are commonly used for blood pressure where I'm sure the effects are well understood. We can't say the same for long QT where its mechanism of action is still under question.
Even if we do come to understand how some particular drug operates at the molecular level, how do you explain our rational preference for using such a drug before an accepted explanation is available. I'm sure we have made some progress in explaining how general anaesthesia works, but I wonder how you explain our use of anaesthetics in the hundreds of years prior?
> Take my earlier example 'marsupials have eyes'. If we know that marsupials are a type of small animal, and that 90% of small animal types have eyes, then we know that posing such new theories would lead us right in 90% of cases. This is what I would call probable support from our existing knowledge.
What are you deducing from what (and then where does a percentage come in)? You said this was related to logical deduction.
---
> Even if we do come to understand how some particular drug operates at the molecular level, how do you explain our rational preference for using such a drug before an accepted explanation is available.
I didn't say a word about understanding it at a molecular level, I said we have *more than zero* understanding of how it works.
https://www.mayoclinic.org/diseases-conditions/long-qt-syndrome/symptoms-causes/syc-20352518
> Long QT syndrome (LQTS) is a heart rhythm condition that can potentially cause fast, chaotic heartbeats. These rapid heartbeats might trigger a sudden fainting spell or seizure. In some cases, the heart can beat erratically for so long that it causes sudden death.
The condition involves a fast heartbeat. Now let's go back to the previous link and read the second paragraph:
https://www.mayoclinic.org/diseases-conditions/high-blood-pressure/in-depth/beta-blockers/art-20044522
> When you take beta blockers, your heart beats more slowly and with less force, thereby reducing blood pressure. Beta blockers also help blood vessels open up to improve blood flow.
Beta blockers slow your heart rate, so it makes sense that that could help with a problem involving a fast heart rate.
So we have more than *zero* knowledge of how beta blockers help with LQTS and what they do.
Even if all we know is that beta blockers affected the heart, rather than the foot (and that LQTS related to the heart, not the foot), that would be more than *zero* knowledge.
I think your problem in both discussions is that you don't think (or use words) in a precise enough way. This has been an ongoing issue (e.g. it's why Dagny stopped talking with you) prior to the two examples discussed in this comment.
> What are you deducing from what (and then where does a percentage come in)? You said this was related to logical deduction.
The syllogism is:
1) 90% of small animal types have eyes (existing knowledge)
2) marsupial are a type of small animal (our theory as a case under the existing knowledge)
3) there is a 90% chance that marsupials have eyes (deduced conclusion)
> ---
> Beta blockers slow your heart rate, so it makes sense that that could help with a problem involving a fast heart rate.
You are more at risk with a fast heart rate, but that is not the root cause. The problem is the prolonged QT interval (repolarization of the heart). Beta blockers reduce the QT interval back to normal levels, but how they do this is unknown.
> Even if all we know is that beta blockers affected the heart, rather than the foot (and that LQTS related to the heart, not the foot), that would be more than *zero* knowledge.
That would be knowledge related to beta blockers, but not knowledge related to how beta blockers work in solving our specific problem. In the medical journals I have read they tell us that the mechanism of action is unknown, but that beta-blockers have been very effective at reducing mortality rates. This is the point I am trying to get across; that the performance of drug tests alone can be enough for us to rationally choose to use one drug over another.
Do you believe it is irrational to use a medication because of its effectiveness in clinical trials?
> 3) there is a 90% chance that marsupials have eyes (deduced conclusion)
So the status of (3) is ... it is 100% implied/supported by its premises. Right? Given the truth of the premises, and that we didn't make a deduction error, then (3) must be true (100% fully true, not 90%). I explained this issue already:
> If X happens in situation Y in 30% of cases then the claim "X always happens in situation Y" is not 30% supported, it's *false*. And the claim "X happens in situation Y in 30% of cases" is not 30% supported, it's *true*.
You are confusing probability *inside* (within, mentioned by) ideas and probability *of* ideas.
> Do you believe it is irrational to use a medication because of its effectiveness in clinical trials?
No medication has ever entered clinical trials while having *literally and exactly zero* knowledge of how it works.
Even knowing one way it *doesn't* work is more than zero knowledge about how it works.
Again, you're just not being precise. You are fudging what zero is.
In all real situations, we have more information than in your hypothetical discussed earlier where you actually gave me zero information. No real scenarios are ever like that.
> So the status of (3) is ... it is 100% implied/supported by its premises. Right? Given the truth of the premises, and that we didn't make a deduction error, then (3) must be true (100% fully true, not 90%). I explained this issue already:
>> If X happens in situation Y in 30% of cases then the claim "X always happens in situation Y" is not 30% supported, it's *false*. And the claim "X happens in situation Y in 30% of cases" is not 30% supported, it's *true*.
> You are confusing probability *inside* (within, mentioned by) ideas and probability *of* ideas.
I think we are on the same page with this. I agree that (3) is true because the premises are true.
The reason I call it probable support, is because we have found, when considering our existing knowledge, that our new theory 'marsupials have eyes' is *probably* true.
>> Do you believe it is irrational to use a medication because of its effectiveness in clinical trials?
> No medication has ever entered clinical trials while having *literally and exactly zero* knowledge of how it works.
> Even knowing one way it *doesn't* work is more than zero knowledge about how it works.
> Again, you're just not being precise. You are fudging what zero is.
> In all real situations, we have more information than in your hypothetical discussed earlier where you actually gave me zero information. No real scenarios are ever like that.
I could grant you that drug X has some effect on the heart, and therefore we have non-zero knowledge relating to drug X. However, this just shifts the target of my questioning to how it is you have this knowledge. Instead of asking 'how do you know drug X will save you?', I would ask 'how do you know drug X will have that same effect on your heart?'.
We end up with the same form of question as I asked previously; is it irrational to expect the same effects of a drug in the future because of its past effectiveness in tests?
> The reason I call it probable support, is because we have found, when considering our existing knowledge, that our new theory 'marsupials have eyes' is *probably* true.
What new theory "marsupials have eyes"? That was not (1), (2) or (3) in the syllogism. I'll call it (4) for now. You are making a claim about support via deduction, so please provide one or more deductive arguments containing the theory (4) that you claim has probabilistic support. Again the issue is your discussion comments are inadequately precise. You have not provided a deductive argument showing probabilistic or percentage support for any theory, nor addressed the general issue that deductive syllogisms reach non-probabilistic conclusions, nor specified the details of the system of deductive logic you're advocating (I want to read through all the stuff about probability in it).
> 'how do you know drug X will have that same effect on your heart?'.
In my view (which is CR's view): by conjecture and refutation, the same way we know anything at all.
>> The reason I call it probable support, is because we have found, when considering our existing knowledge, that our new theory 'marsupials have eyes' is *probably* true.
> What new theory "marsupials have eyes"? That was not (1), (2) or (3) in the syllogism. I'll call it (4) for now. You are making a claim about support via deduction, so please provide one or more deductive arguments containing the theory (4) that you claim has probabilistic support. Again the issue is your discussion comments are inadequately precise. You have not provided a deductive argument showing probabilistic or percentage support for any theory, nor addressed the general issue that deductive syllogisms reach non-probabilistic conclusions, nor specified the details of the system of deductive logic you're advocating (I want to read through all the stuff about probability in it).
My example is that we have come up with (guessed) a new theory 'marsupials have eyes', and we are at the hypothesis stage considering if our new guess is any good.
When I said...
>>Take my earlier example 'marsupials have eyes'.
I was referring to...
>> Say I guess that 'All marsupials have eyes'.
I call it a 'new theory' because in the example it is a new theory, a new guess.
With my deduction we have agreed that (3) is true. What (3) says is that 'there is a 90% chance that marsupials have eyes'. This is not a probabilistic conclusion, but necessarily true given the truth of its premises (logical deduction). The probability exists within the conclusion. I think we agree on this.
Now given (3) I think it is obvious what this says about our new theory, but just in case, I will put it into a syllogism too.
(3) there is a 90% chance that marsupials have eyes
(4) our new theory says 'marsupials have eyes'
(5) therefore, these is a 90% chance our new theory is correct
This is a deduction *about* probabilities.
>> 'how do you know drug X will have that same effect on your heart?'.
> In my view (which is CR's view): by conjecture and refutation, the same way we know anything at all.
So you guess that 'X will continue to have the same effect on people's hearts as has been observed in the past', and I guess 'X will *not* continue to have the same effect on people's hearts as has been observed in the past'. How do you refute my theory?
A marsupial is a category of animal and some marsupials are large. So let's consider short-nosed bandicoots (SNB) which are a particular species of small marsupial.
*If* 90% of all small animals have eyes ("small animals" referring to a particular set of animals defined by a list of all entities that qualify as both "small" and "animal"), and *if* SNB's are a small animal, it *does not follow* that there is a 90% probability that SNBs have eyes.
What follows is that a randomly selected animal from the set of all small animals would be 90% likely to have eyes. Probability becomes involved specifically because of the *physical process* of a random selection. (Probability wasn't involved before. 90% of things in a set having a trait just means that e.g. 630 of 700 do, it's a matter of proportions not probabilities). SNBs were not randomly selected from the set of all small animals. Also, this is pointless because we already checked whether every single small animal had eyes in order to determine that 90% of them do - our knowledge of how many small animals do and don't have eyes was a premise.
I think you have something else in mind with some sort of weaker premise from which you wish to reach a stronger conclusion. Can you clarify? I expect it to be something kinda like "If we saw some things which were small and animals, and most of those had eyes, and then we see a new thing which small and an animal, we can guess it probably has eyes even if we can't see its head." But that is too vague and isn't deduction – it sounds more like a naive version of induction. So I'm hoping you've got something better than that.
> So you guess that 'X will continue to have the same effect on people's hearts as has been observed in the past', and I guess 'X will *not* continue to have the same effect on people's hearts as has been observed in the past'. How do you refute my theory?
How I would refute your theory (or maybe I'd even agree with it) would depend on what X is. The matter is context dependent, which has been my recurring point.
E.g. if X is a particular batch of medicine, maybe it won't keep having the same effect because it goes bad over time. There is no way to arbitrate which ideas are correct without knowing what X is. You have to actually think about the topic (X).
> A marsupial is a category of animal and some marsupials are large. So let's consider short-nosed bandicoots (SNB) which are a particular species of small marsupial.
> *If* 90% of all small animals have eyes ("small animals" referring to a particular set of animals defined by a list of all entities that qualify as both "small" and "animal"), and *if* SNB's are a small animal, it *does not follow* that there is a 90% probability that SNBs have eyes.
I figured, for the sake of argument, we could assume all marsupials are small animals, but if you wish to change the subject of the example to a species of small animal we can do that. The problem is you have changed the existing knowledge from '90% of small animal *types* have eyes' to '90% of small animals have eyes'. You should have changed it to '90% of small animal *species* have eyes', which would have maintained the form of the argument. You are right that the species needs to be drawn randomly for the proportion to convey probability. I left this as an implicit assumption for the argument (as it often is in human reasoning), but we can make it explicit too.
The modified example becomes:
(1) 90% of small animal species have eyes (existing knowledge)
(2) SNB are a species of small animal selected randomly from the set of small animal species
(3) therefore, there is a 90% chance that SNB have eyes
(4) our new theory says 'SNB have eyes'
(5) therefore, these is a 90% chance our new theory is correct
> How I would refute your theory (or maybe I'd even agree with it) would depend on what X is. The matter is context dependent, which has been my recurring point.
Lets say X is a drug like beta-blocker which shortens the QT interval of the heart. We do not know its mechanism of action, but we expect some kind of biochemical reaction is taking place (as does with most other drugs). We have observed in 100'000 randomly sampled cases that it has had this effect 100% of the time. Would you still be unwilling to bet on the drug having similar effects in new cases?
#12857 Premise (1) is vague. By (1), do you mean that you documented every single small animal species and know whether it has eyes? If not, what exactly does it mean?
> Would you still be unwilling to bet on the drug having similar effects in new cases?
It depends on context. Do you actually want me to read scientific papers on beta-blockers? Have you read them? Because that is what I'd have to do to answer the question. But I don't know if you even care about beta blockers in particular or were just trying to throw out an example. Reasonable scientists make judgments using far more information than your paragraph includes, so either I have to rely on their judgment or investigate the matter myself.
And your paragraph already includes more than *zero* information. Are you conceding the point about zero context? Do you now believe some of your previous claims were mistaken? Will you retract anything?
> #12857 Premise (1) is vague. By (1), do you mean that you documented every single small animal species and know whether it has eyes? If not, what exactly does it mean?
Premise (1) is existing background knowledge. It is accepted knowledge that we are considering alongside our new theory.
Remember my original point about the hypothesis stage:
>>We may only find our guess gets partial support, or is rendered only probable, but not necessary, by our existing knowledge.
>> Would you still be unwilling to bet on the drug having similar effects in new cases?
> It depends on context. Do you actually want me to read scientific papers on beta-blockers? Have you read them? Because that is what I'd have to do to answer the question. But I don't know if you even care about beta blockers in particular or were just trying to throw out an example. Reasonable scientists make judgments using far more information than your paragraph includes, so either I have to rely on their judgment or investigate the matter myself.
I have read through papers on beta-blockers. Many papers report their effectiveness in treating long QT based on the results of clinical trials. I have also seen more recent papers proposing possible mechanisms of action to explain how the effects come about (with evidence in their favour). However, I wonder how you account for the use of such drugs before any such theories are available? Is it perhaps enough context for you to have an unrefuted guess that 'beta blockers reduce the QT interval through *some sort* of biochemical process'?
> And your paragraph already includes more than *zero* information. Are you conceding the point about zero context? Do you now believe some of your previous claims were mistaken? Will you retract anything?
I didn't say we use drugs with "*zero* information", which is far too vague a claim to ever satisfy.
I said:
>>Even with *zero* knowledge of how some drugs work, we still use them. We know they will work because they have worked well in the past, not because we have an understanding of how the particular chemical reactions play out.
When I say "knowledge of how some drugs work" I am not talking about any and all knowledge relating to the drug, but I am referring to the knowledge of "how some drugs work", "how the particular chemical reactions play out". My thinking is that we generally do not say we know how a drug works (causation) until we understand its mechanism of action. If you allow strong correlation between the drug and effects on the human body as knowledge of how the drug works, then I will of course retract the *zero*.
> Premise (1) is existing background knowledge. It is accepted knowledge that we are considering alongside our new theory.
But what does it mean? Does it mean our background knowledge involves a complete list (that we accept), or does it mean something else (that we accept)?
> Is it perhaps enough context for you to have an unrefuted guess that 'beta blockers reduce the QT interval through *some sort* of biochemical process'?
It could be, depending on the availability of alternatives and criticism in the situation. Knowing something is a biochemical process involving the heart, rather than a magical process involving the foot, is more than zero knowledge.
Knowing something works by some sort of biochemical process that obeys the laws of physics is not *zero* knowledge about how it works. Will you retract the claim that:
> Even with *zero* knowledge of how some drugs work, we still use them.
?
The point is, in real situations, with real medicines, we always have information that you were leaving out of the original question where you wanted me to judge *only* by sample size.
Another type of information we have in real life situations is *how the sampling was done*. You call it "random" but that's vague and better information is actually available.
> But what does it mean? Does it mean our background knowledge involves a complete list (that we accept), or does it mean something else (that we accept)?
Since it is knowledge about the world, and since it is accepted knowledge, it must have passed the hypothesis stage and the inductive stage. We can start discussing the inductive stage if you like, but we would be moving on from the hypothesis stage.
> It could be, depending on the availability of alternatives and criticism in the situation. Knowing something is a biochemical process involving the heart, rather than a magical process involving the foot, is more than zero knowledge.
> Knowing something works by some sort of biochemical process that obeys the laws of physics is not *zero* knowledge about how it works. Will you retract the claim that:
>> Even with *zero* knowledge of how some drugs work, we still use them.
> ?
Sure, if that is what counts as knowledge of how the drug works then we have non-zero knowledge. If we want to accept this as prior knowledge in my example then I will have some questions.
1) Would it be rational for someone to use the drug based on this knowledge?
2) How do you have this knowledge? I assume it would have to be an unrefuted conjecture?
> Since it is knowledge about the world, and since it is accepted knowledge, it must have passed the hypothesis stage and the inductive stage. We can start discussing the inductive stage if you like, but we would be moving on from the hypothesis stage.
Overall, I'm trying to find out from you how we learn anything *before induction*, because you said a bunch of important stuff happens with no induction. Where and how does learning start?
Also I'm trying to find out how we could learn this particular claim and use it as a premise, and trying to get you to clarify the meaning of the premise. Are you saying we induced it? Can you give a short story of how we'd come to have that premise? I asked if we got the info by making a list of all the small animals and you have repeatedly not answered if that is what's going on or something else is going on.
> 1) Would it be rational for someone to use the drug based on this knowledge?
No, but we actually have far more knowledge than just what's contained in the quoted text. As far as I know, they are reasonable to take given the knowledge currently in existence.
> 2) How do you have this knowledge? I assume it would have to be an unrefuted conjecture?
I don't personally have knowledge about whether it's good to take beta blockers in what situations. I haven't researched it. I have found, in general, that there is a lot of medical misinformation, so I would want to investigate (to gain knowledge I don't currently have) before taking them (or deciding not to take them).
BTW, are there actually two different beta blockers, one of which has been tested with many people, and one with only a few people, and some current controversy about which to take? If not, I don't see how they'll make a good example regarding the original question. They came up for the purpose of clarifying that zero actually means zero, and I think they've now served that purpose.
> Overall, I'm trying to find out from you how we learn anything *before induction*, because you said a bunch of important stuff happens with no induction. Where and how does learning start?
Learning begins at the hypothesis stage where we come up with a new hypothesis that says something new about the world. Consideration of our existing knowledge allows us to elucidate deductive support for or against our new theory at this stage. This what we have been discussing so far. We had our new theory 'SNB have eyes' and we found it was likely true given our existing knowledge.
The next stage would be to put our new theory to the test and infer its truth with an inductive argument. This involves random sampling of deduced cases and confidence intervals/levels.
> Also I'm trying to find out how we could learn this particular claim and use it as a premise, and trying to get you to clarify the meaning of the premise. Are you saying we induced it? Can you give a short story of how we'd come to have that premise? I asked if we got the info by making a list of all the small animals and you have repeatedly not answered if that is what's going on or something else is going on.
The process described above would be the same for the background knowledge. We must assume our background knowledge has already passed the hypothesis stage and has received inductive support.
> No, but we actually have far more knowledge than just what's contained in the quoted text. As far as I know, they are reasonable to take given the knowledge currently in existence.
I would like to confirm where we are at. The general case is that we have some substance that people have consumed to reduce their suffering and/or improve their longevity. The substance is strongly correlated with effects on the human body that are well reported. We know that in all of the numerous randomly sampled cases that this has been true (not a single counter example). We do not know what the mechanism of action is but we suspect it will be some sort of biochemical process as is the case with most other drugs (in fact, as you suggested, we know this to be the case).
With this in mind, you do not think it rational to expect similar effects in new trials?
How, roughly, do you imagine we would learn that 90% of small animals have eyes? You are calling that existing knowledge and I'm asking you how we would have gotten it (because it's a vague statement that doesn't include adequate details about what it means, and so is unsuitable for deducing anything without clarification. Finding out where that knowledge is coming from would help clarify it.) You haven't even specified if the premise is that exactly 90% of small animals have eyes, or that roughly 90% do.
> The general case is that we have some substance that people have consumed to reduce their suffering and/or improve their longevity. The substance is strongly correlated with effects on the human body that are well reported.
That correlation is within a certain limited context. The nature and limits of that context are impossible to know anything about without explanatory knowledge (the statistics/correlations/data alone tell you nothing about it). This is a logical fact which is known outside of CR, e.g. here is basically the same point:
http://bactra.org/weblog/520.html
> To summarize: Heritability is a technical measure of how much of the variance in a quantitative trait (such as IQ) is associated with genetic differences, in a population with a certain distribution of genotypes and environments. Under some very strong simplifying assumptions, quantitative geneticists use it to calculate the changes to be expected from artificial or natural selection in a statistically steady environment. It says *nothing* about how much the over-all level of the trait is under genetic control, and it says *nothing* about how much the trait can change under environmental interventions. If, despite this, one does want to find out the heritability of IQ for some human population, the fact that the simplifying assumptions I mentioned are clearly false *in this case* means that existing estimates are unreliable, and probably too high, maybe much too high.
"Heritability" is a measure of correlation and it tells you *nothing* about what would happen if there was an intervention (that is, if the context was intentionally changed; the same point also applies to unintentional context changes.) The whole article is basically about the logical limits of what one can learn from correlations.
> With this in mind, you do not think it rational to expect similar effects in new trials?
Tons of medical and other studies fail to replicate when people try to replicate previous findings. This is a major crisis in science today (I don't think the past was better, I think we started noticing the problem more). So, who knows, I'd have to look at whether the research is any good. E.g. you mention "randomly sampled cases" but that is imprecise. The samples are random in some respects and not others, and you didn't say what was random and non-random about the samples. They may be good or bad samples depending on the relevant explanations, and you're leaving out all the details by which I could judge whether the sampling is good or bad. You're leaving out the information required for critical thinking. Competent scientists have access to such information and use it to inform their judgments.
> How, roughly, do you imagine we would learn that 90% of small animals have eyes? You are calling that existing knowledge and I'm asking you how we would have gotten it (because it's a vague statement that doesn't include adequate details about what it means, and so is unsuitable for deducing anything without clarification. Finding out where that knowledge is coming from would help clarify it.) You haven't even specified if the premise is that exactly 90% of small animals have eyes, or that roughly 90% do.
The meaning of ‘90% of small animal species have eyes’ is that the proportion of small animal species that have eyes is 90%. If you randomly pick a small animal species you will have a 90% chance of picking a species with eyes.
If we had checked every single small animal species then we would be certain of this knowledge. If we had instead checked only a random sample of small animal species then we would have calculated a confidence interval/level for the theory’s truth. We might have found that with our sampling we have a 95% chance that the proportion of small animal species with eyes is within 89-91%.
> That correlation is within a certain limited context. The nature and limits of that context are impossible to know anything about without explanatory knowledge (the statistics/correlations/data alone tell you nothing about it). This is a logical fact which is known outside of CR, e.g. here is basically the same point:
This is why randomly sampling is important in my view. We are going to sample from various different contexts and therefore with increasing sample size the probability that we would find a context that brings about a fail case grows. The chance that you will be the unlucky bugger who provides the rare (e.g. 1 in a million) context for the drug to not work becomes so minuscule that most people won’t even consider it as a real possibility. Of course this might all change if you were to have other knowledge that tells you the drug will not work for this or that reason, but we are assuming that such knowledge is absent in our example.
> Tons of medical and other studies fail to replicate when people try to replicate previous findings. This is a major crisis in science today (I don't think the past was better, I think we started noticing the problem more). So, who knows, I'd have to look at whether the research is any good. E.g. you mention "randomly sampled cases" but that is imprecise. The samples are random in some respects and not others, and you didn't say what was random and non-random about the samples. They may be good or bad samples depending on the relevant explanations, and you're leaving out all the details by which I could judge whether the sampling is good or bad. You're leaving out the information required for critical thinking. Competent scientists have access to such information and use it to inform their judgments.
For the sake of this hypothetical argument can we please assume that the samples were actually taken randomly (as best we can), and not biased towards people with weak bones, certain personalities, cultures, locations, etc. Can we also assume that the scientists have done the right thing and not fudged their results for financial gains, personal bias, etc. I understand that some reasonable assumptions will have to be made (I am a human, I have access to the medicine, the year is 2019, etc), but you seem to be taking issue with irrelevant practical details that will distract us from what I think we are really interested in; our general theories of knowledge. With these assumptions can you try and answer the question again?
I’ve given this same hypothetical question to a number of people and it has proven useful for elucidating different views on the role of evidence in science. You are the first to call into question whether the random sample is really random, or if the drug has a known expiry date, etc. I think you should be agnostic (assume no knowledge) to any specific knowledge claims that aren't made explicit by the hypothetical argument or which are not reasonably implied by the question, otherwise you will have to ask endless clarification questions. If we later find we are working with important differences in our assumptions then we can call them into question.
https://www.ncbi.nlm.nih.gov/pmc/articles/PMC2654794/
> In 1998 a unique drug for the treatment of narcolepsy was approved by the Food and Drug Administration for the narcolepsy armamentarium. Despite several years of pre-clinical research, the mechanism of action of modafinil was unknown. Almost a decade later there is a plethora of evidence showing that it is effective for treating several sleep disorders (Ballon and Feifel 2006), and there are ongoing clinical trials for its use in fatigue, cocaine addiction, attention deficit disorder, depression, seasonal affective disorder, bipolar depression, nicotine addiction, and schizophrenia. Some preclinical evidence also indicates a possible use in the treatment of neurodegenerative diseases. Most research on modafinil’s wake-promoting mechanism has focused on monoaminergic effects showing modafinil stimulates histamine (HA), norepinephrine (NE), serotonin (5-HT), dopamine (DA), and orexin systems in the brain, but researchers have not been able to isolate a single site of action or locate major receptor binding. Modafinil’s mechanism of action (MOA) remains elusive as pointed out in a recent editorial on modafinil entitled, “Modafinil: a drug in search of a mechanism” (Saper and Scammell 2004). There has also been research into the neuroprotective actions of modafinil, which we propose to be related to its alerting effects. We selectively review a number of preclinical and clinical papers relevant to modafinil’s MOA. We conclude with contemplations of MOA, particularly as it pertains to modafinil’s effects in addictive disorders.
Are the narcolepsy patients who use modafinil irrational for using a drug based on the results of its clinical trails without an explanation of how it works?
> The meaning of ‘90% of small animal species have eyes’ is that the proportion of small animal species that have eyes is 90%.
Exactly 90%, or not? You say:
> If we had checked every single small animal species then we would be certain of this knowledge. If we had instead checked only a random sample of small animal species then we would have calculated a confidence interval/level for the theory’s truth. We might have found that with our sampling we have a 95% chance that the proportion of small animal species with eyes is within 89-91%.
In the first case, it'd be exactly 90%. In the second case, it wouldn't be. So in the two cases *we would have different knowledge*. We'd be working with a different premise. You want to make a deduction based on a premise but you don't precisely specify what the premise is.
> This is why randomly sampling is important in my view. We are going to sample from various different contexts and therefore with increasing sample size the probability that we would find a context that brings about a fail case grows.
Every context you check has some shared features. There are always infinitely many possible relevant aspects of context that you haven't checked. And you have not done any math to back up your claim about probability. (Doing math related to infinity is hard, not trivial, so you need to actually do the math, not just make naive assumptions.)
> For the sake of this hypothetical argument can we please assume that the samples were actually taken randomly (as best we can), and not biased towards people with weak bones, certain personalities, cultures, locations, etc.
No, reality doesn't work that way. All samples are non-random with regard to some attributes. And you haven't specified a way to randomize any attributes. Having an attribute be non-controlled doesn't make it random.
Random sampling is a problematic concept. Much of what is commonly believed about it is inductivist myth. There is an epistemological issue there. The concept of random sampling omits necessary complexity and detail about what's going on and how science makes progress.
And the broader point is that data never speaks for itself. Correlations and patterns can't guide us. The contrary belief is one of the major inductivist errors.
> Are the narcolepsy patients who use modafinil irrational for using a drug based on the results of its clinical trails without an explanation of how it works?
You're asking multiple things at once. Please try to do one at a time.
> In the first case, it'd be exactly 90%. In the second case, it wouldn't be. So in the two cases *we would have different knowledge*. We'd be working with a different premise. You want to make a deduction based on a premise but you don't precisely specify what the premise is.
Whether we find out our new theory is 90% or 91% likely, the difference is only small. We can assume we have checked all small animal species if you like, in which case it is exactly 90% as you say.
> Every context you check has some shared features. There are always infinitely many possible relevant aspects of context that you haven't checked. And you have not done any math to back up your claim about probability. (Doing math related to infinity is hard, not trivial, so you need to actually do the math, not just make naive assumptions.)
You are right that there could always be a very rare exceptional context that will produce a negative case, so rare that in even a huge number of samples we might never come across it. Even though our knowledge would be strictly speaking false, if the negative cases were as rare as this then it would not prevent us from benefiting from our knowledge which would still lead us right in the majority of cases.
As for the difficulty in the mathematics, thank goodness for the mathematicians! As Peirce puts things (https://en.wikisource.org/wiki/Popular_Science_Monthly/Volume_12/April_1878/Illustrations_of_the_Logic_of_Science_IV):
>>As we cannot have an urn with an infinite number of balls to represent the inexhaustibleness of Nature, let us suppose one with a finite number, each ball being thrown back into the urn after being drawn out, so that there is no exhaustion of them. Suppose one ball out of three is white and the rest black, and that four balls are drawn. Then the table on page 713 represents the relative frequency of the different ways in which these balls might be drawn. It will be seen that if we should judge by these four balls of the proportion in the urn, 32 times out of 81 we should find it 1/4, and 24 times out of 81 we should find it 1/2, the truth being 1/3. To extend this table to high numbers would be great labor, but the mathematicians have found some ingenious ways of reckoning what the numbers would be.
> No, reality doesn't work that way. All samples are non-random with regard to some attributes. And you haven't specified a way to randomize any attributes. Having an attribute be non-controlled doesn't make it random.
Ok, if you can't imagine the possibility of a random sample for the sake of a hypothetical argument, then what about an approximately random sample?
> And the broader point is that data never speaks for itself.
Hear, hear!
> You're asking multiple things at once. Please try to do one at a time.
We can flag it for later.
> Whether we find out our new theory is 90% or 91% likely, the difference is only small. We can assume we have checked all small animal species if you like, in which case it is exactly 90% as you say.
OK, so we've checked every small animal species. What, then, is the purpose of picking a random one (that is, numbering every single species and then using a random number generator) and then saying it has a 90% chance to have eyes, when we already know, in advance, whether or not that species has eyes? We already (by premise) have complete, specific, accurate, non-probabilistic knowledge, which you propose to ignore. This makes no sense to me.
> You are right that there could always be a very rare exceptional context that will produce a negative case
"very rare" defined in what way? Rare in your experience? Your experience may not be representative of e.g. what is common or rare in the universe.
Same issue with "exceptional". You mean an exception in terms of your own past experience? That doesn't tell you what is objectively rare or exceptional. Maybe your experience is unusual and what you view as an exception is actually things getting back to normal.
And, in any case, at every instant of your life infinitely many patterns continued and infinitely many patterns broke. And there are infinitely many patterns that continued in the past which you don't actually expect to continue in the future. The mere fact of a pattern doesn't tell you whether it will continue in the future – it doesn't tell you the cause, and whether the cause is mere coincidence (there are always infinitely many coincidences) or something else. It's only the non-coincidences you expect to continue in the future, and the data alone can't tell you which those are, so you're actually basing your expectations on other *unspecified* reasoning.
> Ok, if you can't imagine the possibility of a random sample for the sake of a hypothetical argument, then what about an approximately random sample?
What approximations are used? Be more specific.
> OK, so we've checked every small animal species. What, then, is the purpose of picking a random one (that is, numbering every single species and then using a random number generator) and then saying it has a 90% chance to have eyes, when we already know, in advance, whether or not that species has eyes? We already (by premise) have complete, specific, accurate, non-probabilistic knowledge, which you propose to ignore. This makes no sense to me.
It is not necessary that we would have kept track of exactly which species have eyes and which don't. Maybe we once had this list but it has been lost, or is difficult to access; spread among hundreds of scarcely reproduced zoology textbooks, etc. We are at the hypothesis stage where we are looking to rule out/in plausible theories without having to commit too many resources in doing so. Knowing that '90% of small animal species have eyes' allows us to achieve this. Once we know our theory is at least plausible, then we can start testing our theory by looking through documentation, going on safari, etc.
> And, in any case, at every instant of your life infinitely many patterns continued and infinitely many patterns broke. And there are infinitely many patterns that continued in the past which you don't actually expect to continue in the future. The mere fact of a pattern doesn't tell you whether it will continue in the future – it doesn't tell you the cause, and whether the cause is mere coincidence (there are always infinitely many coincidences) or something else. It's only the non-coincidences you expect to continue in the future, and the data alone can't tell you which those are, so you're actually basing your expectations on other *unspecified* reasoning.
My claim is not that we come to have knowledge about the world through "data alone". Remember the hypothesis stage we have been discussing, where we can guess a new theory before even looking at the data.
> What approximations are used? Be more specific.
Approximate as in the scientists may have accidentally biased their sampling in favor of certain groups. For example, they may have biased their sampling towards people from higher socioeconomic backgrounds because this group of people had greater access to medical care. However, for this example we cannot be sure what biases may exist in the sample, only that the scientists tried their best to obtain a random sample of the population and it is approximate at best. If it helps maybe you can imagine the scientists drawing names from a hat to determine who will be part of the sample.
I'm really quite surprised that you can't conceive of the possibility of a random sample for a hypothetical argument, yet you can imagine all sorts of fantastical alternative theories (x-fall, etc) when running with your own hypotheticals. Are you sure you cannot reconsider your position on this?
> It is not necessary that we would have kept track of exactly which species have eyes and which don't. Maybe we once had this list but it has been lost, or is difficult to access; spread among hundreds of scarcely reproduced zoology textbooks, etc. We are at the hypothesis stage where we are looking to rule out/in plausible theories without having to commit too many resources in doing so. Knowing that '90% of small animal species have eyes' allows us to achieve this. Once we know our theory is at least plausible, then we can start testing our theory by looking through documentation, going on safari, etc.
Don't you find this all rather unrealistic?
If you lose info about your knowledge, *you no longer know if it's true or not*. You can't answer questions or criticisms, or evaluate proposed improvements, so you have to rebuild the knowledge, not just have *faith* in the conclusions b/c some *authority* told you they were *somehow* proved in the past.
> Approximate as in the scientists may have accidentally biased their sampling in favor of certain groups.
Random sampling doesn't mean unbiased sampling, representative sampling, or non-controlled sampling. Did you actually have in mind any of those things?
You have to do certain things to get random sampling. E.g. if you define a set with 100 elements and number them from 1 to 100 and then roll a 100 sided die, that is a way to randomly select an element from the set. Rolling it until you get 10 unique numbers gets you a random sample of size 10. (There are claims that randomness doesn't exist and e.g. the outcome of a die roll is determined by how you throw it. I think we can set that aside and view dice rolls as random for the sake of argument. Computer PRNGs are not actually random, though.)
Granting something is approximate doesn't specify what is done – what set is sampled or how. And it gives no information about e.g. whether the approximation used has an important systematic bias.
> Are you sure you cannot reconsider your position on this?
I can't disregard detail issues on which major epistemological points depend. I think the flaws with typical views on random sampling and statistics are important, and if you seriously try to work out the details correctly, and raise your standards, instead of assuming the details can be fudged, then I think you will find out about some substantial limitations, caveats, etc.
> If you lose info about your knowledge, *you no longer know if it's true or not*. You can't answer questions or criticisms, or evaluate proposed improvements, so you have to rebuild the knowledge, not just have *faith* in the conclusions b/c some *authority* told you they were *somehow* proved in the past.
I didn't say we lose info about our knowledge. I said we lose information about how we came to have our knowledge.
Having lost the knowledge is just one possibility. Another possibility is that I simply do not remember the details for how this knowledge was arrived at, yet I accept and use the knowledge anyway. An example of this are mathematical theorems which I employ in my problem solving. I can still *know* them without remembering their derivations. Another example is in sports/games where I *know* to make certain plays in certain situations without remembering the explanation as to why it works. I could always seek out and come to understand how it is I came to know something, but that isn't necessary for me to know or use it.
> Random sampling doesn't mean unbiased sampling, representative sampling, or non-controlled sampling. Did you actually have in mind any of those things?
It doesn't? Isn't it a random sample if every case under the general rule had an even chance of being selected? If there is no bias towards any particular case during selection, then isn't the chance even?
> You have to do certain things to get random sampling. E.g. if you define a set with 100 elements and number them from 1 to 100 and then roll a 100 sided die, that is a way to randomly select an element from the set. Rolling it until you get 10 unique numbers gets you a random sample of size 10. (There are claims that randomness doesn't exist and e.g. the outcome of a die roll is determined by how you throw it. I think we can set that aside and view dice rolls as random for the sake of argument. Computer PRNGs are not actually random, though.)
This sounds exactly like what I just said about drawing numbers from a hat. You can imagine the scientists using a large dice instead if you prefer.
> Granting something is approximate doesn't specify what is done – what set is sampled or how. And it gives no information about e.g. whether the approximation used has an important systematic bias.
> I can't disregard detail issues on which major epistemological points depend. I think the flaws with typical views on random sampling and statistics are important, and if you seriously try to work out the details correctly, and raise your standards, instead of assuming the details can be fudged, then I think you will find out about some substantial limitations, caveats, etc.
Is there any reasoning based on the results of a random sample that you will accept? Do you accept any science that draws conclusions from the results of random sampling and confidence intervals/levels?
I'm starting to wonder if it is even possible for their to exist a random sample that you wouldn't take issue with.
> I didn't say we lose info about our knowledge. I said we lose information about how we came to have our knowledge.
You're trying to derive probabilistic knowledge from non-probabilistic knowledge that already has the accurate answer. You're only making things worse. The excuse given seemed to be that we'd lost certain information, but now you deny it.
>> Random sampling doesn't mean unbiased sampling, representative sampling, or non-controlled sampling. Did you actually have in mind any of those things?
> It doesn't? Isn't it a random sample if every case under the general rule had an even chance of being selected? If there is no bias towards any particular case during selection, then isn't the chance even?
Random means random – selecting an element from a set with equal probability for all elements. Random sampling may be a way to achieve other things (means to other ends) but it's not identical to those other things (nor are those other things identical to it).
A non-random sample of all the prime numbered elements of the set could easily be unbiased and representative in some respects.
> Is there any reasoning based on the results of a random sample that you will accept? Do you accept any science that draws conclusions from the results of random sampling and confidence intervals/levels?
"Random samples" are an *imprecise concept*. If you investigate the details you find various limitations. They're useful but misunderstood and not as useful as people believe.
> This sounds exactly like what I just said about drawing numbers from a hat. You can imagine the scientists using a large dice instead if you prefer.
You were talking about random samples regarding medicine. Give details for one of those. You mention drawing names from a hat but haven't given details about how the names are selected and put into the hat, nor whether you expect the results to have any relevance to any person whose name was not put into the hat, nor what you do about people who decline to participate in the study, nor whether the people running the study put their own names into the hat.
> You're trying to derive probabilistic knowledge from non-probabilistic knowledge that already has the accurate answer. You're only making things worse. The excuse given seemed to be that we'd lost certain information, but now you deny it.
You have misunderstood me then. We began with talk of background knowledge about a probability (90% of small animal species have eyes) and you asked me where this knowledge could have come from. I told you it could have come from either sampling *OR* from checking every case. You suggested that if we had checked every case then we would already have the knowledge of the particular species we were interested in. In my response I claimed that it isn’t necessary that we would still have this knowledge, in which case we would not already have “the accurate answer”. I wasn’t giving an excuse when I said we could have lost certain information. I only said it is a *possibility* to explain why we no longer had that knowledge. I have also given other possibilities.
You claim the following.
>If you lose info about your knowledge, *you no longer know if it's true or not*.
You need to clarify this, because as I understand I do not agree. If I take a census of everyone living in my street and calculate that 24% of the residents like country music, I do not suddenly lose this knowledge if I throw the census records in a fire (losing information of what music any particular resident likes). This is analogous to me throwing out records of which particular species have eyes but still knowing that 90% had eyes.
> Random means random – selecting an element from a set with equal probability for all elements. Random sampling may be a way to achieve other things (means to other ends) but it's not identical to those other things (nor are those other things identical to it).
So we agree that every element from the set must have an equal chance of being selected. Yet you seem to think this is not the same as selecting without any “bias towards any particular case”. Why not?
> A non-random sample of all the prime numbered elements of the set could easily be unbiased and representative in some respects.
Could you elaborate on this example? If it is non-random sampling then there must be a disproportionate chance that certain elements of the set will be selected. This is a form of bias.
> "Random samples" are an *imprecise concept*. If you investigate the details you find various limitations. They're useful but misunderstood and not as useful as people believe.
I agree there are limitations, and hence why our knowledge is fallible and requires constant corrections. You seem to have an extreme position against reasoning from random samples, maybe you can elaborate on one of these “various limitations” and explain why your position is justified?
Can you give me an example where you find it useful?
If I’m asking too much, we can flag these questions for another time of course.
> You were talking about random samples regarding medicine. Give details for one of those. You mention drawing names from a hat but haven't given details about how the names are selected and put into the hat, nor whether you expect the results to have any relevance to any person whose name was not put into the hat, nor what you do about people who decline to participate in the study, nor whether the people running the study put their own names into the hat.
Since it is a hypothetical scenario we can do as we please. You just have to use a bit of imagination. We take the names of everyone in the country; we put them in the hat; we draw a random selection from the hat and force everyone whose name has been drawn to participate in the clinical trial.
Regarding the small animals and eyes, can we look at a realistic and useful scenario, instead of a tortured scenario where you keep adding unrealistic elements just to try to make your theory work out? I want to know how people learn in general, with a reasonable example, not a rare special case.
So can you drop the idea of losing our knowledge and present something more typical?
> Could you elaborate on this example? If it is non-random sampling then there must be a disproportionate chance that certain elements of the set will be selected. This is a form of bias.
Consider the human-chosen sample {2,3} from the population {1,2,3,4}. It is not biased regarding the mean – the sample and population means are identical. It's also unbiased and representative regarding the percentage of odd elements.
One can select samples, by human choice and design, which are unbiased and representative regarding particular traits.
> I agree there are limitations, and hence why our knowledge is fallible and requires constant corrections. You seem to have an extreme position against reasoning from random samples, maybe you can elaborate on one of these “various limitations” and explain why your position is justified?
Read about the difficulties of political polling. They are constantly running into limitations of random sampling. Lots of the problems (and what they do about those difficulties, and the downsides of such techniques) are well known.
In general, psychology studies have it no better but are less aware of the problems.
Medical studies have it better because there is limited variation in how our genes create our organs and white blood cells and other medically-relevant biological features. People are far more uniform in terms of various traits medicine cares about (and the variation that exists is more often random with statistically convenient distributions) than in terms of intellectual traits (e.g. regarding politics or psychology). This is a major reason the field of medicine is more effective than the field of psychology – medical scientists are working in an area where poor understanding of random sampling happens to matter less. It's far easier to get a decent sample of livers than of ideas. I know this because I understand a lot about the causal processes that create human livers.
> Since it is a hypothetical scenario we can do as we please. You just have to use a bit of imagination. We take the names of everyone in the country; we put them in the hat; we draw a random selection from the hat and force everyone whose name has been drawn to participate in the clinical trial.
You can imagine that, but no medical studies are ever done in that way. So then you must consider what actual medical studies are like, what their limitations are, and how that changes things compared to the imaginary case.
> I’ve given this same hypothetical question to a number of people and it has proven useful for elucidating different views on the role of evidence in science. You are the first to call into question whether the random sample is really random, or if the drug has a known expiry date, etc.
The overall theme of the discussion is that inductivist thinking falls apart when considered with greater logical rigor. Popper was a more precise and logical thinker than his rivals; they glossed over issues that he did not. Deutsch and Temple are like Popper which is why they are the ones who have continued and expanded on Popper’s work. Other people have largely failed to think of a variety of important points. Peirce, like other inductivists, did not address a variety of key issues (he had the good excuse of writing before Popper).
Kieren talked with non-experts and thinks that is comparable to his discussion with Temple. Why is Temple saying things that they didn’t? Because he’s an expert who knows far more about the field and is far better and logic and precision. Kieren does not acknowledge this.
Kieren ought to be impressed that Temple has knowledge Kieren found nowhere else, but instead presents it like it’s a bad thing, like Temple should lower his standards and accept things which other people accept.
Instead of being impressed by higher standards of rigor, or appreciating them, Kieren seems to view them as *picky or pedantic*. He seems to dislike them rather than value them. (I say that based on what Kieren has said. However, he’s still talking, which is a sign that part of him does value such things.)
Kieren lacks the background knowledge and skillset to be precise, logical or rigorous in the ways Temple thinks are necessary for getting the issues right. Kieren is not attempting to learn that stuff, nor is he giving direct arguments about the topic of rigor (how much is needed, how to quantify it, why that’s enough). So there is actually a major impasse here.
I’d be a bit surprised if Kieren knew how to compare the sizes of the sets of all integers and prime integers, or knows what the middle term is in a syllogism, or a variety of other things like that. Does Kieren know about the moods and figures of deduction? Has he ever studied a book on deduction? It doesn’t appear so. (Does he need to know those things to learn CR? Not necessarily. The issue is he keeps making claims related to them. He keeps bringing them up, himself, as part of his attempts to defend induction! But if you’re going to claim to be doing deduction, you better be able to e.g. specify the form of your argument using variables and show it’s correct in general. When confronted with requests for more rigor, we don’t see Kieren saying “OK, no problem” and doing it, even just to demonstrate it one time, instead he e.g. does the sloppy act of combining two inferences in one without labelling anything.)
These issues are negative (they’re about what’s false) because Kieren keeps making incorrect claims and getting criticism. He doesn’t value that much because his own claims aren’t all that serious anyway. He’s just saying stuff.
Some people are picky in pointless ways, but Temple is specifically highlighting issues that matter to the disagreements between CR thinking and inductivist thinking. There are common ideas about correlations, random sampling, probability, context, etc., which CR disagrees with.
I think this messages comes off too harsh when read conventionally. I think Kieren is *mixed*. There’s good in him too, even related to the very areas where I criticize. But it’s the problems that I talk about because those are what merit action and change.
A lot of what Temple is saying isn't specific to CR. Many of the ideas have been known to various serious, rigorous thinkers. One doesn't need to be a CRist to know, in detail, how deduction works, and have higher standards (basically the same standards used by math) about writing out deductions.
My goal is to add some perspective to the conversation. I hope that will help identify some problems and lead to problem solving action. This isn’t meant as idle commentary. I think these issues have already been causing ongoing discussion friction.
> So can you drop the idea of losing our knowledge and present something more typical?
I feel like I'm doing a lot of catering for your preference of the trivial particulars of my examples. These things don't matter unless you think it is impossible in practice that we could have knowledge of a statistic without still having immediate access to the source data for that statistic? I have already provided a number of alternative examples, and you seem to forget that having checked all of the species is only *one* of the ways we could have come to this knowledge.
Can you please clarify the following claim.
>If you lose info about your knowledge, *you no longer know if it's true or not*.
I don't think it is true and I can't proceed with my argument if you disagree.
> Consider the human-chosen sample {2,3} from the population {1,2,3,4}. It is not biased regarding the mean – the sample and population means are identical. It's also unbiased and representative regarding the percentage of odd elements.
> One can select samples, by human choice and design, which are unbiased and representative regarding particular traits.
Yes, one can do this, but is the sample the result of random/unbiased sampling? No.
When I say we have a random/unbiased sample of some phenomena, I mean we have a sample that is the result of a random/unbiased sampling *method*.
> Read about the difficulties of political polling. They are constantly running into limitations of random sampling. Lots of the problems (and what they do about those difficulties, and the downsides of such techniques) are well known.
> In general, psychology studies have it no better but are less aware of the problems.
> Medical studies have it better because there is limited variation in how our genes create our organs and white blood cells and other medically-relevant biological features. People are far more uniform in terms of various traits medicine cares about (and the variation that exists is more often random with statistically convenient distributions) than in terms of intellectual traits (e.g. regarding politics or psychology). This is a major reason the field of medicine is more effective than the field of psychology – medical scientists are working in an area where poor understanding of random sampling happens to matter less. It's far easier to get a decent sample of livers than of ideas. I know this because I understand a lot about the causal processes that create human livers.
The limitations you have mentioned here are limitations in obtaining a random sample, but not limitation in reasoning from a random sample.
This justifies why you might find (supposed) random samples in some applications (medicine) more trustworthy than other applications (psychology), but it doesn't justify a view opposed to reasoning from a random sample (assuming we actually obtained on).
From what you have said about medicine just now has filled me with hope that you might actually be able to give me an answer to my hypothetical :)
> You can imagine that, but no medical studies are ever done in that way. So then you must consider what actual medical studies are like, what their limitations are, and how that changes things compared to the imaginary case.
Can you imagine it too? it would be akin to you assuming we have an actual random sample to base our reasoning off which is all I ever ask in this hypothetical. I want to see if you allow reasoning from a random sample first, then we can jump into the muddy waters of practical detail if you like.
This is similar to when Popper gives the abstract logical view of his falsification based epistemology with reference to the asymmetry between particular and universal statements, etc, and only after this does he start digging deeper into the practical complications and objections.
> I feel like I'm doing a lot of catering for your preference of the trivial particulars of my examples. These things don't matter unless you think it is impossible in practice that we could have knowledge of a statistic without still having immediate access to the source data for that statistic?
I want a regular, realistic example which is representative of how you think we learn, instead of one (that appears to me) full of contortions to dodge criticism. Do you have one like that?
> is only *one* of the ways we could have come to this knowledge.
Pick *any* *one* way and make a *good* example. I don't want an ambiguous example where you keep changing between alternatives, it should be a specific example.
> >If you lose info about your knowledge, *you no longer know if it's true or not*.
> I don't think it is true and I can't proceed with my argument if you disagree.
It's accurate in general but I agree with you that it's possible to construct exceptions.
> Can you imagine it too? it would be akin to you assuming we have an actual random sample to base our reasoning off which is all I ever ask in this hypothetical. I want to see if you allow reasoning from a random sample first, then we can jump into the muddy waters of practical detail if you like.
OK. So you literally get a list of every person, number them, generate some random numbers, and now you have a genuinely random sample of the human population. And for simplicity no one dies, no one is born, no one refuses to participate in the study, etc. OK. I can imagine that hypothetically. And assume the sample is large enough.
Then *some of* the traits in the sample are likely to be approximately representative of the traits in the population *in some respects*. E.g. the mean height in the sample may be likely (e.g. 99% odds, more with a big enough sample) to be within a small margin of error (e.g. 1%) of the mean height in the population.
Which representations of which traits does this work for? It depends on the statistical distribution of the particular trait in the population, which is related to the causality for it. E.g. this works well with things that have a normal distribution (bell curve). It also generally works well with binary traits (e.g. "Taller than 5.5 feet?"), in which case it's equivalent to sampling marbles from a bag with only red and blue marbles and estimating the proportions.
To know which representations (e.g. mean) of which traits (e.g. height) the sample work for (work = be highly likely to have the same result within some small margin of error), you have to understand the statistical distributions involved, which is generally best done by some understanding of causes. Also, without understanding causes, you can't know what other contexts your results will apply too. E.g. if you don't know whether you're dealing with stuff that changes chaotically over time, then the results might change chaotically (that is, be totally different) 1 second later. So you need that kind of background knowledge and understanding that the mean height of the human population does not have chaotic and sudden changes over short periods of time. If you understand how humans grow (a bit of biology, don't need all the details) and some stuff about physics (that macroscopic objects don't change size in large ways, quickly, in general, that only happens when there is a cause) then you'll know to expect that (barring some exceptional circumstances) the mean height of all humans will not have changed much the day (or even decade) after you did your research. You can add an extra margin of error for change over time which increases the more dated your research gets, but given current understanding of human heights we can expect that error margin to be small. That has to be open to criticism, but I don't know a criticism of it.
#12902 Also this random sampling stuff is for *finite sets*. What I described doesn't apply for infinite sets. That's not a big problem when dealing with physical objects but it is a big problem when dealing with categories of ideas. Idea categories commonly contain infinitely many ideas.
Some of the sampling stuff is basic and well known to educated men of integrity, e.g.:
https://explorable.com/simple-random-sampling
> One of the most obvious limitations of simple random sampling method is its need of a complete list of all the members of the population. Please keep in mind that the list of the population must be complete and up-to-date. This list is usually not available for large populations.
https://research-methodology.net/sampling-in-primary-data-collection/random-sampling/
> However, application of random sampling methods in practice can be quite difficult due to the need for the complete list of relevant population members and a large sample size.
But some educational material on this topic is bad, e.g.:
https://www.verywellmind.com/what-is-a-representative-sample-2795798
> A representative sample is a group that closely matches the characteristics of its population as a whole. In other words, the sample is a fairly accurate reflection of the population from which the sample is drawn.
This ignores the fact that a sample can be representative in one way and unrepresentative in another way, at the same time. E.g. a sample could be representative in terms of gender but not age. They are treating representativeness as if deals with only one dimension instead of many dimensions.
In general, there are infinitely many ways that a sample is representative of the population, as well as infinitely many ways it's unrepresentative.
> I want a regular, realistic example which is representative of how you think we learn, instead of one (that appears to me) full of contortions to dodge criticism. Do you have one like that?
> Pick *any* *one* way and make a *good* example. I don't want an ambiguous example where you keep changing between alternatives, it should be a specific example.
If you don't like the scenario where we learnt the statistic by checking every small animal species, then assume we only know it from checking a sample of small animal species (via induction). I've said it a number of times now that we could have checked all of the cases *OR* just a sample. If you want a more realistic example then assume the latter.
> It's accurate in general but I agree with you that it's possible to construct exceptions.
I would have thought you'd see these exceptions as counter examples that refute your claim, but instead you say it is "accurate in general". Doesn't this fly in the face of your Yes/No philosophy?
When you say "accurate in general", do you mean something like correct 90% of the time? in most cases?
> OK. So you literally get a list of every person, number them, generate some random numbers, and now you have a genuinely random sample of the human population. And for simplicity no one dies, no one is born, no one refuses to participate in the study, etc. OK. I can imagine that hypothetically. And assume the sample is large enough.
You make me so happy Curi :)
> Then *some of* the traits in the sample are likely to be approximately representative of the traits in the population *in some respects*. E.g. the mean height in the sample may be likely (e.g. 99% odds, more with a big enough sample) to be within a small margin of error (e.g. 1%) of the mean height in the population.
> Which representations of which traits does this work for? It depends on the statistical distribution of the particular trait in the population, which is related to the causality for it. E.g. this works well with things that have a normal distribution (bell curve). It also generally works well with binary traits (e.g. "Taller than 5.5 feet?"), in which case it's equivalent to sampling marbles from a bag with only red and blue marbles and estimating the proportions.
> To know which representations (e.g. mean) of which traits (e.g. height) the sample work for (work = be highly likely to have the same result within some small margin of error), you have to understand the statistical distributions involved, which is generally best done by some understanding of causes. Also, without understanding causes, you can't know what other contexts your results will apply too. E.g. if you don't know whether you're dealing with stuff that changes chaotically over time, then the results might change chaotically (that is, be totally different) 1 second later. So you need that kind of background knowledge and understanding that the mean height of the human population does not have chaotic and sudden changes over short periods of time. If you understand how humans grow (a bit of biology, don't need all the details) and some stuff about physics (that macroscopic objects don't change size in large ways, quickly, in general, that only happens when there is a cause) then you'll know to expect that (barring some exceptional circumstances) the mean height of all humans will not have changed much the day (or even decade) after you did your research. You can add an extra margin of error for change over time which increases the more dated your research gets, but given current understanding of human heights we can expect that error margin to be small. That has to be open to criticism, but I don't know a criticism of it.
I think I agree with pretty much everything you have just said. I also think it is an application of our existing knowledge that will tell us if the statistical distribution is such that we can get a representative sample. Do you see it as a deductive argument where we infer a statistical conclusion using the methods you just described? Perhaps you could give an example in syllogistic form?
I think we have just made good progress here.
> If you don't like the scenario where we learnt the statistic by checking every small animal species, then assume we only know it from checking a sample of small animal species (via induction).
If you change it to that, then I will have questions/criticisms about that. I have issues with both alternatives. In the first case, we begin with complete knowledge, and then you propose that we somehow lose that knowledge but retain some summary statistics, so then we can use summary statistics as premises. *That is atypical* and I'm trying to find out how learning works in your system in general, not in rare cases. In the alternative, you propose induction which is problematic both because *how do you randomly sample a set without knowledge of every member of the set* and because *I am trying to ask you how the non-inductive part of learning works*, because it comes first, and you're now introducing induction again for some reason. When I question the induction you've introduced, I predict the following will happen: you will again bring up the non-inductive part of your system, so we'll be going in circles.
> I would have thought you'd see these exceptions as counter examples that refute your claim, but instead you say it is "accurate in general". Doesn't this fly in the face of your Yes/No philosophy?
I was attempting to explain a concept, not write something airtight. The concept is useful for some but not all things. I did not fully specify the limits of applicability. The limits come from how it works – that is, they are implied by understanding the concept (rather than being arbitrary limits which are tacked on to handle criticism). If the concept is understood well enough, including its inherent limits, then I don't think there would be exceptions.
> I think I agree with pretty much everything you have just said. I also think it is an application of our existing knowledge that will tell us if the statistical distribution is such that we can get a representative sample. Do you see it as a deductive argument where we infer a statistical conclusion using the methods you just described? Perhaps you could give an example in syllogistic form?
Deduction is stuff like: http://markmcintire.com/phil/validforms.html
Deduction is equivalent to math and can be computer-checked without inventing AGI.
Deduction is quite limited. I believe you overestimate what can be done with deduction. (This comes up reasonably often. E.g. it came up in my discussion with Robert Spillane found here. From memory, he claimed that arguments about psychiatry and various other issues were deductive. When I asked him to put them into the form of syllogisms, he put them into a form which was not syllogisms. When I pointed that out, he thought I was too picky and soon stopped speaking to me.) It's a common issue that (from my perspective) people have trouble recognizing arguments as not being deductive nor induction (nor abductive) – just regular arguments like you find people using all the time (e.g. lots of what both of us have said here) which don't actually fit any of the categories nicely. CR is totally comfortable with such things (arguments that don't fall into some well-defined, named category) but many other philosophies aren't.
So no I don't think I was using deduction, and I won't attempt to convert what I said into deductive syllogisms. Maybe you'd like to try doing that and see how hard or easy it is and what problems come up.
Or perhaps a good next step would be to begin examining the limits of the representativeness of samples. They always lose information (being a sample instead of the whole) so they are never fully representative. They are equivalent to lossy compression (like h264 or jpg) rather than lossless compression (like zip or png). Trying to understand a population from a sample is like looking at a jpg and seeing compression artifacts – the reconstructed picture makes guesses to fill in the blanks that the smaller data file left out, so it doesn't look the same as the original.
Those are high level issues. I think it helps to examine simple examples. E.g. consider a population of integers: {1, 3, 5000}. In what ways would you expect a random sample of this population (of size 2) to be representative and in what ways unrepresentative? Which possible sample do you think would be the most representative one, and what are some ways it's representative and unrepresentative?
The important fact about this population is it's *nothing like a bell curve*. The same thing can be done with a large population and large sample size. No matter the statistical distribution, samples are always going to be unrepresentative in many ways, but some of the problems and limitations are more apparent (at least to people from our culture who have certain intuitions about samples) with some distributions than others.
#12624
> The induction implied by HTV is deduced as follows.
>
> (1) A HTV theory is one in which each of its concepts is constrained by some past observed phenomena.
> (2) When we reflect back on past observations to see how constrained our concepts are, it is the same as reflecting back to see how well confirmed our concepts are.
> (3) Therefore, every concept involved in a hard to vary theory must have support from past observations.
>
> From this conclusion we see that the HTV criteria is really a requirement of support for the concepts employed by our theories. The harder to vary, the more support, the better the theory is for our acceptance. This is induction.
"Constrained" isn't the same as "supported".
Also, as explained by DD in chapter 2 of BoI, an observation is a guess about some set of events. For example, you might expose a photographic plate to light from the night sky and guess about what the plate is showing when it's developed. It's easy and common to make mistakes when trying to understand observations. You can't use them to support anything.
#12917
> If you change it to that, then I will have questions/criticisms about that. I have issues with both alternatives. In the first case, we begin with complete knowledge, and then you propose that we somehow lose that knowledge but retain some summary statistics, so then we can use summary statistics as premises. *That is atypical* and I'm trying to find out how learning works in your system in general, not in rare cases. In the alternative, you propose induction which is problematic both because *how do you randomly sample a set without knowledge of every member of the set* and because *I am trying to ask you how the non-inductive part of learning works*, because it comes first, and you're now introducing induction again for some reason. When I question the induction you've introduced, I predict the following will happen: you will again bring up the non-inductive part of your system, so we'll be going in circles.
I’ve provided details of the non-inductive part; the hypothesis stage. We start by conjecturing a new theory (SNB have eyes), and then through deductive application of our existing background knowledge (most small animal species have eyes) we can come to determine whether our theory is any good. Talk of induction has only comes up because you asked me how it is that we formed our background knowledge (without checking all cases). So if you want to continue discussing the hypothesis stage without reference to induction then you will need to assume we have some existing background knowledge. Otherwise we will need to discuss the inductive stage that was involved in creating the background knowledge.
> So no I don't think I was using deduction, and I won't attempt to convert what I said into deductive syllogisms. Maybe you'd like to try doing that and see how hard or easy it is and what problems come up.
I wouldn’t try and put it into a deductive argument because I see it as an inductive argument instead. Since you reject induction I figured you might instead proceed deductively, but it seems that is not the case. I’ve assumed that most arguments can be put into deductive, inductive, and abductive form, but I am also tempted to the view that there may be arguments which fit no such categories. Maybe this is getting off topic, but you mention that such category defying arguments are commonplace, and that we have made such arguments in our discussion so far; can you provide an example?
> If you understand how humans grow (a bit of biology, don't need all the details) and some stuff about physics (that macroscopic objects don't change size in large ways, quickly, in general, that only happens when there is a cause) then you'll know to expect that (barring some exceptional circumstances) the mean height of all humans will not have changed much the day (or even decade) after you did your research.
Above is an instance where I imagine some amount of induction is required.
Why should we allow our background knowledge; “macroscopic objects don't change size in large ways, quickly, in general”, to influence our future expectations if all we know is that it has been successful in the past? Do you refute all of the other possible futures?
> Those are high level issues. I think it helps to examine simple examples. E.g. consider a population of integers: {1, 3, 5000}. In what ways would you expect a random sample of this population (of size 2) to be representative and in what ways unrepresentative? Which possible sample do you think would be the most representative one, and what are some ways it's representative and unrepresentative?
Pick any characteristic you want. Since the sample/population sizes are small, we can easily check all possible cases and see how well our reasoning would lead us. For example:
If we choose ‘numbers greater than 5000’ (true proportion = 0%) or ‘non-negative numbers’ (true proportion = 100%), we would find that such a sample would lead us to the true proportion ~100% of the time for both cases.
If we choose ‘numbers containing the digit 3’ (true proportion ~ 33%) or ‘odd numbers’ (true proportion ~66%), we find that such a sample would lead us to the true proportion ~66% of the time for both cases.
So in the worst case our reasoning would only lead us wrong in only 33% of samples.
I think Peirce provides a better example to be considered:
>>As we cannot have an urn with an infinite number of balls to represent the inexhaustibleness of Nature, let us suppose one with a finite number, each ball being thrown back into the urn after being drawn out, so that there is no exhaustion of them. Suppose one ball out of three is white and the rest black, and that four balls are drawn. Then the table on page 713 represents the relative frequency of the different ways in which these balls might be drawn. It will be seen that if we should judge by these four balls of the proportion in the urn, 32 times out of 81 we should find it 1/4, and 24 times out of 81 we should find it 1/2, the truth being 1/3. To extend this table to high numbers would be great labor, but the mathematicians have found some ingenious ways of reckoning what the numbers would be.
> The important fact about this population is it's *nothing like a bell curve*. The same thing can be done with a large population and large sample size. No matter the statistical distribution, samples are always going to be unrepresentative in many ways, but some of the problems and limitations are more apparent (at least to people from our culture who have certain intuitions about samples) with some distributions than others.
In “The Order of Nature”, Peirce gives a logical demonstration that any group of objects can be shown to agree fully in at least one way, and to disagree entirely in at least one other way. I think you have made the same point.
Important to Peirce was the idea that the character/attribute we are interested in should be selected before we begin sampling instead of selecting a character based on its prevalence in the sample (after the sample has been obtained). The latter case invalidates our reasoning. This is what I have in mind when I make the point that we must have a hypothesis before we can proceed with our induction, because it is the hypothesis which provides the character that we are interested.
Relevant Peirce below.
>>In the last of these papers we examined the nature of inductive or synthetic reasoning. We found it to be a process of sampling. A number of specimens of a class are taken, not by selection within that class, but at random. These specimens will agree in a great number of respects. If, now, it were likely that a second lot would agree with the first in the majority of these respects, we might base on this consideration an inference in regard to any one of these characters. But such an inference would neither be of the nature of induction, nor would it (except in special cases) be valid, because the vast majority of points of agreement in the first sample drawn would generally be entirely accidental, as well as insignificant. To illustrate this, I take the ages at death of the first five poets given in Wheeler's "Biographical Dictionary." They are:
>>Aagard, 48.
>>Abeille, 70.
>>Abulola, 84.
>>Abunowas, 48.
>>Accords, 45.
>>These five ages have the following characters in common:
>>1. The difference of the two digits composing the number, divided by three, leaves a remainder of one.
>>2. The first digit raised to the power indicated by the second, and divided by three, leaves a remainder of one.
>>3. The sum of the prime factors of each age, including one, is divisible by three.
>>It is easy to see that the number of accidental agreements of this sort would be quite endless. But suppose that, instead of considering a character because of its prevalence in the sample, we designate a character before taking the sample, selecting it for its importance, obviousness, or other point of interest. Then two considerable samples drawn at random are extremely likely to agree approximately in regard to the proportion of occurrences of a character so chosen. The inference that a previously designated character has nearly the same frequency of occurrence in the whole of a class that it has in a sample drawn at random out of that class is induction. If the character be not previously designated, then a sample in which it is found to be prevalent can only serve to suggest that it may be prevalent in the whole class. We may consider this surmise as an inference if we please—an inference of possibility; but a second sample must be drawn to test the question of whether the character actually is prevalent.
> I’ve provided details of the non-inductive part; the hypothesis stage. We start by conjecturing a new theory (SNB have eyes), and then through deductive application of our existing background knowledge (most small animal species have eyes) we can come to determine whether our theory is any good.
And then I asked for details about one of the things you introduced in your explanation (that background knowledge) and you still have not provided those details. To reason from an auxiliary premise you must detail what that auxiliary premise says, it’s nature, etc. You haven’t done that even though your example as a whole depends on those details. Did begin doing it, but didn’t want to deal with critical scrutiny in detail because you didn’t think it mattered and had alternatives anyway.
Can you give an example that does not rely on any pre-existing inductive knowledge, and which has nothing to do with induction? I think that would be better. Otherwise, can you try again to clarify what is deduced from what, beginning by giving the form of the argument using only variables, and then giving the full, topical version using only *unambiguous* premises?
> Why should we allow our background knowledge; “macroscopic objects don't change size in large ways, quickly, in general”, to influence our future expectations if all we know is that it has been successful in the past? Do you refute all of the other possible futures?
Dealing with this follows the standard CR pattern: guesses and criticism. You use guesses and criticism to consider in what ways the future does and does not relate to the past. Induction may have a monopoly on believing the future resembles the past, generically, without specifying in which ways, and treating that as assumption to be taken on faith. But induction has no monopoly on relating the future and the past at all.
And our understanding of objects says how they behave over time. Worrying that things will act arbitrarily differently in the future is no different than worrying they will exact arbitrarily differently at different locations or while held by a person with a particular tatoo design.
We have understandings of things like macroscopic motion of objects (inertia, gravity, friction, acceleration, etc). This understanding says the behavior depends on certain contextual elements (e.g. gravity would be stronger a planet with greater mass) but not others (time, location, observer height, observer’s wishes, etc.) We also have microscopic understanding of things like temperature, the structure of atoms, what makes atoms stable, how atoms combine into larger structures, etc. This understanding also specifies, as parts of its explanation, what factors are relevant and irrelevant (what does and doesn’t affect these things). How time matters is addressed extensively. Time does not matter, according to our prevailing physics explanations, in a way along the lines of e.g. “after date D, the rules change and gravity repels things instead of attracting them and there is friction in vacuums and microscopic stuff no longer jiggles and temperature no longer exists”.
> So in the worst case our reasoning would only lead us wrong in only 33% of samples.
>
> I think Peirce provides a better example to be considered:
There are worse cases, e.g. there are no samples for which the mean matches the population mean. That’s why I picked these numbers – because they are not similar to a bell curve. Your comments didn’t cover that issue. I am making points other than the ones Peirce made in the quotes.
Peirce claims:
>>> It is easy to see that the number of accidental agreements of this sort would be quite endless. But suppose that, instead of considering a character because of its prevalence in the sample, we designate a character before taking the sample, selecting it for its importance, obviousness, or other point of interest. Then two considerable samples drawn at random are extremely likely to agree approximately in regard to the proportion of occurrences of a character so chosen.
I agree with the first sentence. But I don’t think choosing characteristics in advance solves the problem. E.g. if I choose “mean” in advance, there are many populations where random samples are not actually likely to have a similar mean to the population mean.
I imagine I’m supposed to make advance choices for reasons, not arbitrarily hoping to get lucky. So guidance for how to do that would be needed.
However, I notice Peirce is only talking there about proportions of occurrences. Is your concept for samples only to be representative in terms of proportions of occurrences, but nothing else? Forget means, medians, modes, standard deviations, and many other things like e.g. “Is this data compatible with a universe in which ‘3’ doesn’t exist?” If you dramatically limit in what ways data samples are analyzed then you may be able to avoid some problems while also losing lots of tools and methods which are in widespread use today. Is that your intention? If so, I think it would have made sense to explicitly state it upfront as an important part of your system.
And if that's the idea, what about populations with lots of uniqueness? E.g. the characteristic we might be interested in is color, and we might be dealing with a population where every object has a unique color (unique at the level of precision we care about). How will you productively deal with this matter when only considering e.g. “What proportion of this sample is purple?” when the whole population has at most one purple object.
Regular Arguments
kieren wrote:
> Maybe this is getting off topic, but you mention that such category defying arguments are commonplace, and that we have made such arguments in our discussion so far; can you provide an example?
I use regular arguments in #12946 . By regular I mean not deduction nor induction. I don’t think it uses abduction either, but I don’t think the term “abduction” is well-defined so it’s hard to comment on that. Here's an example section with regular arguments:
> And then I asked for details about one of the things you introduced in your explanation (that background knowledge) and you still have not provided those details. To reason from an auxiliary premise you must detail what that auxiliary premise says, it’s nature, etc. You haven’t done that even though your example as a whole depends on those details. [You did] begin doing it, but didn’t want to deal with critical scrutiny in detail because you didn’t think it mattered and had alternatives anyway.
>
> Can you give an example that does not rely on any pre-existing inductive knowledge, and which has nothing to do with induction? I think that would be better. Otherwise, can you try again to clarify what is deduced from what, beginning by giving the form of the argument using only variables, and then giving the full, topical version using only *unambiguous* premises?
Similarly, you used regular arguments in this paragraph (the one my two paragraph quote was replying to):
> I’ve provided details of the non-inductive part; the hypothesis stage. We start by conjecturing a new theory (SNB have eyes), and then through deductive application of our existing background knowledge (most small animal species have eyes) we can come to determine whether our theory is any good. Talk of induction has only comes up because you asked me how it is that we formed our background knowledge (without checking all cases). So if you want to continue discussing the hypothesis stage without reference to induction then you will need to assume we have some existing background knowledge. Otherwise we will need to discuss the inductive stage that was involved in creating the background knowledge.
Typical regular argument example:
> Rent control is bad because it makes it harder for young people to get homes and they are our future.
This is an incomplete, mediocre argument. It’s kinda vague. Nevertheless, it is an argument with some content. It’s not nothing. And it’s not deduction nor induction.
The majority of arguments build on prior knowledge rather than dealing directly with observations or how a learning system gets started from zero or near-zero knowledge (e.g. whatever it is that babies do). If it doesn’t deal directly with observations, it’s not induction (not all arguments dealing directly with observations are induction, but all inductions deal directly with observations – I’m guessing you’ll agree with that).
As to deduction, it’s very limited. It’s stuff like http://markmcintire.com/phil/validforms.html and modus ponens and some math with logic operators. Most arguments simply don’t use or mention such things. If you read a textbook on deductive logic and then go read 20 political arguments online, you’ll find the articles try to argue a bunch of points but are not using the deductive methods from the textbook (it wouldn’t surprise me of the 20 articles contained zero deductive arguments, though you might find some, especially if you read between the lines a lot).
Many people claim that the issue here is informal writing, and that all the arguments are either incorrect *or* else can be written in a more precise way which would be deduction. I don’t think so and have never seen anyone successfully do this informal-to-deduction translation in any substantial real-world case (e.g. with the arguments in Szasz’s book *The Myth of Mental Illness*, which is the example where Robert Spillane quickly gave up despite being a Szasz friend/fan/colleague and believing the book’s arguments are great, so he didn’t have the excuse of saying the problem is that the arguments are incorrect). If such translations were possible in general, one would expect academics to already have done them (or just argued with pure deduction in the first place) about some important, controversial topics like quantum physics, politics, psychology, etc., but I don't think that exists. I think the excuse for it not existing is you need induction too, but I'm unaware of any book in those fields where every argument is rigorously labelled as either induction or deduction and is careful to clearly follow the methods for that type of argument.
#12946
> And then I asked for details about one of the things you introduced in your explanation (that background knowledge) and you still have not provided those details. To reason from an auxiliary premise you must detail what that auxiliary premise says, it’s nature, etc. You haven’t done that even though your example as a whole depends on those details. Did begin doing it, but didn’t want to deal with critical scrutiny in detail because you didn’t think it mattered and had alternatives anyway.
> Can you give an example that does not rely on any pre-existing inductive knowledge, and which has nothing to do with induction? I think that would be better. Otherwise, can you try again to clarify what is deduced from what, beginning by giving the form of the argument using only variables, and then giving the full, topical version using only *unambiguous* premises?
So the premise is ‘90% of small animal species have eyes’. What details could make this clearer? If you want to know how we came to accept this knowledge then I can’t do so without us either assuming we at some stage checked every case, or talking about induction.
It’s hard for me to give an example without relying on existing knowledge, because I don’t think that is ever the case. Maybe you come across pain for the first time and you conjecture something as simple as ‘falling causes pain’, but I imagine we could always show how some sort of instinctual knowledge of physical objects, the self, time, etc is being invoked.
> Dealing with this follows the standard CR pattern: guesses and criticism. You use guesses and criticism to consider in what ways the future does and does not relate to the past. Induction may have a monopoly on believing the future resembles the past, generically, without specifying in which ways, and treating that as assumption to be taken on faith. But induction has no monopoly on relating the future and the past at all.
> And our understanding of objects says how they behave over time. Worrying that things will act arbitrarily differently in the future is no different than worrying they will exact arbitrarily differently at different locations or while held by a person with a particular tatoo design.
> Time does not matter, according to our prevailing physics explanations, in a way along the lines of e.g. “after date D, the rules change and gravity repels things instead of attracting them and there is friction in vacuums and microscopic stuff no longer jiggles and temperature no longer exists”.
Say we guess that the laws of physics are such that we will float down safely to ground floor if we jump out the window tomorrow instead of taking the elevator. How would you criticize this?
Do we refute it because we have an understanding that the laws of physics are not arbitrarily dependent on time/people/locations like this?
>> So in the worst case our reasoning would only lead us wrong in only 33% of samples.
>>
>> I think Peirce provides a better example to be considered:
> There are worse cases, e.g. there are no samples for which the mean matches the population mean. That’s why I picked these numbers – because they are not similar to a bell curve. Your comments didn’t cover that issue. I am making points other than the ones Peirce made in the quotes.
> Peirce claims:
>>>> It is easy to see that the number of accidental agreements of this sort would be quite endless. But suppose that, instead of considering a character because of its prevalence in the sample, we designate a character before taking the sample, selecting it for its importance, obviousness, or other point of interest. Then two considerable samples drawn at random are extremely likely to agree approximately in regard to the proportion of occurrences of a character so chosen.
> I agree with the first sentence. But I don’t think choosing characteristics in advance solves the problem. E.g. if I choose “mean” in advance, there are many populations where random samples are not actually likely to have a similar mean to the population mean.
> I imagine I’m supposed to make advance choices for reasons, not arbitrarily hoping to get lucky. So guidance for how to do that would be needed.
> However, I notice Peirce is only talking there about proportions of occurrences. Is your concept for samples only to be representative in terms of proportions of occurrences, but nothing else? Forget means, medians, modes, standard deviations, and many other things like e.g. “Is this data compatible with a universe in which ‘3’ doesn’t exist?” If you dramatically limit in what ways data samples are analyzed then you may be able to avoid some problems while also losing lots of tools and methods which are in widespread use today. Is that your intention? If so, I think it would have made sense to explicitly state it upfront as an important part of your system.
> And if that's the idea, what about populations with lots of uniqueness? E.g. the characteristic we might be interested in is color, and we might be dealing with a population where every object has a unique color (unique at the level of precision we care about). How will you productively deal with this matter when only considering e.g. “What proportion of this sample is purple?” when the whole population has at most one purple object.
You are right that Peirce’s induction is based on the proportion of occurrences. I see your point that if we want to consider other population parameters such as the mean, standard deviation, etc, then we will need to make more assumptions than just random sampling. As per your example, we have to assume the population distribution is a certain way (normal) to calculate the mean for small sample sizes. We don’t have to discard these other statistical measures because they require additional assumptions. What we can do is consider the mean as a mathematical deduction from certain premises (of particular interest; the premise that the distribution is normal). These premises are either supported by our existing knowledge or they are conjectures that we can test and infer inductively. Deductive support might come from our knowledge that the phenomena we are sampling is one of a class of phenomena that exhibits a normal distribution. Support for a normal distribution by induction would involve obtaining samples of the population and checking for normality. We could do this by graphing our samples and checking for a bell curve. This checking would involve finding the proportion of samples that fit a normal distribution. So what we get is our contemporary statistical measures depending on premises which are checked using Peirce’s proportional success measure.
> So the premise is ‘90% of small animal species have eyes’. What details could make this clearer?
For example the detail of whether that is exactly or approximately 90%. And the detail of what constitutes a "small animal species", how is that defined.
> It’s hard for me to give an example without relying on existing knowledge, because I don’t think that is ever the case.
I think you misread. The issue was pre-existing *inductive* knowledge, not any kind. You could avoid that by e.g. referring to inborn knowledge or by using a non-empirical topic like moral philosophy or epistemology.
> Say we guess that the laws of physics are such that we will float down safely to ground floor if we jump out the window tomorrow instead of taking the elevator. How would you criticize this?
> Do we refute it because we have an understanding that the laws of physics are not arbitrarily dependent on time/people/locations like this?
Yes. The prevailing (currently non-refuted in debates, IMO) explanations of physics specify what factors are relevant and why, and they say time is not relevant for this, gravity functions the same at different times but differently (e.g. stronger) for different amounts of mass.
Explanations say what matter or not and those explanations are evaluated with critical debate.
If someone wants to propose a guess which is contrary to prevailing explanations (existing knowledge) then he needs to add something to the state of the debate. Give some criticism of the existing knowledge. If he has no criticism of the existing knowledge, but the existing knowledge does already have a criticism of his new guess, then that's asymmetric against the guess.
> Support for a normal distribution by induction would involve obtaining samples of the population and checking for normality.
But that will only work for some statistical distributions and not others. You're proposing a statistical test for distribution type, the effectiveness of which itself depends on distribution type. E.g. this approach won't work well for a distribution where most data points fit a bell curve and also there are a small number of positive outliers which are *way* above the mean.
> We could do this by graphing our samples and checking for a bell curve.
FYI you can check that mathematically a lot better than by eyeballing a graph. Eyeballing a graph is good as a first approximation and helps give you an idea of which math tests to try (like you can see it looks like it might be a bell curve, then use math tests for whether it is a bell curve).
> You are right that Peirce’s induction is based on the proportion of occurrences.
OK so has anyone worked out how limiting that is, or how much can or can't be done with that? Did Peirce write anything about this limit and its consequences? It seems to disallow a lot of stuff that people try to use induction for.
Has anyone *already* tried to extend Peirce's approach to include e.g. means, or noticed this issue before? Cuz I think extending a system in a major way merits major deliberation and research, not a few quick comments.
To a first approximation, I read it as "only use 'induction' in the tiny minority of cases where certain statistical techniques work, and define 'induction' as referring only to those statistical techniques which are similar to those used for guessing the number of blue marbles in an urn known to contain only red and blue marbles and from which we've randomly drawn a sample of marbles and know the total number of marbles." That looks to me like it might be an anti-inductivist position which rejects what ~all other inductivists are currently doing and claiming. It might be so limited that Popper would say "hey that is not what anyone means by 'induction'" rather than claiming to have refuted it. Popper (and me and DD) was not against basic statistics used in appropriate scenarios like randomly pulling colored marbles from urns and scenarios equivalent to that. But I'm not yet very clear on how limited this Peirce system is without extending it.
i wrote the below to think through some of the Peirce stuff b/c the "proportions of occurrences *only*" idea was not familiar to me.
# Peirce’s Proportions of Occurrences “Induction”
Requires random samples. This generally requires being able to generate random integers, a finite population size, well-defined population elements (easy with marbles, harder with liquids), and knowledge of the population (e.g. a list of every population member). Sometimes knowledge of the population may be different, e.g. a person fills a bag with marbles and you don’t look in the bag, so you don’t know how many there are, but he told you it has some number of marbles which are all red or blue.
Random sampling of marbles can be done with or without replacement (meaning: do you put each marble back before pulling out another one?). This changes the math a bit. Also not knowing the number of marbles in the population prevents you from doing confidence estimates or knowing how big a sample you need.
Pierce’s idea is roughly: only use statistical methods in regards to scenarios equivalent to pulling random colored marbles from a bag and estimating what proportions in the population have each color. I believe this works OK with more than two colors. I think the number of colors should be much lower than the sample size.
How do you get this kind of scenario in the wild, as a scientist? Suppose you have a factory that produces widgets and you’re sampling the output for quality control purposes. You could define a particular batch of widgets to be the population, e.g. the 5000 produced today, and then sample 300 of them. Then see what proportion are defective by some well-defined criteria for defectiveness. This would not logically (deductively) imply anything about tomorrow’s production but could be used in critical arguments that dealt with explanations. This is standard use of statistics which is used within CR. This is not induction. If you say “assume the future with resemble the past. therefore it is likely that a similar proportion will be defective tomorrow.” then you’d be an inductivist. That is a poor argument and we can do better.
If you don’t know the exact population size, but you know it’s within 1% of 5000, that may be good enough.
Proportions of occurrences only deals with categories. It can’t deal with a trait like height. But it can deal with e.g. “height under 5 ft; height 5 to 6 ft; height over 6 feet”. Then there are just 3 categories instead of everyone having a unique height. It can also deal with height rounded to the nearest inch, in which case human beings will fall into around 100 separate categories.
Similarly for color, you have to define things like the “red marble category” so that many marbles fall into the same category. You have to define a range of colors and treat that range as all one type of marble. Rounding does this implicitly because it maps a whole range to a particular value (everything that rounds to a specific value is one category).
So suppose I want to know if the sun will rise tomorrow. I define all motions of the sun during particular hours into two categories, “rise” or “not rise”. Then I select a random sample of days from the big bang. Then I discover our historical records are incomplete and give up. If I just looked at the last 50,000 days that would not be a random sample.
So let’s define the population as the last 50,000 days and randomly sample 1000 days from that and check if the sun rose. (We number all the days and then generate random integers from 1-50,000 until we get 1000 unique ones. Alternatively we could do the later integer generations in a way that can’t repeat. Alternatively we could allow repeats, which changes the confidence math a bit (lowers confidence; means a little larger sample size is needed for the same results).) And we find the sun rose 100% of the time in the sample. That’s pointless because I already know what the data is like in the entire population. But, OK, what would it tell us? That if we sampled more days from that population we’d be likely to get a similar proportion of rise to non-rise. And that we can guess the proportion in the whole population is likely to be the same within some error bounds.
Does that tell us anything about whether the sun will rise tomorrow? Not directly or logically, because tomorrow was not in the population of days that we sampled from. So how can we know anything about tomorrow? By critical argument, not by statistics. Statistics just help us deal with datasets a bit which gives us some premises to work with in our arguments. The sun rising proportion in the last 50,000 days could be brought up in an argument about what will happen tomorrow. What (if anything) it means depends on what arguments are able to argue that it means. These arguments are neither deduction nor induction and they totally govern the meaning of our data and also of mathematical functions of our data (which is just our data presented in a different form). It’s not a function of just our data though, it also relies on some premises about our knowledge of the population and about our sampling. That’s how all data works though. When you measure the position of something, you rely on premises about your knowledge of how your measuring instrument works, it’s not just pure data. There is always some theory (ideas) mixed in.
What would the arguments look like? E.g. “Why do you expect the sun rising proportion to be different in the next 500 days than it was in the last 50,000 days? Is there any reason? Do you have any explanation for what you think will happen and why? If you give me details of that, I can attempt to criticize it and/or change my mind. I think the sun is, in that timeframe, regular and one of the things that will do similar behavior over time rather than acting chaotically (in regards to rising behavior, as defined previously, not all behaviors). Do you have any criticism of this belief? Did you find some problem with it? I think it is implied by the prevailing understanding of physics combined with our observations of our sun that give us some knowledge of what type of physical object it is. Do you have a criticism of the prevailing understanding of physics? Do you have a criticism of our observations of our sun and categorization of it as a particular type of star with various traits like approximate size, approximate distance from Earth, and approximate current chemical makeup (like amount of hydrogen and helium)? Do you have a criticism of my epistemology? Do you think all the theory and data are fine but a mathematical error was made when doing calculations about the sun? If so, we can debate any of those topics. If not, what do you take issue with?” None of that is induction nor deduction. It’s also, IMO, not the best way to argue about the sun – I think randomly sampling past days is an inelegant, unnecessary complication. But for the sake of example, you can involve that sampling and still win the debate with a guy who expects the sun not to rise tomorrow, it’s not wrong (there are often many ways to argue the same point and still get the correct answer).
Does limiting the statistics to only proportions of occurrences get rid of the need to know anything in advance about the population distribution? Not entirely. You need to know the categories you’re using cover the population. This can be pretty easy, e.g. you could have 5 categories based on mass, and they could cover all masses (cuz the top categories is anything above X and the bottom category is anything below Y and the 3 in the middle don’t leave any masses out btwn X and Y). You need to advance knowledge that the population has physical objects with masses and that an object has exactly one mass and that the mass won’t change (much) during the sampling and measuring time period. You need some auxiliary premises. That ruins pure induction approaches but it’s fine. As far as the statistical distribution, as long as you know everything fits in e.g. 5 categories then I don’t think you care. I think that matters to means but not to proportions in categories. I think proportions in categories are limited and simple enough to be ok given sample size is much larger than number of categories. (If you had e.g. 100 marbles with unique colors then sampled 10, you would estimate those 10 colors were each 10% of the population, and you’d be wrong. But if there are only 3 colors you won’t have that problem, it’ll work way better.)) You have to define the categories in addition to defining the population and random sampling methods. Then your sample is representative with regard to the defined categories that have the right properties.
Defining extra categories after having the sample can lead to bias, e.g. you could define specific mass ranges for marbles based on what marbles are in your sample. Defining the categories beforehand is one technique, of many, that can help avoid bias. In general it’s highly inadequate alone.
Summary: Calling carefully limited statistical methods “induction” does not have anything to do with the philosophical tradition of induction, and those methods are OK.
A standard thing inductivists do (not accusing Peirce, just speaking generally) is define some carefully limited thing (so it’s not wrong and survives criticism) and then also, at other times, make large ad hoc extensions to it – they define one thing to defend in argument but use another in practice.
#12978
> For example the detail of whether that is exactly or approximately 90%. And the detail of what constitutes a "small animal species", how is that defined.
I don’t think it matters for this example whether it is exact or approximate because this background knowledge is only being used to deem our knowledge as probable/acceptable. Since we can’t have certain knowledge about the world, assume it is approximately 90%.
A “small animal species” could be defined as any animal species whose average weight is less than 30Kg. I think this is just another irrelevant detail that will distract us though. It doesn’t really matter for the example.
> I think you misread. The issue was pre-existing *inductive* knowledge, not any kind. You could avoid that by e.g. referring to inborn knowledge or by using a non-empirical topic like moral philosophy or epistemology.
Sure, but I really don’t think it's necessary to provide such an example. All I’ve essentially been trying to say is that we consider new conjectures under the lights of our existing background knowledge before we move on to experimental testing. I don’t think this should be so so troubling that we cannot move on in our discussion.
An example would be something like supporting the conjecture “I’m happy when eating ice cream” based on my memories of happily eating ice cream, and therefore my *instinctive* identification of experiences which I regard as memories of past experience.
>> Say we guess that the laws of physics are such that we will float down safely to ground floor if we jump out the window tomorrow instead of taking the elevator. How would you criticize this?
>> Do we refute it because we have an understanding that the laws of physics are not arbitrarily dependent on time/people/locations like this?
> Yes. The prevailing (currently non-refuted in debates, IMO) explanations of physics specify what factors are relevant and why, and they say time is not relevant for this, gravity functions the same at different times but differently (e.g. stronger) for different amounts of mass.
> Explanations say what matter or not and those explanations are evaluated with critical debate.
> If someone wants to propose a guess which is contrary to prevailing explanations (existing knowledge) then he needs to add something to the state of the debate. Give some criticism of the existing knowledge. If he has no criticism of the existing knowledge, but the existing knowledge does already have a criticism of his new guess, then that's asymmetric against the guess.
Say our currently non-refuted theory says that the mechanics of gravity is independent of time (now and in the future), but my new conjecture says that the mechanics of gravity, whilst appearing independent of time in the past, are really dependent on time starting tomorrow. So here we have two theories consistent with what they say about the past, but differing in their future predictions.
If you want to criticize my new guess because it contradicts the current guess, then I can also criticize your current guess because it contradicts my new guess. This is a symmetry.
You need a method for deciding between such cases, but you must not rely on induction (if you want to maintain the position that we never use it).
> But that will only work for some statistical distributions and not others. You're proposing a statistical test for distribution type, the effectiveness of which itself depends on distribution type. E.g. this approach won't work well for a distribution where most data points fit a bell curve and also there are a small number of positive outliers which are *way* above the mean.
Induction may lead us to conclude that every human with a certain gene grows to be taller than 6ft, but unknown to us in some small pocket of the world there exists a small group of outliers; exceptional cases of people with this gene who grew no taller than 5ft. Admitting the possibility of *exceptional* cases implies that our knowledge will still lead us right in the majority of typical cases (to our benefit). When we do come across the exceptional cases (if ever) then our knowledge can be corrected at this point by guessing anew and with new/updated inductions. The process is self correcting with new data and new guesses.
Similarly, if the parameter (e.g. mean) we are trying to obtain does depend on the distribution (FYI, the distribution of the sample mean approaches normality with greater sample size irrespective of underlying population distribution) and we guess it (the distribution) incorrectly, then we can find (with an induction) that our distribution isn’t correct. We can discover this because the distribution tells us the assumed probability distribution of a parameter and our inductions tell us the probability of certain values of this parameter found through testing. A mismatch between the probabilities we find inductively and the probabilities expected from our assumed distribution allow us to reject it. After guessing a new distribution we can come to determine (with another induction) that it is a better fitting distribution. Again, there is the possibility for error correction. It is a mistake for anti-inductivists to believe that induction must work in every case for it to be valid.
If we are approaching a new phenomena for the first time we might start by assuming normality and then later check this assumption. We may choose normality because it has been the most common distribution found in the past. This knowledge (e.g. 90% of studied phenomena has been normally distributed) is the result of another induction.
> OK so has anyone worked out how limiting that is, or how much can or can't be done with that? Did Peirce write anything about this limit and its consequences? It seems to disallow a lot of stuff that people try to use induction for.
> Has anyone *already* tried to extend Peirce's approach to include e.g. means, or noticed this issue before? Cuz I think extending a system in a major way merits major deliberation and research, not a few quick comments.
After re-reading some Peirce I’m not so sure we can say he has limited himself to proportion of occurrences. It may be more accurate to say he has *focused* on proportion of occurrences since his focus was on probability (relative frequency) because we also see quotes like the following.
>>Such average statistical numbers as the number of inhabitants per square mile, the average number of deaths per week, the number of convictions per indictment, or, generally speaking, the number of x's per y, where the x's are a class of things some or all of which are connected with another class of things, their y's, I term relative numbers. Of the two classes of things to which a relative number refers, that one of which it is a number may be called its relate, and that one per which the numeration is made may be called its correlate.
>>Probability is a kind of relative number; namely, it is the ratio of the number of arguments of a certain genus which carry truth with them to the total number of arguments of that genus, and the rules for the calculation of probabilities are very easily derived from this consideration. They may all be given here, since they are extremely simple, and it is sometimes convenient to know something of the elementary rules of calculation of chances.
AND
>>In such a noumenal world, there is no room for probability. For what is probability? It is primarily an attribute of an argument or inference belonging to a class of inferences which from true premises sometimes lead to true and sometimes to false conclusions. The probability of the inference is the ratio of true conclusions to all the conclusions which would be drawn in the long run from true premises by inferences of the same kind. Probability is therefore essentially based on the existence of a statistical average, by which I mean a ratio between the number of objects of one class and the number of connected objects of another class, according to their actual occurrence in the long run; and the doctrine of chances may advantageously be extended so as to embrace the entire theory of statistical averages. Such averages have nothing to do with the essences or forms of things, but merely with frequencies of different kinds of actual occurrences in nature. Thus, probability has as little concern with the ideal world as mathematics has with the actual world.
So it would seem Peirce views probability as one type of statistical average, namely, the ratio of successful cases to all cases. So whilst he does focus on probability he also does allow “the doctrine of chances may advantageously be extended so as to embrace the entire theory of statistical averages”. He is right too, as I mentioned above, the sample average can be assumed to be normally distributed with larger and larger sample sizes (30 samples is often given as the magic number). I’ve recently started reading more of Peirce’s later works, so I’ll get back to you if I come across a more explicit answer.
> To a first approximation, I read it as "only use 'induction' in the tiny minority of cases where certain statistical techniques work, and define 'induction' as referring only to those statistical techniques which are similar to those used for guessing the number of blue marbles in an urn known to contain only red and blue marbles and from which we've randomly drawn a sample of marbles and know the total number of marbles." That looks to me like it might be an anti-inductivist position which rejects what ~all other inductivists are currently doing and claiming. It might be so limited that Popper would say "hey that is not what anyone means by 'induction'" rather than claiming to have refuted it. Popper (and me and DD) was not against basic statistics used in appropriate scenarios like randomly pulling colored marbles from urns and scenarios equivalent to that. But I'm not yet very clear on how limited this Peirce system is without extending it.
It is not limited to cases where we know all the possible types of cases (could be any number of colours, not just two known colours). We could have an urn with infinite colours, but if 60% of the marbles are blue, then this is something we can guess and be assured of through an induction from a sample.
It doesn’t have to be an urn either. The urn takes the place of nature where each marble being drawn is an analogy to each experience of a phenomenon provided to us by nature under particular circumstances (as defined by the theory). This applies to our scientific study of phenomena; hence why so many studies report results with confidence intervals/levels (the tools laid out by Peirce for his theory of induction).
We also don’t need to know the total number of possible experiences (total number of marbles in the jar) to make our inductions. We obtain our objective measure (proportion of successful cases divided by total cases observed) without having to know how many cases are going to ultimately be observed.
So your “first approximation” of Peirce’s induction as being far too limited is not correct.
> I don’t think it matters for this example whether it is exact or approximate because this background knowledge is only being used to deem our knowledge as probable/acceptable. Since we can’t have certain knowledge about the world, assume it is approximately 90%.
You claimed you were doing a deduction. Deductions are exact – no fudging – or they aren't deductions.
Let's try this. Can you specify the form of the deduction(s) that you're trying to use? That means you present the deduction with variables (structure words to show the *form* of the argument and that it doesn't depend on the specific content, which is why it's called "formal" logic), e.g.:
All X are Y.
Z is an X.
Therefore Z is a Y.
After you specify that and also specify the meanings of the variables, then we'll be able to see what the argument actually is and what issues are relevant. One thing we won't find is that the conclusion follows approximately 90% from the premises – that is not how deduction works and is not coherent.
> A “small animal species” could be defined as any animal species whose average weight is less than 30Kg.
Does it include extinct species? Species on other planets in other galaxies? Species that will exist in the future? You are not being nearly precise/careful/exact enough to do deduction. Did you mean mass rather than weight? How do you know the average weight or mass of a species (you aren't going to be able to use random sampling)? What about the issue that the weight or mass of an animal varies over time during its life? Deduction is *very very rigorous*. Either be way more rigorous or stop claiming to be using deduction. You seem to be doing regular, casual, informal arguing – to the standards of like college students having a late night argument, not to the standards of effective philosophy – and then calling it, of all things, *deduction*.
Also – not terribly important but it shows sloppiness – according to some info online, gray wolves, Mongolian gazelles and multiple species with "giant" in their name are 30kg or less. I think that's pretty heavy and isn't a reasonable cutoff.
> All I’ve essentially been trying to say is that we consider new conjectures under the lights of our existing background knowledge before we move on to experimental testing. I don’t think this should be so so troubling that we cannot move on in our discussion.
You find what you're saying kinda obvious and trivial, yet it seems to be beyond your skill to say it correctly and clearly. That should trouble you! I was, generously, letting you try repeatedly instead of just dismissing you for being wrong, but you think I should be far more generous for some reason and just ignore a bunch of errors.
The summary you give now *does not in fact match* some of the claims you have made so far. I have been responded to your claims. If you don't remember and don't wish to take responsibility for your own claims – if you can't be bothered to keep track of everything you said and to vouch for it and consider it important – then we have a serious problem.
> Say our currently non-refuted theory says that the mechanics of gravity is independent of time (now and in the future), but my new conjecture says that the mechanics of gravity, whilst appearing independent of time in the past, are really dependent on time starting tomorrow. So here we have two theories consistent with what they say about the past, but differing in their future predictions.
Yes, so you have to differentiate them using criticism and it'll have to be criticism of types other than "Theory T is wrong b/c it contradicts data D". If you give an example where you're unable to come up with criticisms, I can tell you some. Otherwise you'd have to content yourself with abstract concepts, some of which you've already read in Popper and DD, and some of which I've already mentioned and also linked to. Remember that FoR ch. 7 covers this with an extended example.
> Induction may lead us to conclude that every human with a certain gene grows to be taller than 6ft, but unknown to us in some small pocket of the world there exists a small group of outliers; exceptional cases of people with this gene who grew no taller than 5ft. Admitting the possibility of *exceptional* cases implies that our knowledge will still lead us right in the majority of typical cases (to our benefit).
I said and admitted nothing about how common such distributions (ones where your proposal will give the wrong answer) are. If you'd like to admit that your methods do not work in the general case, you could then move on to trying to analyze in what cases they do and don't work and how common those cases are universally. But I don't think you can do that.
> (FYI, the distribution of the sample mean approaches normality with greater sample size irrespective of underlying population distribution)
Proof?
Actually that is trivially false. If you are competent at the matters you are claiming to have knowledge of, you ought to be able to *disprove* that. If you cannot find a disproof, will you admit you have much less skill at these topics than I do? You ought to be able to find a disproof within 10 minutes (it took me under 30 seconds), IMO, but you can have a week if you want. If you don't know what you're doing mathematically, that is OK but you ought to acknowledge the situation and stop making claims about areas where you don't know. You could try to ask questions and get help studying rather than make assertions that you are unable to actually judge/evaluate.
> After re-reading some Peirce I’m not so sure we can say he has limited himself to proportion of occurrences.
Fine, sure, no problem, and that's not surprising ... but then all my criticisms apply. I was specifically interested in that limited idea because it was the only thing that has come up which would prevent most of my criticisms from refuting his approach. I was exploring that possible system to see whether it could do anything like the job of induction while staying within that limit (I decided that it can't).
> We could have an urn with infinite colours, but if 60% of the marbles are blue, then this is something we can guess and be assured of through an induction from a sample.
An urn with infinite colors has infinitely many marbles in it. It is impossible to pull out a random marble (with equal probabilities for all marbles) from a set of infinite marbles.
What you propose is much like attempting to randomly sample the positive integers (impossible) and then (suppose, counter-factually, that you had a sample) expecting the sample mean to correspond to the population mean. (That's a problem because what is the population mean for positive integers?)
I think you should acknowledge you're out of your depth logically and mathematically, and stop making a stream if false assertions. If you want to learn, there are better, more effective ways to proceed than a succession of false claims about matters where you don't know enough to reasonably reach any conclusion.
PS I plan to hopefully go back to *two things at a time* (one question or argument, one reply) next post, so I recommend that you state which one thing you most want a response to.
#12947
> I use regular arguments in #12946 . By regular I mean not deduction nor induction. I don’t think it uses abduction either, but I don’t think the term “abduction” is well-defined so it’s hard to comment on that. Here's an example section with regular arguments:
>> And then I asked for details about one of the things you introduced in your explanation (that background knowledge) and you still have not provided those details. To reason from an auxiliary premise you must detail what that auxiliary premise says, it’s nature, etc. You haven’t done that even though your example as a whole depends on those details. [You did] begin doing it, but didn’t want to deal with critical scrutiny in detail because you didn’t think it mattered and had alternatives anyway.
>>
>> Can you give an example that does not rely on any pre-existing inductive knowledge, and which has nothing to do with induction? I think that would be better. Otherwise, can you try again to clarify what is deduced from what, beginning by giving the form of the argument using only variables, and then giving the full, topical version using only *unambiguous* premises?
My understanding is that most “regular” arguments are of deductive/inductive form, but for reasons of practicality, obvious premises are not explicitly stated. For example, you gave the following argument.
>>To reason from an auxiliary premise you must detail what that auxiliary premise says, it’s nature, etc.
We get the following deductive syllogism.
For your reasoning to be efficacious you must provide the details of your premises and conclusions.
An auxiliary premise is a type of premise.
Therefore, for your reasoning involving auxiliary premises to be efficacious you must provide the details of your auxiliary premise.
You didn’t explicitly state (1) or (2) because it was reasonable for you to assume that they could be brought to my mind whilst I considered your conclusion (3). If I had asked for clarification then you may have actually responded with premises similar to (1) or (2).
> Typical regular argument example:
>> Rent control is bad because it makes it harder for young people to get homes and they are our future.
> This is an incomplete, mediocre argument. It’s kinda vague. Nevertheless, it is an argument with some content. It’s not nothing. And it’s not deduction nor induction.
Again we will find there are premises not made explicit. We get the following deduction.
Policies that negatively affect our future are bad.
Young people are our future.
Therefore policies that negatively affect young people are bad.
Policies that prevent young people from getting homes negatively affects young people.
Therefore policies that prevent young people from getting homes are bad.
Rent control is a policy that prevents young people from getting homes.
Therefore rent control is bad.
So while it is far less vague when we include the missing premises (making it easier for us to point out its weaknesses), it is not wrong for us to leave out these premises since it affords us a much more efficient means of communication (so long as we don’t leave out so many premises as to cause a misunderstanding).
It would be interesting to study the threshold of premises that could be left out of an argument before it is too frequently misunderstood. I wonder what rules of thumb we could find :)
#13013
Numbering of premises was left out of my examples, doh! hopefully you can understand.
> We get the following deductive syllogism.
That is *not similar to* what the original sentence meant, and I would not have clarified with anything similar to that. I give an example for the other one below.
> Again we will find there are premises not made explicit. We get the following deduction.
Stop mixing together multiple deductions (and then calling them a singular deduction!?). Mixing them makes it harder for you to tell if your deduction is valid and harder for anyone to read what you're trying to say. You're taking problematic shortcuts instead of trying to be rigorous. And even just the first 3 lines are problematic. You don't appear to be following standard deductive rules. (Could you name what rules you think you're following and specify exactly how that syllogism follows a valid form and reference some source(s) that you're getting your info from? And could you write the form of the argument with variables and then, separately, define the variables?) And line 4 has a typo.
And the argument *does not mean* what you're taking it to mean. E.g. it never said that "[All] Policies that negatively affect our future are bad." You're reading it as making claims it did not make and which its author could easily disagree with.
https://arxiv.org/pdf/1108.5329.pdf
> Confidence regions are subsets of the state space in which the true state lies with high probability, independently of any prior assumption on the distribution of the possible states.
Physicists are more careful with their claims than Kieren. They know *at least* that making prior assumptions about distributions is something to be careful with (and actually specify in detail if you do it), and preferably just avoid doing. Alternatively they might just think they couldn't do it.
#13009
> Let's try this. Can you specify the form of the deduction(s) that you're trying to use? That means you present the deduction with variables (structure words to show the *form* of the argument and that it doesn't depend on the specific content, which is why it's called "formal" logic), e.g.:
> All X are Y.
> Z is an X.
> Therefore Z is a Y.
The form of the argument is:
1) 90% of X have Y.
2) is a randomly selected X.
3) Therefore, there is a 90% chance Z has Y
I elaborated on this form of ‘deduction about probabilities’ earlier and you seemed ok with it, so I won't repeat myself again.
> After you specify that and also specify the meanings of the variables, then we'll be able to see what the argument actually is and what issues are relevant. One thing we won't find is that the conclusion follows approximately 90% from the premises – that is not how deduction works and is not coherent.
X is ‘species of small animal’ (species of animals who don’t grow larger than 30Kg say - or whatever requirement you prefer)
Y is the attribute ‘eyes’
Z is a species of animal, e.g. the Short-Nosed Bandicoot (SNB).
We end up with.
1) 90% of small animal species have eyes.
2) SNB is a randomly selected small animal species.
3) Therefore, there is a 90% chance SNB have eyes.
If we inquire about premise (1) or (2) we find it is synthetic knowledge and therefore fallible and only approximate (not certain) knowledge. To the degree our premises are uncertain, anything that follows from it will also be determined with uncertainty. We may accept it as a valid deductive argument, but qualify its soundness with mention of our uncertainty in its premises. Valid but only approximately sound.
Compare with Popperians falsifying scientific theories through deductive refutation (modus tollens).
1) If all men have fingers, then socrates has fingers.
2) Socrates does not have fingers.
3) Therefore, not all men have fingers.
Since this is synthetic knowledge, our premises are fallible and uncertain. Yet if you employ this kind of reasoning I am still going to refer to it as deductive, even if we are going to qualify its soundness with mention of the uncertainty of the premises.
> Does it include extinct species? Species on other planets in other galaxies? Species that will exist in the future? You are not being nearly precise/careful/exact enough to do deduction. Did you mean mass rather than weight? How do you know the average weight or mass of a species (you aren't going to be able to use random sampling)? What about the issue that the weight or mass of an animal varies over time during its life? Deduction is *very very rigorous*. Either be way more rigorous or stop claiming to be using deduction. You seem to be doing regular, casual, informal arguing – to the standards of like college students having a late night argument, not to the standards of effective philosophy – and then calling it, of all things, *deduction*.
You will always be able to ask for more details and more clarification, no matter how much detail I provide. At some point you have to make some reasonable assumptions to allow an understanding of what someone is talking about. I feel like these are all somewhat irrelevant details that you could reasonably assume answers to without having to ask me. For example, generally the scientists interested in categorizing species limit their enquiries to species here on earth. I think this is something you could have reasonably assumed to allow the discussion to progress. Even if you assumed different answers to these questions, so long as you did so with good faith, then I doubt it will affect my argument. For example, whether our knowledge includes extinct species or only those currently alive makes very little difference to the deduction we are discussing (reasonably assuming SNB are alive). Do you really want me to explicitly answer all of these questions or are you ok with making some reasonable assumptions to allow the argument to proceed and only highlighting *important* differences in our assumptions (differences that prevent you from following the argument) when they arise?
> The summary you give now *does not in fact match* some of the claims you have made so far. I have been responded to your claims. If you don't remember and don't wish to take responsibility for your own claims – if you can't be bothered to keep track of everything you said and to vouch for it and consider it important – then we have a serious problem.
Which of my earlier claims is this not consistent with?
Seems consistent with my initial claim:
>>Once we have a guess, we then consider if it is worth taking seriously. We look at what our guess says about the world, and then we compare against what our existing theories (background knowledge) says about the world. If we find our guess can be deduced from our existing knowledge, then we may not even need to move onto the testing (inductive) stage.
> Yes, so you have to differentiate them using criticism and it'll have to be criticism of types other than "Theory T is wrong b/c it contradicts data D". If you give an example where you're unable to come up with criticisms, I can tell you some. Otherwise you'd have to content yourself with abstract concepts, some of which you've already read in Popper and DD, and some of which I've already mentioned and also linked to. Remember that FoR ch. 7 covers this with an extended example.
I’ve been directed to ch. 7 a few times now by different Popperians, but each time I read through it I am unconvinced, and identify vague ‘whiffs’ of induction coming in from David. I can revisit it again if you like. Is there a quote from this chapter that you find most convincing?
What are your criticisms (abstract or not) of the ‘floater’ theory I am referring to?
> Actually that is trivially false. If you are competent at the matters you are claiming to have knowledge of, you ought to be able to *disprove* that. If you cannot find a disproof, will you admit you have much less skill at these topics than I do? You ought to be able to find a disproof within 10 minutes (it took me under 30 seconds), IMO, but you can have a week if you want. If you don't know what you're doing mathematically, that is OK but you ought to acknowledge the situation and stop making claims about areas where you don't know. You could try to ask questions and get help studying rather than make assertions that you are unable to actually judge/evaluate.
I was referring to central limit theorem. What is your disproof?
> An urn with infinite colors has infinitely many marbles in it. It is impossible to pull out a random marble (with equal probabilities for all marbles) from a set of infinite marbles.
> What you propose is much like attempting to randomly sample the positive integers (impossible) and then (suppose, counter-factually, that you had a sample) expecting the sample mean to correspond to the population mean. (That's a problem because what is the population mean for positive integers?)
You are right that in such cases where the number of cases is infinite (or might as well be, e.g. inferring something about the stars in the universe) that it doesn’t make sense (it’s impossible) for us to throw all instances into a bag, shake them up, and then draw out a random sample. The drawing of a sample like that is the ideal case. In practice, where the cases we care about are endless, we take what samples we can. We try our best to avoid biases in our sample, but are limited practically. We make our inferences regardless of these limitations and approximations. Peirce talks about how our methods assure us that we will be led right in the long run, so long as we survive to continue conjecturing new hypotheses and drawing more samples (error correction).
> And the argument *does not mean* what you're taking it to mean. E.g. it never said that "[All] Policies that negatively affect our future are bad." You're reading it as making claims it did not make and which its author could easily disagree with.
Then it is a good example of how a vague argument can be misunderstood. Clarify it if you want. My point was only to show how it could be presented deductively.
Kieren, I'm really busy currently and haven't read much of what you wrote. But 2 quick things:
> > Actually that is trivially false. If you are competent at the matters you are claiming to have knowledge of, you ought to be able to *disprove* that. If you cannot find a disproof, will you admit you have much less skill at these topics than I do? You ought to be able to find a disproof within 10 minutes (it took me under 30 seconds), IMO, but you can have a week if you want. If you don't know what you're doing mathematically, that is OK but you ought to acknowledge the situation and stop making claims about areas where you don't know. You could try to ask questions and get help studying rather than make assertions that you are unable to actually judge/evaluate.
> I was referring to central limit theorem. What is your disproof?
And the text under discussion was:
> (FYI, the distribution of the sample mean approaches normality with greater sample size irrespective of underlying population distribution)
I misread it. But I think it doesn't make sense. I read it without the word "mean". I read "... the distribution of the sample approaches normality ..."
It doesn't make sense with the word "mean" after "sample" because means don't have or approach normality. I expected the word "normality" to be related to the normal distribution which had been part of the discussion.
Similarly, the text "the distribution of" only makes sense if talking about the sample, not the sample mean. A sample, but not a mean, has a distribution.
So there were two textual indicators to indicate it'd be talking about the sample, not the sample mean. But I see now that it says sample mean. Maybe it's a typo and you actually meant what I misread, or maybe something else is going on, let me know.
---
> The form of the argument is:
> 1) 90% of X have Y.
> 2) is a randomly selected X.
> 3) Therefore, there is a 90% chance Z has Y
I assume that (2) is meant to begin with "Z".
This does not fit a standard deductive pattern. It introduces non-standard terms outside of variables. Standard terms are things like "all", "are" or "therefore". Can you provide a reference to material on logic which gives this form? Here are some standard deductive forms so you can see what they are like: https://en.wikipedia.org/wiki/Syllogism (Barbara, Celarent, etc., are deductive forms, but you aren't using any of those)
Substantive, non-standard terms that you've used are "90%", "randomly selected", and "chance". Deduction is supposed to be based on *minimal axioms and logic* (e.g. our understanding of "some" or "not"), not based on a pre-existing, complex knowledge of random sampling and probability. That way, the correctness of deductive conclusions depends only on very minimal assumptions, not on e.g. the correctness of one's beliefs about random sampling. (It's like how the correctness of the standard syllogism about Socrates does not depend on our understanding of mortality. That's one of the main points of it.)
#13136 Shouldn't 90% be N%? The argument doesn't depend on it being 90 rather than 77, so there is no reason to introduce 90 as part of the constant form of the argument instead of as a variable part.
Similarly, "%" means "per 100" but the argument would work equally well if it was per 500. So "90%" would be better as "N per M". There are two variable parts there (maybe some other wording could reduce that to one). The non-variable part is the "per" or, in other words, the concept of a ratio or fraction (varying "per" to e.g. "plus" would ruin the argument).
>> (FYI, the distribution of the sample mean approaches normality with greater sample size irrespective of underlying population distribution)
> I misread it. But I think it doesn't make sense. I read it without the word "mean". I read "... the distribution of the sample approaches normality ..."
> It doesn't make sense with the word "mean" after "sample" because means don't have or approach normality. I expected the word "normality" to be related to the normal distribution which had been part of the discussion.
> Similarly, the text "the distribution of" only makes sense if talking about the sample, not the sample mean. A sample, but not a mean, has a distribution.
> So there were two textual indicators to indicate it'd be talking about the sample, not the sample mean. But I see now that it says sample mean. Maybe it's a typo and you actually meant what I misread, or maybe something else is going on, let me know.
It’s not a typo. “The distribution of the sample mean” *does* make sense.
See http://www.stat.yale.edu/Courses/1997-98/101/sampmn.htm for example.
>>The most important result about sample means is the Central Limit Theorem. Simply stated, this theorem says that for a large enough sample size n, the distribution of the sample mean 𝒙 will approach a normal distribution. This is true for a sample of independent random variables from any population distribution, as long as the population has a finite standard deviation 𝛔.
>>> If you cannot find a disproof, will you admit you have much less skill at these topics than I do?
I didn’t find this question very helpful by the way. I don’t care who has the most skill. I’m interested in our ideas. I hope we are on the same page.
> ---
>> The form of the argument is:
>> 1) 90% of X have Y.
>> 2) is a randomly selected X.
>> 3) Therefore, there is a 90% chance Z has Y
> I assume that (2) is meant to begin with "Z".
Yeah, my bad.
> This does not fit a standard deductive pattern. It introduces non-standard terms outside of variables. Standard terms are things like "all", "are" or "therefore". Can you provide a reference to material on logic which gives this form? Here are some standard deductive forms so you can see what they are like: https://en.wikipedia.org/wiki/Syllogism (Barbara, Celarent, etc., are deductive forms, but you aren't using any of those)
> Substantive, non-standard terms that you've used are "90%", "randomly selected", and "chance". Deduction is supposed to be based on *minimal axioms and logic* (e.g. our understanding of "some" or "not"), not based on a pre-existing, complex knowledge of random sampling and probability. That way, the correctness of deductive conclusions depends only on very minimal assumptions, not on e.g. the correctness of one's beliefs about random sampling. (It's like how the correctness of the standard syllogism about Socrates does not depend on our understanding of mortality. That's one of the main points of it.)
Peirce calls this sort of deduction a ‘statistical deduction’. It is a necessary inference where the subject matter is probabilities. Maybe it is clearer if I break it into two deductions.
1) The probability of obtaining (through random sampling) an A from a set is equal to the proportion of A’s within that set.
2) The proportion of X’s that have Y is 90%.
3) Therefore, the probability of a randomly sampled X having Y is 90%.
1) The probability of a randomly sampled X having Y is 90%
2) Z is a randomly selected X.
3) Therefore, Z has a 90% probability of having Y.
The mark of a deduction is that the conclusion necessarily follows from its premises (if they are true). We see this in both of the above deductions. I think they are both cases of Barbara and we could be more explicit in showing this, but we can skip this exercise if you can see them as deductions in their current form.
I’ve had a look back on chapter 7 in FoR.
>”But of course, the premise of all this, namely that your theory is taken for granted and embodied in the prevailing language, is preposterous. Theory or no theory, language or no language, in reality no rational person would entertain the possibility of such a glaring physical anomaly without there being a very powerful explanation in its favour.”
It is comments like these which are convincing for David’s crypto-inductivist opponent, but which don’t convince me. He makes a common sense argument that theories which postulate anomalies are irrational for us to accept. He is right about this. It would be irrational for us to accept the floater theory over the standard theory of gravity. David says it is irrational because we have no explanation in its favour. I don’t like this reasoning because surely we could always come up with an arbitrary explanation as to why David will float. Theories that postulate anomalies aren't all necessarily explanationless. Also, an “explanation in its favour” hints at some kind of requirement for justification. Maybe David only has in mind those explanations which he refers to as “good” explanations, but then this begs the question of what makes an explanation “good”, and does a “good” explanation rely on inductive support or not.
Maybe you can clarify some of chapter 7 for me? Is there a quote that you think is convincing?
> It’s not a typo. “The distribution of the sample mean” *does* make sense.
You have not explained how it makes sense and the quote you give does not explain how it makes sense. A mean of (a trait of) a sample is a single number. A single number does not have a distribution.
>> It’s not a typo. “The distribution of the sample mean” *does* make sense.
> You have not explained how it makes sense and the quote you give does not explain how it makes sense. A mean of (a trait of) a sample is a single number. A single number does not have a distribution.
You should read the first paragraph of the page I linked. Does it make sense then?
> You should read the first paragraph of the page I linked. Does it make sense then?
I already read that. No. Talking about plural *means* with the singular word *mean* does not make sense. And that page just never really explains what it's talking about.
An example of a page which has a more reasonable explanation is https://bolt.mph.ufl.edu/6050-6052/module-9/sampling-distribution-of-x-bar/ I hope you can see the difference.
To be clear, the issue is not whether I understand Central Limit Theorem (CLT) or CLT makes sense to me. It's that particular explanations of CLT are bad and do not make sense even though I already know what CLT says.
Do you believe CLT has any exceptions?
(I'm still very busy FYI.)
#13181
Ok, so it was the grammar of 'distribution of sample mean' vs 'distribution of sample means' which was the confusion. You understand what I was referring to now which is good.
#13332 Repeating: Do you believe CLT has any exceptions?
#13337
If we want to consider applications outside of CLT's defined area of applicability, then I'm sure we could say it has exceptions. Such as trying to find the mean of a population which has an undefined mean.
If you look back you will see that my reference to CLT was a side note to my point about how we error correct with induction. Lets say we come across such a nasty *exceptional* distribution in nature where increasing sample size increases the variability of our sample mean. Can we not infer (inductively) the general nastiness of this distribution from our particular experiences with it in the past?
#13340 Let's try this again. CLT has exceptions. They are well known and Googlable. It's also not that hard to think of some yourself. They extend to a lot more cases than an undefined mean.
Are you familiar with and do you understand some of the exceptions? If not, what about after seeing these two pages?
https://math.stackexchange.com/questions/164456/some-case-when-the-central-limit-theorem-fails
https://stats.stackexchange.com/questions/348972/are-there-any-examples-of-where-the-central-limit-theorem-does-not-hold
I think what you wrote previously is incorrect because of CLT having these exceptions. So I want to know if you are surprised that they exist, or already knew but don't think they're a problem, or deny them, or what.
Yes. CLT has requirements for its "area of applicability" (e.g. mean and variance of the distribution must exist, finitely). So if we are dealing with a distribution that fails one of these requirements then we can't apply CLT exactly.
#13342 There are more requirements than that, including ones that can easily come up in daily life. Agree or disagree?
Do you mean more requirements than what is provided by its mathematical definition?
What do you have in mind?
#13344 For example, imagine a population of a million widgets where the value of their foo trait is 7 for all of them. You take 1000 samples of 1000 widgets and record the mean foo trait in the sample. Each time the mean is 7. So *you do not get a normal distribution*. Right?
Note for context that you claimed:
> Similarly, if the parameter (e.g. mean) we are trying to obtain does depend on the distribution (FYI, the distribution of the sample mean approaches normality with greater sample size irrespective of underlying population distribution) and we guess it (the distribution) incorrectly, then we can find (with an induction) that our distribution isn’t correct.
Your example breaks one of CLT's definitional requirements (non-zero variance). Fortunately, our inference of the mean is still going to lead us right in this case.
I'm not sure we will be making much progress here. Did you wanna have a look at some of my main points from earlier? I don't mind waiting if you're busy.
> Your example breaks one of CLT's definitional requirements (non-zero variance).
You did not state that exception despite my asking about exceptions. So I stated it. I take it that you agree. So then isn't the claim:
> (FYI, the distribution of the sample mean approaches normality with greater sample size irrespective of underlying population distribution)
false?
And false in a significant variety of cases. I guessed that maybe your position was the exceptions could be ignored because it was just a few technicalities like situations where there is no mean. Why else would you ignore the exceptions and make a false statement and then carry on with it instead of retracting it? But the exceptions aren't like that. Your statement is not just technically wrong in a few rare cases, it's broadly wrong in many cases. The case of a uniform population (in regards to a particular trait of the population members) is common IRL.
I plan to get to the rest later but I also want to continue about this. I regard this as important for two main reasons. One is that I think it's important to resolve issues instead of just giving up and dropping them. If we can't resolve a relatively simple and clear point, I don't expect to resolve major points. The other reason is that you were contradicting one of my major claims. I was claiming – and this is important to my overall position – that having *no* information (not a little, but exactly none) about the population distribution is a *big problem* for dealing with it. You contradicted that by claiming that *irrespective of underlying population distribution* we can know certain major things about the population. You claimed that *zero* information is adequate for some significant stuff. If you were correct about that, I would have a lot to reconsider. So I think this is a crucial claim to address.
Yes, that FYI is technically false outside CLT, but I did clarify that I was referring to CLT in my follow up response.
However, the FYI was not a major point of my argument being used to refute you as you suggest. It was a side note that I kept brief. My actual main argument granted that we could be dealing with a non-normal distribution and error correct our assumptions.
If I go back to what you regard as the main point, my expectation is that another sub-point will come up where you're wrong. I expect that will repeat indefinitely because you do not appreciate and resolve corrections on sub-points, and the errors on sub-points will prevent successful resolution of the main point(s). I think this has already been happening. *Do you have a solution to this problem to propose?* I don't want to ignore it and just rely on luck to make it turn out OK – I want something better than that.
I'm also finding it difficulty to understand your perspective here and also finding your responses unhelpful when I've tried to get more information about it (I still don't know why, from your perspective, it was a good idea to write a strongly worded and false statement that contradicted one of my important claims, and I still have not found out whether you knew it was false at the time you wrote it or you've learned something new or what).
Meanwhile, I don't think you understand my perspective nor do you seem interested in it. I don't see how you could be mentally modeling me such that you could expect your latest few comments to seem like good comments to my perspective. And you have not been (as far as I can tell) seeking information about my perspective in order to mentally model me better. You don't seem to be paying much attention to what I'm trying to do or why, which is one of the reasons you've written a series of responses which are (from my perspective) ambiguous, incorrect or uninformative on the issues I've been trying to talk about. When neither of us has an effective mental model of what's going on with the other person, we won't make progress. I suspect you want to avoid mental models and focus on the epistemology issues – something like that – but we're trying to communicate about complex matters and that requires mental models
(The need for mental models to facilitate complex communication is actually a similar issue to the need for a conceptual/explanatory understand of an empirical population in order to deal with it effectively. In both cases, blind assumptions won't work, nor will a bad model made subconsciously with little thought. Instead, people need to think about and understand various aspects of the context of what they're doing.)
Let me try be clearer then. I was not trying to contradict one of your claims with my sub point. I was just trying to allude to the fact that CLT means that we are standing on good grounds for inferring the mean for the types of populations we had been discussing. I didn't provide the exact mathematical grounds for CLT because I was being brief.
> I was not trying to contradict one of your claims with my sub point.
Regardless of your intention, you made a false claim which *did* contradict me in a big way, right? And it would not have contradicted me if you'd made the non-exaggerated, true version of the claim instead?
> for the types of populations we had been discussing
What types of populations had we been discussing? I thought we had been discussing all populations in general.
> I didn't provide the exact mathematical grounds for CLT because I was being brief.
The issue is that your statement contradicted those mathematical grounds, not that it omitted them.
Also comment #13358 is non-responsive to most of what I said in #13354 For example, you still have left it unclear whether you knew what you were writing was false at the time that you wrote it.
> Regardless of your intention, you made a false claim which *did* contradict me in a big way, right? And it would not have contradicted me if you'd made the non-exaggerated, true version of the claim instead?
> The issue is that your statement contradicted those mathematical grounds, not that it omitted them.
That was not my intended goal, but yes, left unclarified my side note is too broad in its conclusion.
> What types of populations had we been discussing? I thought we had been discussing all populations in general.
I mean the examples we had been discussing with respect to inferring the mean. e.g. drawing a sample from a set of integers. I imagine it is those sorts of examples I had in mind when I wrote that side note.
> Also comment #13358 is non-responsive to most of what I said in #13354 For example, you still have left it unclear whether you knew what you were writing was false at the time that you wrote it.
I knew that what I was writing was correct in general, and I felt that was sufficient for a brief side note that wasn't a premise to my argument and that we could later clarify if it became relevant.
It is unreasonable to say "irrespective" of X when you know that it only works with some X and not other X. That is conditional on X, not irrespective of X. That's sort of the opposite. So you made a mistake. But you still seem to be unwilling to judge that you made a mistake, even after the various clarifications and explanations. You're making the discussion hard and slow. That is something you're doing, even if you aren't consciously aware of it. It shouldn't have been this hard to correct your error. I do *not* think the problem in this case is you struggling with the material (e.g. not understanding the CLT-related math well enough), which would have been a different sort of reason for it to go slowly. So I think you're resistant to error correction, which I don't think is an ignorable problem.
You do not think that I have already admitted the error in my statement?
#13367
> I knew that what I was writing was correct in general, and I felt that was sufficient for a brief side note that wasn't a premise to my argument and that we could later clarify if it became relevant.
This text appears to deny that it was an error.
It claims "correct in general" then claims what you wrote was "sufficient" in context and then says "could later clarify if it became relevant" (suggesting it's not a problem or error, just a reasonable choice not to include every detail upfront). None of that admits that it was an error. None of that acknowledges that it is *not irrespective*, period, and that claim is just wrong. The claim about irrespective isn't just leaving out details, it's false and there was no reason to ever write it (other than making a mistake). And your text still doesn't make it clear whether you knew what you wrote was false at the time you wrote it or not (maybe you thought it really was irrespective when you wrote that, idk, that would make more sense to me than being fully consciously aware that it's conditional and then intentionally writing "irrespective" (= not conditional) anyway).
> That was not my intended goal, but yes, left unclarified my side note is too broad in its conclusion.
This is also unclear. Clarifications reduce ambiguity. The problem with your statement wasn't ambiguity. The problem is that it was unambiguously false. Also "too broad" is not a clear or direct way to say "false".
> You will always be able to ask for more details and more clarification, no matter how much detail I provide.
Deduction is only *airtight* arguments where there are no details or clarifications left out. E.g.:
All men are mortal.
Socrates is a man.
Therefore, Socrates is mortal.
Do you have any details or clarifactions to ask about for that? I don't.
A genuine deduction is *as airtight as that one*. That's one of the archtypical deductions, it's representative of what deduction is like. If your argument is less airtight or less complete or worse in any way, it's not deduction.
> For example, generally the scientists interested in categorizing species limit their enquiries to species here on earth. I think this is something you could have reasonably assumed to allow the discussion to progress.
Standard deductions, like the Socrates mortality one, do not limit their domain of applicability to Earth (neither explicitly nor as an unstated thing for readers to assume).
For deduction, all limitations on domain (conditions) should be stated. And all complex terms should be defined in a way that would satisfy the pickiest lawyers or logicians. If you aren't doing that, you aren't doing deduction. (Which would be fine. In most of life, including most science, we don't use deduction much. You're claiming deduction plays a major role in your philosophical system; I'm not. But then because that doesn't work you want to lower the quality standards for deduction, which I object to.)
> Do you really want me to explicitly answer all of these questions or are you ok with making some reasonable assumptions to allow the argument to proceed and only highlighting *important* differences in our assumptions (differences that prevent you from following the argument) when they arise?
I want you to speak for yourself. I don't want to both make up the details of your claim for you *and* criticize it. I don't want to do both sides of the discussion. You should make your own claims instead of asking me figure out what you mean for you.
I don't think it's that hard for you to clarify what you're talking about. It seems like you want to avoid committing yourself to a specific version of your claim so that I don't have a clear target for criticism.
There are different branches you can take, different options you have. I would have different criticisms depending on your choices. It doesn't make sense for me to make those choices for you, nor for me to preemptively cover every claim you might make.
The issues I brought up are not random details to split hairs. They are important to how you know what small animals there are and how you randomly select one. You know I regard random sampling details as crucially important to our disagreements, so you should provide adequate detail regarding that key issue. What you've provided so far is so incomplete that I can't discuss random sampling yet. I have tried multiple times to get details so that we'd have an example that could be critically analyzed in regards to the random sampling aspects, but you have put more effort into resisting giving information (even though you already know why I regard is as relevant) than it would have taken to give the info.
> > > All I’ve essentially been trying to say is that we consider new conjectures under the lights of our existing background knowledge before we move on to experimental testing. I don’t think this should be so so troubling that we cannot move on in our discussion.
>
> > You find what you're saying kinda obvious and trivial, yet it seems to be beyond your skill to say it correctly and clearly. That should trouble you! I was, generously, letting you try repeatedly instead of just dismissing you for being wrong, but you think I should be far more generous for some reason and just ignore a bunch of errors.
>
> > The summary you give now *does not in fact match* some of the claims you have made so far. I have been responded to your claims. If you don't remember and don't wish to take responsibility for your own claims – if you can't be bothered to keep track of everything you said and to vouch for it and consider it important – then we have a serious problem.
>
> Which of my earlier claims is this not consistent with?
I didn't say inconsistent. I said doesn't match. Your summary leaves out e.g. your claims related to proportions of occurrences. Also e.g. your claims related to deduction.
The context of this exchange was that I wanted to know, in your system, how learning works that *doesn't involve induction in any way at all*. You then (IIRC) gave examples that involved induction (via using premises that you believed to have been learned by induction) and resisted giving one that doesn't.
According to you, induction comes into play in a later stage in your epistemology. So how do the early stages work *the first time*, before you've ever done the later stages? Or, in the alternative, as I suggested and you resisted, you could also address how learning about a non-empirical topic works.
> You are right that in such cases where the number of cases is infinite (or might as well be, e.g. inferring something about the stars in the universe) that it doesn’t make sense (it’s impossible) for us to throw all instances into a bag, shake them up, and then draw out a random sample. The drawing of a sample like that is the ideal case. In practice, where the cases we care about are endless, we take what samples we can.
There is no way to approximate a random sample of an infinite set. The claim that "we take what samples we can" does not address this problem.
> We try our best to avoid biases in our sample, but are limited practically. We make our inferences regardless of these limitations and approximations.
The problem is you can't do this *at all*. You can't do it approximately. Being willing to fudge things doesn't solve the fundamental, logical problems. There is no set of steps you can do to get an approximately random sample from an infinite set.
Regarding bias or representativeness, this is the basic issue of what is similar to what? That's a hard issue which people don't realize is hard. How do you define what counts as more similar when dealing with a large or infinite number of different dimensions/traits on which to compare things? When you say we try our best to be unbiased it doesn't address how we do that or how we could do that. It has no particular theory of what we're doing and what its merits and limitations are. It reads to me as simply not knowing how people think or do science or whatever. It's like saying we try, we put in effort, and in high level terms we aim for integrity, lack of bias, creativity, etc. That is not an epistemology nor an understanding of how thinking works, it's just some non-technical common sense commentary.
> Peirce talks about how our methods assure us that we will be led right in the long run, so long as we survive to continue conjecturing new hypotheses and drawing more samples (error correction).
(I take it by assure you meant a *certain guarantee*.)
But they don't and can't *assure* us. There are no 100% guarantees. This is like your false claim about *irrespective*. Because of reasons including the standard logical arguments for falliblity and the issue that various statistics stuff *does not* work irrespective of population distribution, we *cannot* be assured.
> Then it is a good example of how a vague argument can be misunderstood. Clarify it if you want. My point was only to show how it could be presented deductively.
What you showed is that a *different and much simpler argument* could be presented deductively, but you did not show the actual argument could be.
>> Can you provide a reference to material on logic which gives this form?
>
> [no answer]
I think it's important to differentiate original knowledge re e.g. deduction from standard published arguments. You don't seem to be claiming to have rejected and improved on mainstream ideas about deduction. You're not claiming originality, I think. So in that case, you should have sources for where you're getting this stuff from. So what specific section of what text covers this stuff about probabilistic deductions that you're trying to argue? I'd rather read your source than have you summarize your source to me.
> Maybe it is clearer if I break it into two deductions.
We were trying to talk about the *form* of the deductive. I put effort into getting you to speak to that. And you began to. But now you've gone right back to
> 1) The probability of obtaining (through random sampling) an A from a set is equal to the proportion of A’s within that set.
Is this intended to apply to all sets, only finite sets, or some other limitation(s)?
And, topically, this is not a form of an argument. It's a complex argument relating to probability, stats, etc. Agreement or disagreement with it depends on one's understanding of the subject matter rather than only on the form of the argument.
A key thing with the Socrates mortality argument is you don't need to know what mortality is in any kinda detail. Expertise about mortality is *irrelevant*. Whereas with this argument, expertise about probability is relevant to evaluating the argument correctly. That shows it's not a formal (form-based) argument.
> The mark of a deduction is that the conclusion necessarily follows from its premises (if they are true).
This is incorrect in multiple ways. One way is that isn't *the* mark of a deduction. A different mark of a deduction is that it's a *formal* argument – one true by virtue of its form instead of the particular content. (E.g. if you replace Socrates with Plato it still works, the argument is not dependent on the particular attributes of Socrates, it's more generic than that.)
Another problem is that "necessarily follows" is redundant or unclear. What do you think "necessarily" adds and how does necessary following differ from regular following? Are you using "necesarily" to refer to following a priori without any dependence on anything empirical, so that you believe it would still follow in a different universe with different laws of physics? Do you mean follows without any exceptions (that's what follows already means by itself)?
After you clarify I may have other criticisms.
> I think they are both cases of Barbara and we could be more explicit in showing this, but we can skip this exercise if you can see them as deductions in their current form.
If you could show their *exact equivalence* to Barbara, with *literally zero errors of any sort in your presentation*, that'd be great. I think they are dissimilar to Barbara b/c e.g. they do not use the same number of terms as Barbara. Your current presentation is not anywhere near the standard of correctness, so this would only be possible if you weren't really trying before and could start actually trying.
> I’ve had a look back on chapter 7 in FoR.
I discussed this in my video, linked below.
---
Big picture, even if your epistemological methods worked (they logically don't), what is the result? A system involving approximations that tries to gloss over or ignore some known problems and errors because they are hard to deal with. That might sound pretty good, but it is bad compared to my epistemology which, if it works (and no one has pointed out some logical flaw for why it can't work), offers a system of clear, decisive answers rather than approximations, and it offers ideas and solutions with *no known errors or problems*, rather than finding error too hard to deal with and giving up to some extent. If they both work (if you somehow rebutted various criticisms), my proposed system is dramatically better and would supercede yours anyway. So does that interest you enough to try to learn my epistemology enough to evaluate whether you can see anything decisively wrong with it?
PS I made a video while writing this comment which says a lot more than the comment. Watch at https://youtu.be/4E5gR9P5qyE
> #13367
> It claims "correct in general" then claims what you wrote was "sufficient" in context and then says "could later clarify if it became relevant" (suggesting it's not a problem or error, just a reasonable choice not to include every detail upfront). None of that admits that it was an error.
“Correct in general” implies that it is not absolutely true. Earlier I was more explicit in admitting the error with the following.
>> Yes, that FYI is technically false outside CLT, but I did clarify that I was referring to CLT in my follow up response.
In this quote, did I not agree with you and admit that my original (unclarified) statement was in error?
#13373 Why did you describe your FYI as "technically false" instead of just plain "false"?
> #13373 Why did you describe your FYI as "technically false" instead of just plain "false"?
Because whilst it is false for some cases, which seem to me as special cases (in the context of studying a population for its mean), it is correct for many others.
#13370
>Deduction is only *airtight* arguments where there are no details or clarifications left out. E.g.:
>All men are mortal.
>Socrates is a man.
>Therefore, Socrates is mortal.
>Do you have any details or clarifactions to ask about for that? I don't.
I could always ask for clarification about what these terms mean. For example, do you include fictional men under your category of man? Similarly, you asked me if I include extinct animals in my category of small animal species.
> A genuine deduction is *as airtight as that one*. That's one of the archtypical deductions, it's representative of what deduction is like. If your argument is less airtight or less complete or worse in any way, it's not deduction.
> For deduction, all limitations on domain (conditions) should be stated. And all complex terms should be defined in a way that would satisfy the pickiest lawyers or logicians. If you aren't doing that, you aren't doing deduction. (Which would be fine. In most of life, including most science, we don't use deduction much. You're claiming deduction plays a major role in your philosophical system; I'm not. But then because that doesn't work you want to lower the quality standards for deduction, which I object to.)
I’m getting the impression that you limit your concept of deduction to only those arguments which are stated in the precise form of a classical syllogism. What if someone said “My friend Socrates is going to die because he is a man and all men are mortal”? Would you be ok with calling this a deductive argument?
If so, then what about “John has a high chance of suffering memory loss in later life because he is a footballer and 90% of footballers suffer from memory loss in later life”?
>According to you, induction comes into play in a later stage in your epistemology. So how do the early stages work *the first time*, before you've ever done the later stages? Or, in the alternative, as I suggested and you resisted, you could also address how learning about a non-empirical topic works.
I will try to provide a bit of an overview of the steps involved in my model.
1. Create a new hypothesis (creative conjecture)
2. Check hypothesis against existing knowledge
3. Deduce testable consequences from your hypothesis
4. Test the deduced consequences and induce conclusions.
Step 4 is where the induction takes place. We are stuck at step 2 because it involves discussion of existing knowledge, which in order to have been accepted it had to pass each of the steps already (including the inductive step). However, we have a few options to get out of this. One option is to move forward with the assumption that we already have some existing knowledge to work with (perhaps assuming it is instinctive knowledge, or a rule of thumb provided to us by our parents). Another option is to just assume we have no relevant prior knowledge whatsoever, meaning we skip step 2. However I don’t think this second option is realistic as I mentioned previously with the following response.
>> It’s hard for me to give an example without relying on existing knowledge, because I don’t think that is ever the case. Maybe you come across pain for the first time and you conjecture something as simple as ‘falling causes pain’, but I imagine we could always show how some sort of instinctual knowledge of physical objects, the self, time, etc is being invoked.
I’ll try respond to more of what you wrote when I get the chance.
> “Correct in general” implies that it is not absolutely true.
Making a weaker statement does *not* imply that (the speaker believes that) a stronger statement would be false.
>>> Yes, that FYI is technically false outside CLT, but I did clarify that I was referring to CLT in my follow up response.
> In this quote, did I not agree with you and admit that my original (unclarified) statement was in error?
Your claim was non-technically false (uniform populations are not a rare, technical issue).
You only said it was false "outside CLT" and said you were referring to CLT. None of that is clearly changing your mind. Mentioning CLT upfront would not have helped make the "irrespective" claim true. CLT says *conditionally*, not irrespective, so mentioning CLT + talking about "irrespective" is contradicting yourself rather than fixing the problem.
You seem to be claiming that your clarification that you were talking about CLT meant you were no longer in error, whereas actually at that point you were contradicting yourself.
> “Correct in general” implies that it is not absolutely true.
Do you mean *logically* implies, or did you bring up some other kind of implication (what? vague, ambiguous, maybe-hinting?) in a discussion involving logical deduction, without labelling or explanation, would be a good idea?
It looks like you are not a competent logician and ought not to be making the claims you have about logic b/c you don't know what you're doing.
> I’ll try respond to more of what you wrote when I get the chance.
To be clear (since I didn't say anything), my plan is just to wait for this.
I've recently moved interstate and started out with a new job. Busy sorting things out, but I should be able to get back to this conversation soon.
I have not read or replied to #13382
I am caught up on the rest.
Documenting this for if/when kieren comes back.
Hey, It is me again. Hope you guys have been well. I sort of just replied to everything, but maybe we can identify some important issues to focus on. I will try limit myself to replying to what I see as the important points from now on. I like the idea that for each response we split between defending our own view, and levelling criticism at our opponents view.
> There is no way to approximate a random sample of an infinite set. The claim that "we take what samples we can" does not address this problem.
>> We try our best to avoid biases in our sample, but are limited practically. We make our inferences regardless of these limitations and approximations.
> The problem is you can't do this *at all*. You can't do it approximately. Being willing to fudge things doesn't solve the fundamental, logical problems. There is no set of steps you can do to get an approximately random sample from an infinite set.
The problem isn’t specifically that we need a random sample. More generally It’s that we need a representative sample. A random sample as I have described it (pulling samples from a bag) is just one way to get a representative sample (for finite samples as you point out). I think the problem you are getting at is: how do we know our finite sample of experiences is representative of the essentially infinite experiences yet to come. To overcome this it seems to me that we must assume that future samples of a certain type of experience (e.g. heating water to 100 degrees) will be similar to our past experiences of this type. I believe that we do make this sort of assumption. Our default position (our nature maybe) is to assume that the character of future experiences will be similar to the character of past experiences unless we have reason to think otherwise. So with these sorts of assumptions we can proceed with our induction in unideal cases. If we are to one day overturn one of these assumptions, then I would imagine it is happening with an induction in the opposite direction (the character of this sort of experience has not been stable in the past, therefore …).
> Regarding bias or representativeness, this is the basic issue of what is similar to what? That's a hard issue which people don't realize is hard. How do you define what counts as more similar when dealing with a large or infinite number of different dimensions/traits on which to compare things? When you say we try our best to be unbiased it doesn't address how we do that or how we could do that. It has no particular theory of what we're doing and what its merits and limitations are. It reads to me as simply not knowing how people think or do science or whatever. It's like saying we try, we put in effort, and in high level terms we aim for integrity, lack of bias, creativity, etc. That is not an epistemology nor an understanding of how thinking works, it's just some non-technical common sense commentary.
What is similar to what should follow from your hypothesis that you are testing. If you understand your hypothesis then you understand what it says about the world. You understand what cases it subsumes, and you understand what counts as a pass or failure.
> (I take it by assure you meant a *certain guarantee*.)
> But they don't and can't *assure* us. There are no 100% guarantees. This is like your false claim about *irrespective*. Because of reasons including the standard logical arguments for falliblity and the issue that various statistics stuff *does not* work irrespective of population distribution, we *cannot* be assured.
It is an assurance that with error correcting methods we will end up with the correct answer so long as we survive long enough to continue the process. It is a claim tied up with his pragmatism which we haven't really discussed, so maybe we should move this point to the side.
>> Then it is a good example of how a vague argument can be misunderstood. Clarify it if you want. My point was only to show how it could be presented deductively.
> What you showed is that a *different and much simpler argument* could be presented deductively, but you did not show the actual argument could be.
Then please express the argument less vaguely so it is not misunderstood.
>>> Can you provide a reference to material on logic which gives this form?
>>
>> [no answer]
See the beginning of Peirce’s “Deduction, Induction, and Hypothesis”. I’ve quoted the relevant example in #12816.
https://en.wikisource.org/wiki/Popular_Science_Monthly/Volume_13/August_1878/Illustrations_of_the_Logic_of_Science_VI
I see these sorts of statistical deductions as regular deductions, but with proportions/probability as their subject matter.
>> Maybe it is clearer if I break it into two deductions.
> We were trying to talk about the *form* of the deductive. I put effort into getting you to speak to that. And you began to. But now you've gone right back to
>> 1) The probability of obtaining (through random sampling) an A from a set is equal to the proportion of A’s within that set.
> Is this intended to apply to all sets, only finite sets, or some other limitation(s)?
Finite sets is what I had in mind (the set of small animal species).
> And, topically, this is not a form of an argument. It's a complex argument relating to probability, stats, etc. Agreement or disagreement with it depends on one's understanding of the subject matter rather than only on the form of the argument.
> A key thing with the Socrates mortality argument is you don't need to know what mortality is in any kinda detail. Expertise about mortality is *irrelevant*. Whereas with this argument, expertise about probability is relevant to evaluating the argument correctly. That shows it's not a formal (form-based) argument.
It may not fit your criteria for “form-based” argument, but it is deductive right?
See this example from https://www.iep.utm.edu/ded-ind/
>>”The mathematical proof technique called "mathematical induction" is deductive and not inductive. Proofs that make use of mathematical induction typically take the following form:
>>Property P is true of the natural number 0.
>>For all natural numbers n, if P holds of n then P also holds of n + 1.
>>Therefore, P is true of all natural numbers.
>>When such a proof is given by a mathematician, and when all the premises are true, then the conclusion follows necessarily. Therefore, such an inductive argument is deductive. It is deductively sound, too.”
To evaluate this argument correctly you must understand what the set of natural numbers are, and their relation to 0, etc. Therefore, you must deny that this argument is deductive?
>> The mark of a deduction is that the conclusion necessarily follows from its premises (if they are true).
> This is incorrect in multiple ways. One way is that isn't *the* mark of a deduction. A different mark of a deduction is that it's a *formal* argument – one true by virtue of its form instead of the particular content. (E.g. if you replace Socrates with Plato it still works, the argument is not dependent on the particular attributes of Socrates, it's more generic than that.)
I’m guessing when you say an argument is true, you mean it infers a true conclusion?
Assume Plato is actually an immortal man. If we replace Socrates with Plato, then the argument no longer infers a true conclusion as you suggest. I don’t think your definition of deduction works.
> Another problem is that "necessarily follows" is redundant or unclear. What do you think "necessarily" adds and how does necessary following differ from regular following? Are you using "necesarily" to refer to following a priori without any dependence on anything empirical, so that you believe it would still follow in a different universe with different laws of physics? Do you mean follows without any exceptions (that's what follows already means by itself)?
I use “necessarily follows” for deduction to contrast with induction where the conclusion doesn’t have to be true, given true premises.
>> I think they are both cases of Barbara and we could be more explicit in showing this, but we can skip this exercise if you can see them as deductions in their current form.
> If you could show their *exact equivalence* to Barbara, with *literally zero errors of any sort in your presentation*, that'd be great. I think they are dissimilar to Barbara b/c e.g. they do not use the same number of terms as Barbara. Your current presentation is not anywhere near the standard of correctness, so this would only be possible if you weren't really trying before and could start actually trying.
Does this sit with you any better?
We have the following valid deductive form.
1) All X are Y
2) z is an X
3) Therefore, z is a Y
With the following term substitutions.
X: randomly selected small animal species
Y: species that have a 90% chance of having eyes
z: SNB
>> I’ve had a look back on chapter 7 in FoR.
> I discussed this in my video, linked below.
I listened to your video a while back. I’ve just rewatched your response to me in regards to FoR.
You point out correctly that David does not say that all theories that entail anomalies are irrational, but only those that also lack a good explanation for the anomalous behaviour. I admit unclear writing from my end. However, my concluding point still holds; that saying we need a good explanation in its favour is begging the question of what makes an explanation good. If the inductivists position is that a good explanation relies on inductive support, then this line of argument doesn’t help them to see an induction-less theory of science.
I guess what I see missing is a criteria for what makes a ‘good explanation’; a criteria that doesn’t rely on inductive reasoning. Have you got something in writing that addresses your views on what makes a ‘good explanation’? Or would you like me to point out where I see induction being snuck into David’s arguments against the floater theory?
> Big picture, even if your epistemological methods worked (they logically don't), what is the result? A system involving approximations that tries to gloss over or ignore some known problems and errors because they are hard to deal with. That might sound pretty good, but it is bad compared to my epistemology which, if it works (and no one has pointed out some logical flaw for why it can't work), offers a system of clear, decisive answers rather than approximations, and it offers ideas and solutions with *no known errors or problems*, rather than finding error too hard to deal with and giving up to some extent. If they both work (if you somehow rebutted various criticisms), my proposed system is dramatically better and would supercede yours anyway. So does that interest you enough to try to learn my epistemology enough to evaluate whether you can see anything decisively wrong with it?
As I understand it you follow closely Popper’s epistemology which I do find error with. It is Popper’s rejection of confirmation (positive reason, justification, etc) that I have issue with.
There is a 1981 paper by Wesley Salmon that you might be familiar with. A quote below.
>>”This view of corroboration holds serious difficulties. Watkins and Popper agree, I take it, that statements which report observations of past and present events do not, in and of themselves, have any predictive content. Moreover, they maintain, statements about the corroboration of conjectures do not, in and of themselves, have any predictive content. Conjectures, hypotheses, theories, generalisations-call them what you will-do have predictive content. The problem is that there are many such statements, rich in predictive content, which make incompatible predictive claims when conjoined with true statements about past and present occurrences. The fact that a general statement has predictive content does not mean that what it says is true. In order to make a prediction, one must choose a conjecture which has predictive content to serve as a premise in a predictive argument. In order to make a rational prediction, it seems to me, one must make a rational choice of a premise for such an argument. But from our observational evidence and from the statements about the corroboration of a given conjecture, no predictive appraisal follows. Given two conjectures which, in a particular situation, will lead to incompatible predictions, and given the corroboration ratings of these two hypotheses, nothing follows about their comparative predictive capacities. Thus, it seems to me, corroboration-the ground for theoretical preference-furnishes no rational basis for preference of one conjecture to another for purposes of practical prediction. I am not complaining that we are not told for sure that one will make a correct prediction and that the other will not. I am complaining that no rational basis whatever has been furnished for a preference of this type.”
#14625
>>> We try our best to avoid biases in our sample, but are limited practically. We make our inferences regardless of these limitations and approximations.
>>
>> The problem is you can't do this *at all*. You can't do it approximately. Being willing to fudge things doesn't solve the fundamental, logical problems. There is no set of steps you can do to get an approximately random sample from an infinite set.
>
> The problem isn’t specifically that we need a random sample. More generally It’s that we need a representative sample. A random sample as I have described it (pulling samples from a bag) is just one way to get a representative sample (for finite samples as you point out). I think the problem you are getting at is: how do we know our finite sample of experiences is representative of the essentially infinite experiences yet to come. To overcome this it seems to me that we must assume that future samples of a certain type of experience (e.g. heating water to 100 degrees) will be similar to our past experiences of this type. I believe that we do make this sort of assumption. Our default position (our nature maybe) is to assume that the character of future experiences will be similar to the character of past experiences unless we have reason to think otherwise. So with these sorts of assumptions we can proceed with our induction in unideal cases. If we are to one day overturn one of these assumptions, then I would imagine it is happening with an induction in the opposite direction (the character of this sort of experience has not been stable in the past, therefore …).
The idea that the laws of physics don't change over time is irrelevant to the problem of induction because it gives you no information about what features of physical systems don't change. Only the actual laws of physics do that.
> You point out correctly that David does not say that all theories that entail anomalies are irrational, but only those that also lack a good explanation for the anomalous behaviour. I admit unclear writing from my end. However, my concluding point still holds; that saying we need a good explanation in its favour is begging the question of what makes an explanation good. If the inductivists position is that a good explanation relies on inductive support, then this line of argument doesn’t help them to see an induction-less theory of science.
DD would say a good explanation would explain how and why that explanation solves some problem and why the proposed alternatives don't solve that problem. Nothing about that standard refers to induction.
> As I understand it you follow closely Popper’s epistemology which I do find error with. It is Popper’s rejection of confirmation (positive reason, justification, etc) that I have issue with.
>
> There is a 1981 paper by Wesley Salmon that you might be familiar with. A quote below.
>
>>>”This view of corroboration holds serious difficulties. Watkins and Popper agree, I take it, that statements which report observations of past and present events do not, in and of themselves, have any predictive content. Moreover, they maintain, statements about the corroboration of conjectures do not, in and of themselves, have any predictive content. Conjectures, hypotheses, theories, generalisations-call them what you will-do have predictive content. The problem is that there are many such statements, rich in predictive content, which make incompatible predictive claims when conjoined with true statements about past and present occurrences. The fact that a general statement has predictive content does not mean that what it says is true. In order to make a prediction, one must choose a conjecture which has predictive content to serve as a premise in a predictive argument. In order to make a rational prediction, it seems to me, one must make a rational choice of a premise for such an argument. But from our observational evidence and from the statements about the corroboration of a given conjecture, no predictive appraisal follows. Given two conjectures which, in a particular situation, will lead to incompatible predictions, and given the corroboration ratings of these two hypotheses, nothing follows about their comparative predictive capacities. Thus, it seems to me, corroboration-the ground for theoretical preference-furnishes no rational basis for preference of one conjecture to another for purposes of practical prediction. I am not complaining that we are not told for sure that one will make a correct prediction and that the other will not. I am complaining that no rational basis whatever has been furnished for a preference of this type.”
The rational way to judge which theory to use for a given problem is to look for a theory that solves the problem and has no known criticisms:
https://yesornophilosophy.com/argument
In the case of any important and difficult practical problem you don't, in general, just pick a particular prediction and use it. Rather, you guess about how to solve the problem and criticise the guesses. You also come up with ways of monitoring whether the solution is working as intended and ways of dealing with what happens when the solution fails. For example, to write a program, you find out what data you want to collect and how you want to deal with it. You then write various parts of the program and test them in isolation. You may also write integration tests that combine various parts of the solution. You may also have programs that record what happens to your program when you deploy it and have ways of rolling back a deployment if something goes wrong. None of this contradicts critical rationalism.
So why should we use a refuted theory, inductivism, when there is an unrefuted theory with no known problems?
>The idea that the laws of physics don't change over time is irrelevant to the problem of induction because it gives you no information about what features of physical systems don't change. Only the actual laws of physics do that.
What I was trying to say is not just that the laws of physics don’t change over time, but that when we are performing an induction (perhaps for a physical law), we do so with the assumption that *specific* aspects of our future experiences will be similar to those of our past experiences, (unless we have a reason to think otherwise). Say we are investigating the phenomena of heating water. We suppose that heating water over a fire causes it to bubble. We collect experiences of this phenomena, and look back at our past experiences of it. We might see that our hypothesis is true in all the cases we know of, and therefore we conclude it probably true for future cases collected in a similar manner. We could have supposed that the bubbling will not be experienced by an observer standing more than 10m away from the fire, or that there will be no bubbling in the future, or that it will not bubble in any other location, but since we have no reason to suppose these things, we don’t, and our assumptions continue to hold.
>DD would say a good explanation would explain how and why that explanation solves some problem and why the proposed alternatives don't solve that problem. Nothing about that standard refers to induction.
The floater theory solves a problem. It solves the problem of predicting how physical objects (such as DD) will act in the future. How does the regular theory of gravity explain the floater theory as being unable to solve this problem?
>The rational way to judge which theory to use for a given problem is to look for a theory that solves the problem and has no known criticisms:
That is ok, but I haven't found any criticisms of floater type theories (as intended for practical action) that don’t rely on inductive reasoning. DD might point out that the floater theory is not hard-to-vary, but I would point out (as this discussion began) that DD’s hard-to-vary criteria sneaks induction back into Popper’s epistemology.
>So why should we use a refuted theory, inductivism, when there is an unrefuted theory with no known problems?
I’m not arguing for classical inductivism if that is what you mean. I’m arguing that we use induction, and that it is involved in our reasoning about the world. As far as I can tell, there is a problem with your epistemology; you reject induction yet you rely on it to decide between good/bad theories.
#14760
> DD might point out that the floater theory is not hard-to-vary, but I would point out (as this discussion began) that DD’s hard-to-vary criteria sneaks induction back into Popper’s epistemology.
How does the hard-to-vary criterion sneak induction back it?
> we need a representative sample. A random sample as I have described it (pulling samples from a bag) is just one way to get a representative sample (for finite samples as you point out). I think the problem you are getting at is: how do we know our finite sample of experiences is representative of the essentially infinite experiences yet to come.
Any sample is always representative of a superset in some ways and unrepresentative in other words.
This is the same issue as when an inductivist claims "the future resembles the past" (or let's assume that it does and I respond "The future always resembles the past in some ways and does not resemble it in other ways". That is actually the kind of thing Kieren said next (I hadn't read ahead).
So when you speak of a representative sample, the first question is: representative in which ways and why those ways? Representative in *all* ways is impossible, so you need to specify.
> However, my concluding point still holds; that saying we need a good explanation in its favour is begging the question of what makes an explanation good.
If you don't know what "begging the question" means, don't say it. Say normal words that explain what you mean. Throughout this discussion you've been making incorrect claims related to logic jargon and formulas and they're causing ongoing problems.
What we need is a non-refuted explanation.
re Salmon paper, he does a decent job explaining some of the problems in the field. Popper's basic answer, which Salmon doesn't comment on in that quote, is to use critical discussion to criticize ideas. That's how you rationally choose between conjectures.
> How does the hard-to-vary criterion sneak induction back it?
I had a little write up here. I posted this to twitter which started this discussion.
https://docs.google.com/document/d/17chWJ2M0HlD47FFt1ZxsZr6Ogf6K-LW5-dGOfdxBxao/edit
> So when you speak of a representative sample, the first question is: representative in which ways and why those ways? Representative in *all* ways is impossible, so you need to specify.
It's laid out in the specification of the theory that we we wish to test. The theory specifies what we are looking for (what counts as a sample). It is here that I would say we specify in what ways our sample will be representative.
> If you don't know what "begging the question" means, don't say it. Say normal words that explain what you mean. Throughout this discussion you've been making incorrect claims related to logic jargon and formulas and they're causing ongoing problems.
I do know what it means. The circularity I see is something like this: 'The anomaly explanation is bad, not because it lacks inductive support (justification), but because it is a bad explanation'. The premise assumes the conclusion.
> What we need is a non-refuted explanation.
> re Salmon paper, he does a decent job explaining some of the problems in the field. Popper's basic answer, which Salmon doesn't comment on in that quote, is to use critical discussion to criticize ideas. That's how you rationally choose between conjectures.
Yes, we use critical discussion, but what Salmon points out is that the tools that Popper allows into critical discussion (level of corroboration, etc) are insufficient for choosing between conjectures when it comes to "practical prediction".
Do you plan to respond to the rest of my response?
> It's laid out in the specification of the theory that we we wish to test. The theory specifies what we are looking for (what counts as a sample). It is here that I would say we specify in what ways our sample will be representative.
Let's say my example theory is "Minimum wage laws are bad." I take it you think the correctness of this claim should be settled by testing with data samples (I don't). Where does this theory specify what counts as a representative sample? Or do you think this theory is no good and want to propose a similar theory that includes a specification?
> Do you plan to respond to the rest of my response?
No, I plan to do one or two things at a time and keep them short. Say up to one thing and respond to up to one thing. You can bring things up again one at a time to get responses.
> Let's say my example theory is "Minimum wage laws are bad." I take it you think the correctness of this claim should be settled by testing with data samples (I don't). Where does this theory specify what counts as a representative sample? Or do you think this theory is no good and want to propose a similar theory that includes a specification?
So if I understand your example correctly it implies something like “In any economic system, the establishment of minimum wage laws (in isolation to any other changes) does more harm than good”. So the samples would be those economic systems that have had minimum wage laws introduced. What we expect this sample to be representative of is the outcome of the new laws (did things get better or worse?). We assume these past samples will be representative of future samples unless we have some other existing knowledge that tells us otherwise.
> No, I plan to do one or two things at a time and keep them short. Say up to one thing and respond to up to one thing. You can bring things up again one at a time to get responses.
If I could bring up just one more point, I would like you to please elaborate on how Popper’s “critical discussion” is an answer to the problems raised by Salmon.
> We assume these past samples will be representative of future samples unless we have some other existing knowledge that tells us otherwise.
Wait, you take *any* economic system you happen to have on hand for data, use that as a sample, and then *assume* its representative unless you know a reason it's not? Why? I would, by default, assume our experience with something is *not* representative of all possible experiences. And you haven't provided something like criteria of representativeness which I could criticize some data for failing to satisfy, so there's no guidance for what sort of criticism you'd accept.
> If I could bring up just one more point, I would like you to please elaborate on how Popper’s “critical discussion” is an answer to the problems raised by Salmon.
Please link your sources in the future. The Salmon paper, titled "Rational Prediction", is:
http://www.homepages.ucl.ac.uk/~ucessjb/Salmon.pdf
> This view of corroboration holds serious difficulties. Watkins and Popper agree, I take it, that statements which report observations of past and present events do not, in and of themselves, have any predictive content. Moreover, they maintain, statements about the corroboration of conjectures do not, in and of themselves, have any predictive content. Conjectures, hypotheses, theories, generalisations-call them what you will-do have predictive content. The problem is that there are many such statements, rich in predictive content, which make incompatible predictive claims when conjoined with true statements about past and present occurrences. The fact that a general statement has predictive content does not mean that what it says is true. In order to make a prediction, one must choose a conjecture which has predictive content to serve as a premise in a predictive argument. In order to make a rational prediction, it seems to me, one must make a rational choice of a premise for such an argument. But from our observational evidence and from the statements about the corroboration of a given conjecture, no predictive appraisal follows. Given two conjectures which, in a particular situation, will lead to incompatible predictions, and given the corroboration ratings of these two hypotheses, nothing follows about their comparative predictive capacities. Thus, it seems to me, corroboration-the ground for theoretical preference-furnishes no rational basis for preference of one conjecture to another for purposes of practical prediction. I am not complaining that we are not told for sure that one will make a correct prediction and that the other will not. I am complaining that no rational basis whatever has been furnished for a preference of this type.
OK a few points about this.
1) We can drop "corroboration" entirely from CR without losing the important content of CR (in very short, the evolutionary epistemology and the refutation of induction). I do not care about defending corroboration.
2) CR's solution to this problem is *critical discussion*. It's creative, imaginative critical thinking/discussion, the seeking out of errors, which enables us to make progress. Focusing on math and formal logic blinds some philosophers to what most actual productive discussions are like. In short, we can't have perfect foundations (like criteria for good arguments or errors/criticisms) so instead in discussions we find some points of agreement (many are just assumed as background knowledge, rather than actively found) and use those as foundations (though we may change our mind midway and question them). The issue is not can we prove a particular method of arguing is good, but does anyone suspect it of being an error and object? And the issue is not can we create a complete system from the ground up, but can we agree on enough premises to have a productive conversation right now.
3) Although CR has some good ideas about this stuff which are *not known to be wrong* (in contrast to other epistemologies which make wrong claims, which are indefensible in argument, rather than merely being incomplete), there is certainly room to develop CR further and make it more helpful. The topic area in the Salmon quote is a particularly good place to improve CR further, which I have done in Yes or No Philosophy.
> Wait, you take *any* economic system you happen to have on hand for data, use that as a sample, and then *assume* its representative unless you know a reason it's not? Why? I would, by default, assume our experience with something is *not* representative of all possible experiences. And you haven't provided something like criteria of representativeness which I could criticize some data for failing to satisfy, so there's no guidance for what sort of criticism you'd accept.
I see it as a natural assumption that humans are making when reasoning inductively. The more you allow your sample to be representative, the more applicable your knowledge, but the less secure your inference. I believe it is fundamental to our reasoning to not consider our experience as exceptional (unrepresentative) unless we have reason to believe so.
The criteria for representativeness is in the theory. If you give a vague theory and don’t define your terms, then the criteria is ambiguous and open to misinterpretation by those who test it. If you define clearly what you mean by “minimum wage laws”, and “bad”, then it is clear what counts as a sample, what a success/failure looks like, etc. Maybe you have something else in mind when you say “Criteria of representativeness”?
> 2) CR's solution to this problem is *critical discussion*. It's creative, imaginative critical thinking/discussion, the seeking out of errors, which enables us to make progress. Focusing on math and formal logic blinds some philosophers to what most actual productive discussions are like. In short, we can't have perfect foundations (like criteria for good arguments or errors/criticisms) so instead in discussions we find some points of agreement (many are just assumed as background knowledge, rather than actively found) and use those as foundations (though we may change our mind midway and question them). The issue is not can we prove a particular method of arguing is good, but does anyone suspect it of being an error and object? And the issue is not can we create a complete system from the ground up, but can we agree on enough premises to have a productive conversation right now.
Mmmm… So what if the foundational premises that we agree on are such that induction can proceed? This is my understanding of the situation. You claim you do not rely on inductive reasoning, so I would need to see how you reason in favour of one prediction over another without invoking induction or Popper’s idea of corroboration.
#15716: Kieren, have you seen https://yesornophilosophy.com/argument ?
This explains how decision making works on refuted and unrefuted ideas in a boolean way, with no degrees of certainty or probability required.
I have read that article. Yes/No is still based on argument and criticism. Induction is a type of reasoning/inference. So I would need to see how criticism can be performed without ever relying on induction.
For example. If someone claims that eating grass prevents pneumonia from the Corona virus. We might criticize this idea by saying they have no cases to show where this was true, but this means we are asking for an inductive justification.
We don't actually need any cases to ask for or analyze an explanation of how grass would prevent pneumonia. We could criticize the explanation, and only one of the criticisms might be that it hasn't been tested yet. But we might dismiss it long before testing it simply if we can refute the given explanation
> The criteria for representativeness is in the theory.
Give an example of appropriate criteria in a pro or anti minimum wage theory.
> Mmmm… So what if the foundational premises that we agree on are such that induction can proceed? This is my understanding of the situation. You claim you do not rely on inductive reasoning, so I would need to see how you reason in favour of one prediction over another without invoking induction or Popper’s idea of corroboration.
You proceed by criticizing stuff. Look for errors. (You aren't being specific enough and anyway I have a ton of writing covering this general area, including in the blog post above.)
> We don't actually need any cases to ask for or analyze an explanation of how grass would prevent pneumonia. We could criticize the explanation, and only one of the criticisms might be that it hasn't been tested yet. But we might dismiss it long before testing it simply if we can refute the given explanation
But can you do it in every instance of criticism without ever using induction?
How sure are you that none of your prior knowledge that you rely on for your criticism hasn't been established by induction?
> Give an example of appropriate criteria in a pro or anti minimum wage theory.
Not sure I know what you want. My criteria for what a minimum wage law is would a definition of what a minimum wage law is. See wikipedia for such a definition, etc.
> You proceed by criticizing stuff. Look for errors. (You aren't being specific enough and anyway I have a ton of writing covering this general area, including in the blog post above.)
So we have infinite theories that explain the same things about the past, but which differ in their predictions of the future. When we need to make a prediction, which of these theories do we choose?
You would need to have some kind of general criticism that can refute infinite of these theories such that you have just one theory remaining. What is this general critisism?
> Not sure I know what you want. My criteria for what a minimum wage law is would a definition of what a minimum wage law is. See wikipedia for such a definition, etc.
Wikipedia doesn't give you criteria to judge what is a representative sample of minimum wage laws, nor what is a representative sample of cities/states/locations where the laws could be tested.
> So we have infinite theories that explain the same things about the past, but which differ in their predictions of the future. When we need to make a prediction, which of these theories do we choose?
Do critical thinking to decide. Can't decide without knowing what the theories actually are and thinking about them. Yes you have to find patterns of error – criticize categories instead of only individual ideas.
Look maybe you should try this: find a quote from CR writing (let's say a DD book or Popper selection from http://fallibleideas.com/books#popper ) and point out a way you think it's clearly, factually false.
> Wikipedia doesn't give you criteria to judge what is a representative sample of minimum wage laws, nor what is a representative sample of cities/states/locations where the laws could be tested.
The definition tells you what counts as a minimum wage law. It is up to you to try and get a random sample. We have already established the difficulty in obtaining such a sample. I accept it as a limitation of this type of reasoning, but it is not fatal. Even an approximately random sample is useful, and we correct for errors as our sample size grows in the future, and as we identify important biases in our sample.
>> So we have infinite theories that explain the same things about the past, but which differ in their predictions of the future. When we need to make a prediction, which of these theories do we choose?
> Do critical thinking to decide. Can't decide without knowing what the theories actually are and thinking about them. Yes you have to find patterns of error – criticize categories instead of only individual ideas.
Any theory that explains some past phenomena, and which makes predictions of the future has infinite variations which vary only in what they say about the future. For example, the theory that DD will float tomorrow is a variation on the theory of gravity. Do you have a general criticism to refute these infinite theory's which all predict arbitrary, exceptional occurrences in the future?
> Look maybe you should try this: find a quote from CR writing (let's say a DD book or Popper selection from http://fallibleideas.com/books#popper ) and point out a way you think it's clearly, factually false.
It would not be just a single quote from Popper. It would be at least two. It would be where he denies our use of induction, and where he claims to have a criteria for choosing the best available theory.
When I say two quotes from Popper. I mean that they aren't false by themselves, but together lead to contradiction.
#15736 >> Look maybe you should try this: find a quote from CR writing (let's say a DD book or Popper selection from http://fallibleideas.com/books#popper ) and point out a way you think it's clearly, factually false.
>
> It would not be just a single quote from Popper. It would be at least two. It would be where he denies our use of induction, and where he claims to have a criteria for choosing the best available theory.
Pointing out a factual error doesn't require two quotes. For example, you know the sentence "All penguins have red feathers." is false without having two quotes to compare.
I mean that Popper holds the two positions.
1) Induction is not used by CR.
2) CR accounts for how we choose between theories for making predictions.
On their own they may not be false, but I find them in contradiction because I believe induction is required for choosing between theories.
#15739 How does induction help one choose between theories? Does induction help one figure out if a theory solves a problem or not?
Kieren, you seem to be ignoring that I specified a *factual* falsehood, and I don't think you understand the purpose that I had in mind. So I'll explain it. The point is basically to find the most isolated, self-contained error that you think is important. We want the error that's easiest to discuss and reach a conclusion about. Factual errors are particular good for self-contained evaluation *and* are particularly good for objective evaluation.
The disagreement you're trying to bring up is on the far end of the spectrum. It's highly not-self-contained, complex, hard to evaluate objectively, and also it involves multiple frameworks at the same time. It's a lot easier to discuss a within-framework error in CR than a clash between frameworks. You aren't talking about a direct logical contradiction between two CR ideas, you're talking about them leading to conclusions that, using many auxiliary arguments that CR disagrees with (like that induction actually works at all), end up conflicting. I'd only want to discuss framework clash if you had already granted things like that CR has no factual errors, no logical errors, no within-framework errors, etc.
If the (1) and (2) really conflict, then at least one is wrong, and so the way CR reaches it should contain a smaller and more self-contained error that you could point out.
Bigger picture, you come off as not very familiar with what CR says and not really that interested in learning about CR or FI ideas. You seem like you're trying to debate stuff prior to knowing much about what it says or why, in which case IMO you should be undecided on its correctness.
> #15739 How does induction help one choose between theories? Does induction help one figure out if a theory solves a problem or not?
Induction lets us identify differing levels of support for our theories. E.g. If we have two medical treatments to choose from, with all else being equal, we would choose the one which has had the most success in the past.
> If the (1) and (2) really conflict, then at least one is wrong, and so the way CR reaches it should contain a smaller and more self-contained error that you could point out.
Assuming (1) then, I will try and show the error of (2). This would be a within-framework error (internal contradiction of CR).
So one way Popper attempted to account for practical prediction was through his theory of verisimilitude. Similar to my medical examples (where we want to choose the best of two known-to-be-false theories), Popper mentions the social sciences. See quote below from Popper’s ‘Conjectures and Refutations’.
>>“Ultimately, the idea of verisimilitude is most important in cases where we know that we have to work with theories which are at best approximations—that is to say, theories of which we actually know that they cannot be true. (This is often the case in the social sciences.) In these cases we can still speak of better or worse approximations to the truth (and we therefore do not need to interpret these cases in an instrumentalist sense).”
I’m not sure if I have to add any more criticism to Popper’s theory of verisimilitude then apart from the fact that it was found to fail for these “most important cases”. It is tied up with his theory of corroboration which you seem to think we can do without. So I will not try and show how Popper sneaks induction back into his epistemology with his corroboration/verisimilitude.
However. Popper had tried to solve the problem of practical prediction with his theories of verisimilitude and corroboration, and so I wonder what your alternative solution to this problem is? Your response seems to be the same as Popper; that critical discussion can achieve this without the use of induction. You have not demonstrated this as Popper at least tried.
In Popper’s ‘Objective Knowledge’ we see quotes like the following.
>>“The critical discussion can never establish sufficient reason to claim that a theory is true; it can never 'justify' our claim to knowledge. But the critical discussion can, if we are lucky, establish sufficient reasons for the following claim:'This theory seems at present, in the light of a thorough critical discussion and of severe and ingenious testing, by far the best (the strongest, the best tested) ; and so it seems the one nearest to truth among the competing theories .'”
This quote seems to suggest that all else being equal, the theory which has survived the most falsification attempts is the one to be preferred. This seems to me a principle of induction. It reads like ‘The rational preference is for the theory which has made more correct predictions in the past’. This contradicts my point (1) if it is the case.
Mostly I’m just now interested in your solution to the problem of practical prediction. It’s not clear to me how it works without essentially resulting in the use of inductive inferences.
#15927 Do you think you know what evolution has to do with CR and with knowledge?
#16113
Yes I believe so; ideas as replicators that go through the process of variation (conjecture), and selection (criticism).
Information + evolution = knowledge
Evolution adapts information to a purpose.
Knowledge is purpose-having information. (Solving a problem is a purpose.)
Yes?
I think I follow, yes.
So how does induction create knowledge? Does induction do or involve evolution or adaptation? Is induction unable to create this kind of knowledge, but it creates a different kind of knowledge (what kind)?
Before we diverge, could I get a reply to my previous response? In particular, do you provide an alternative to Popper's theories of corroboration/verisimilitude, or do you not think the problem he was trying to solve with these is actually a problem?
> In particular, do you provide an alternative to Popper's theories of corroboration/verisimilitude, or do you not think the problem he was trying to solve with these is actually a problem?
Popper himself already provided an alternative to those: judging ideas by critical discussion/thinking. Popper (particularly early on) attempted to formalize that and make some points more specific and mathematical. If you reject that formalization, it doesn't leave any gap in CR. You still have the broad answer, the big picture, the overall explanation of what to do and why, as well as dozens of other particulars Popper gave. There's certainly room to fill in more details and give more guidance on various specifics, as there is with every area of CR. That's something I work on.
Do you understand the problem I have with your "broad answer"? I will try to spell it out a bit below.
Popper claims to provide an epistemology that is free from induction, and that can account for how we choose between theories for practical action. Therefore, he will need to give an account of theory choice that is explicitly induction-less. The broad answer "critical discussion/thinking" does not explicitly rule out induction, because for all we know your "critical discussion/thinking" could involve inductive inferences.
It concerns me when Popperians claim we do not use induction, but then I see them approaching inductive inferences when they attempt to account for theory choice; often referencing corroboration, verisimilitude, hard-to-vary, etc.
So it doesn't sound like you have a general account of theory choice that you can demonstrate as induction-less? For example, how do we choose between two known-to-be-false theories?
Induction is excluded from critical discussion and critical thinking (the broad CR answer for choosing between theories) because it's a myth which is impossible to do (unless you redefine the word "induction" to dramatically change the meaning from the variety of standard and traditional meanings that Popper criticized and rejected – I mention this because it's fairly common for inductivists to do substantial redefining and IIRC I haven't found your statement of what induction is to be adequately clear.) Popper gave multiple extensive arguments covering this.
So we (CRists) don't have to be more specific about theory-choice in order to say induction isn't part of it, since we already, separately, excluded induction from all of thinking.
Re an induction alternative, CR offers an explanation of how we can learn that doesn't explicitly rely on induction and has no fundamental/mysterious gaps where we'd need a breakthrough to see how it could even be possible that it works. That's enough given also excluding induction from thinking entirely. We don't have to nail down every detail of everything to prove there's no induction anywhere because induction is literally impossible.
>Induction is excluded from critical discussion and critical thinking (the broad CR answer for choosing between theories) because it's a myth which is impossible to do (unless you redefine the word "induction" to dramatically change the meaning from the variety of standard and traditional meanings that Popper criticized and rejected – I mention this because it's fairly common for inductivists to do substantial redefining and IIRC I haven't found your statement of what induction is to be adequately clear.) Popper gave multiple extensive arguments covering this.
I don’t believe Popper demonstrated that it was impossible to perform an induction. I think he instead followed Hume in the conclusion that it is impossible to justify our inductive inferences without circularity, or other problems. Just because a type of inference is not justified, doesn’t mean it is impossible for someone to perform one.
Maybe I’m wrong and Popper did demonstrate that it is impossible to perform an induction. Any relevant chapter in one of his books where you think he demonstrated this?
If in fact Popper did not demonstrate this, then what is lacking is a demonstration that his epistemology is induction-less.
I found this on the Stanford Encyclopedia of Philosophy “The Problem of Induction” page (https://plato.stanford.edu/entries/induction-problem/). It is another way of stating the problem.
>>Popper’s account appears to be incomplete in an important way. There are always many hypotheses which have not yet been refuted by the evidence, and these may contradict one another. According to the strictly deductive framework, since none are yet falsified, they are all on an equal footing. Yet, scientists will typically want to say that one is better supported by the evidence than the others. We seem to need more than just deductive reasoning to support practical decision-making (Salmon 1981). Popper did indeed appeal to a notion of one hypothesis being better or worse “corroborated” by the evidence. But arguably, this took him away from a strictly deductive view of science. It appears doubtful then that pure deductivism can give an adequate account of scientific method.
#16228
> I don’t believe Popper demonstrated that it was impossible to perform an induction. I think he instead followed Hume in the conclusion that it is impossible to justify our inductive inferences without circularity, or other problems. Just because a type of inference is not justified, doesn’t mean it is impossible for someone to perform one.
What do you think induction can be used for and how does one implement it?
> Maybe I’m wrong and Popper did demonstrate that it is impossible to perform an induction. Any relevant chapter in one of his books where you think he demonstrated this?
What have you read and not read from this list? http://fallibleideas.com/books#popper
Note the entire list, both best and second best, is 538 total pages – a lot shorter than some of Popper's individual books. It's a reasonable amount to read to know about Popper.
> If in fact Popper did not demonstrate this, then what is lacking is a demonstration that his epistemology is induction-less.
Side point:
An epistemology which is not 100% completely specified (as no ideas ever are), but has no *known* induction anywhere in it, would still be notable.
A scenario like "We didn't search every possible location (because there are trillions or infinitely many), but we searched a lot and didn't find it yet." is meaningful.
> What have you read and not read from this list? http://fallibleideas.com/books#popper
> Note the entire list, both best and second best, is 538 total pages – a lot shorter than some of Popper's individual books. It's a reasonable amount to read to know about Popper.
To begin with, I have read (not front to back) a number of Popper's books; "Conjectures and Refutations", "Logic of Scientific Discovery", and "Objective Knowledge". I have focused especially on the chapters that deal with his solution to the problem of induction, theory appraisal, probability, corroboration, and practical theory choice.
I can't recall Popper demonstrating the impossibility of performing an induction, only his demonstration of the impossibility of justifying an induction. I’m having a look through Popper’s “Realism and the Aim of Science” now because you list it under Popper’s best, but so far it looks like more of the same.
Any particular chapter (quotes would be great!) where you think Popper provides this argument?
> Side point:
> An epistemology which is not 100% completely specified (as no ideas ever are), but has no *known* induction anywhere in it, would still be notable.
> A scenario like "We didn't search every possible location (because there are trillions or infinitely many), but we searched a lot and didn't find it yet." is meaningful.
Take what you just said as an example. Are you not accepting/believing the truth-likeliness of the conclusion that your epistemology is induction-less, based on the premise that the past sample of arguments that you analysed were found to be induction-less?
#16230
> What do you think induction can be used for and how does one implement it?
Inductive arguments can be used to infer the approximate truth, truth likeliness, or belief in a theory based on the past success of the theory. It can be used to decide between multiple theories (e.g. which medical treatment to use) based on one theory's greater success. Therefore, it can be used to solve the problem of theory choice that Popper struggled with.
You start with premises that tell you that you have a representative sample of predictions derived from your theory, and the level of success that these predictions have had during testing. With an inductive argument you then conclude that your theory approximates the truth. Unlike deductive arguments; if the premises of an inductive inference are true, it does not necessitate that the conclusion is true.
In my stream today, a little after 2 hours in, i read and comment on Alan’s relevant post “Salmon on rational prediction”
Do you plan on answering my previous question?
>I can't recall Popper demonstrating the impossibility of performing an induction, only his demonstration of the impossibility of justifying an induction. I’m having a look through Popper’s “Realism and the Aim of Science” now because you list it under Popper’s best, but so far it looks like more of the same.
>Any particular chapter (quotes would be great!) where you think Popper provides this argument?
Also, I found your sports example inductive. If I spell it out:
1) X is a sample of the results from trying out a new sports play.
2) X shows the play had success 40% of the time.
3) Therefore, X will will continue to work approximately 40% of the time.
Haven't read your comments yet but I wrote this on 2020-04-02, didn't get around to working on it more but maybe it'll help:
---
Summary involving some guesses:
You associate induction with statistics.
You have many ideas about statistics.
Some of your ideas about statistics are basically correct and useful. But some are wrong and don’t work.
You conclude: Even if some of your ideas about statistics are flawed, *some of that stuff does work*. It isn’t all wrong. It isn’t thoroughly wrong.
I agree with the reasonableness of that judgment and the conclusion. While some particular ideas are broken, statistics isn’t thoroughly wrong or refuted.
You further conclude that therefore induction works, at least some inductive stuff to some extent. Because you associate induction and statistics.
Here I disagree. Lots of statistics has nothing to do with induction. Careful analysis of which parts of statistics are broken, and which parts are related to induction, will show that all the working stuff is non-inductive. But that analysis will require, first, better understanding and specifying what induction is. You need to be able to tell what counts as induction, or not, before you can do the analysis. Popper has sophisticated views on this matter that fit the history of philosophy and fit the views of other philosophers he talked with. However, due to Popper’s criticisms of induction, a lot of the response has been to start redefining induction or making it more vague or broad. So today a lot of people don’t have a good grasp of the meaning of induction that Popper and his predecessors and opponents largely agreed on, which is the thing Popper refuted. Popper’s refutations also have lots of applications to other similar claims, but there are also some kinda similar looking claims that are not refuted and which CR people do not consider inductive. Until you understand the distinction of what CR considers induction or not and why, you aren’t in a position to even judge whether you agree that “induction” (as CR sees it) is refuted.
One of the major inductive ideas is that the future will (or is likely to) resemble the past. Another is that correlations hint as causations. Another is that we can induce conclusions (that are likely to be true or whatever) from raw data without intellectual interpretation – just look at the patterns in the data for guidance. Another is that “evidence X supports conclusion Y” is a reasonable, coherent and useful concept. Another (older) inductive idea is that if we get rid of biases and preconceptions, and empty and open our mind and observe, we can learn the truth that way. These are some of the things that CR refuted. Understanding the extent and applications of these ideas, and what else is similar to them (so you can recognize the wide variety of variants of them), and how they are connected to each other, is a significant undertaking.
> I have read (not front to back) a number of Popper's books; "Conjectures and Refutations", "Logic of Scientific Discovery", and "Objective Knowledge". I have focused especially on the chapters that deal with his solution to the problem of induction, theory appraisal, probability, corroboration, and practical theory choice.
> I can't recall Popper demonstrating the impossibility of performing an induction, only his demonstration of the impossibility of justifying an induction. I’m having a look through Popper’s “Realism and the Aim of Science” now because you list it under Popper’s best, but so far it looks like more of the same.
Can you point out any topical error in any of this material, especially one with major consequences for what conclusions to reach? Or do you broadly accept what Popper says and just don't see how it's incompatible with induction?
> Are you not accepting/believing the truth-likeliness of the conclusion that your epistemology is induction-less, based on the premise that the past sample of arguments that you analysed were found to be induction-less?
That doesn't resemble my reasoning. I reject induction due to logical arguments criticizing it.
> You start with premises that tell you that you have a representative sample of predictions derived from your theory
Do you agree with me that if you take any subset/sample of a set, the subset/sample is always unrepresentative in some respects?
> Can you point out any topical error in any of this material, especially one with major consequences for what conclusions to reach? Or do you broadly accept what Popper says and just don't see how it's incompatible with induction?
As I said earlier. I think Popper showed the impossibility of justifying induction, but I don't believe he demonstrated the impossibility of performing an induction.
My view is that induction is a natural way in which humans reason about the world/reality. Under this view it is not necessary for induction to be justified as absolutely true. Instead induction is a part of our reasoning, and is used to do the justifying.
Do you know of anywhere in Popper's writing where he demonstrates the impossibility of performing an induction?
>> You start with premises that tell you that you have a representative sample of predictions derived from your theory
> Do you agree with me that if you take any subset/sample of a set, the subset/sample is always unrepresentative in some respects?
Yes. What does this mean then?
>> Can you point out any topical error in any of this material, especially one with major consequences for what conclusions to reach? Or do you broadly accept what Popper says and just don't see how it's incompatible with induction?
> As I said earlier. I think Popper showed the impossibility of justifying induction, but I don't believe he demonstrated the impossibility of performing an induction.
> My view is that induction is a natural way in which humans reason about the world/reality. Under this view it is not necessary for induction to be justified as absolutely true. Instead induction is a part of our reasoning, and is used to do the justifying.
> Do you know of anywhere in Popper's writing where he demonstrates the impossibility of performing an induction?
Yeah but hold on, let me try asking my question again in a different way.
When you read Popper, was your general impression the following:
You agreed with most of it. You didn't find a bunch of logic errors, wrong facts, bad arguments, etc. Like most paragraphs are fine, you agree, no objections.
Your issue is a mix of 1) disagreeing with a few big picture points which you don't see as implied by the various detail arguments 2) maybe you also didn't even see a few big picture points as present or claimed at all that i think are there.
is that right?
i'm trying to differentiate this from a situation of someone who thinks lots of what Popper said is wrong, many errors all over, disagree with many sentences, etc. i think you just have a few disagreements but agree with most of the parts that you know of. but i wanna confirm that before proceeding.
>>> You start with premises that tell you that you have a representative sample of predictions derived from your theory
>> Do you agree with me that if you take any subset/sample of a set, the subset/sample is always unrepresentative in some respects?
> Yes. What does this mean then?
It means that "a representative sample" is underspecified or under-defined or something. It doesn't have a clear meaning without more elaboration about e.g. representative in what respects/traits/dimensions. So saying "you have a representative sample" is either wrong or incomplete.
> Yeah but hold on, let me try asking my question again in a different way.
> When you read Popper, was your general impression the following:
> You agreed with most of it. You didn't find a bunch of logic errors, wrong facts, bad arguments, etc. Like most paragraphs are fine, you agree, no objections.
> Your issue is a mix of 1) disagreeing with a few big picture points which you don't see as implied by the various detail arguments 2) maybe you also didn't even see a few big picture points as present or claimed at all that i think are there.
> is that right?
> i'm trying to differentiate this from a situation of someone who thinks lots of what Popper said is wrong, many errors all over, disagree with many sentences, etc. i think you just have a few disagreements but agree with most of the parts that you know of. but i wanna confirm that before proceeding.
Yes that seems quite right. A mixture of 1) and 2).
There are certainly times when I am reading Popper and I feel like he has the wrong idea about something (such as his writings about Hume). However, these are not significant issues that I can't charitably tolerate, and I am still able to follow his main arguments despite them.
> It means that "a representative sample" is underspecified or under-defined or something. It doesn't have a clear meaning without more elaboration about e.g. representative in what respects/traits/dimensions. So saying "you have a representative sample" is either wrong or incomplete.
Right.
My view is that our theory tells us in what ways the sample needs to be representative.
E.g.
If I have a theory that says "all of the beans drawn from this bag are blue", then the theory tells us that the sample will need to be representative of the colour of the beans drawn from the bag.
We had this discussion earlier. It ended with my response:
>>The definition tells you what counts as a minimum wage law. It is up to you to try and get a random sample. We have already established the difficulty in obtaining such a sample. I accept it as a limitation of this type of reasoning, but it is not fatal. Even an approximately random sample is useful, and we correct for errors as our sample size grows in the future, and as we identify important biases in our sample.
If you need footnotes for a claim, please mention them upfront instead of making incomplete statements that you expect me to object to.
But this footnote doesn't solve the issue. Saying what is in set X does not define what is a "representative" sample from set X.
An example of defining a "representative sample" is: The set is swans. I claim 90% of swans are black. I define a "representative" sample of swans as any subset of swans where 88% more are black.
A different definition of representative would be if the percentage of black swans in the sample was within 5% of the percentage of black swans in the full set – that'd be a sample that's representative *with respect to black color percentage* (a specific way of looking at a specific trait) but it's not representative in general (there's no such thing). With the second definition, you have to already know the true value before you can judge whether a set is representative.
A random sample is a different matter than a representative sample. It is both useful and problematic in different ways. You need to differentiate between the two concepts.
When you talk about biases in the sample you're also missing the same point as above: all samples are biased in some respects and representative (unbiased) in other respects. There is no such thing as an unbiased sample in general anymore than a representative sample.
g2g so will put off replying re what popper says about induction until later. is any of this stuff about representative sets making sense to you? it's closely related to what's wrong with induction.
Sorry for the delay. Got lost in one of my hobbies for a couple months.
Ok, I see what you are getting at. It is a question of how we can know if our sample is representative in those respects that we care about.
My understanding is that an induction usually runs with the premise that we have a random, or essentially random sample of the given phenomena. Logically it follows from this premise that such a sample would lead us right more often than not.
So what do I mean by "essentially random", well I’m not so sure how well I can currently describe this, but I will try. For games of chance, or other well understood physical phenomena, we have a clear idea of what is required for a random sample (rolling a dice 30 times, etc), but for more complicated phenomena, such as involved when learning a new skateboard trick, or understanding a social dynamic, etc, then it becomes less clear what is a fair random sample of the phenomena. However, In all cases it seems that we rely on our background knowledge to judge (deduce) the randomness of a sample.
For example, let's say I decide to try and concentrate on throwing myself higher in the air when trying to perform a skateboard trick (in an effort to improve my execution). After a few attempts at this I might conclude that this technique does indeed improve my execution of the trick. My conclusion here is based on the assumption that I have just witnessed a practically, or an “essentially random” sample of the uses of this technique. One reason why I believe this is a random sample is because I might have learned many other ticks and skills in the past in a similar manner. My background knowledge in such a case is something like ‘Focusing my mind on adjusting the movement of my body during the execution of a skill/trick usually has a direct and consistently repeatable outcome on the success of the execution’. So from this I deduce that I would likely be getting a practically random sample of the phenomena (practical for my purposes of improving my execution of this trick, not for predicting the outcome of all such uses of this technique from now and until the end of the universe).
> However, In all cases it seems that we rely on our background knowledge to judge (deduce) the randomness of a sample.
This is a concession that we don't and can't learn by induction and that CR is right. I don't think you're very clear on 1) what inductivist philosophy says 2) what CR says
re the skateboard trick, you had a causal understanding of why the technique might work before you tried it. then when you tried it several times, you e.g. observed that none of the trials contradicted your causal understanding – you never got results out of line with your mental model like going way higher or lower than expected. your mental model has some approximations, estimates, etc., instead of being totally precise. in the context of having an explanatory understanding of what's going on and what data is relevant, then having a several data points helps you improve those estimates.
> This is a concession that we don't and can't learn by induction and that CR is right.
I do not see how you conclude this.
> re the skateboard trick, you had a causal understanding of why the technique might work before you tried it. then when you tried it several times, you e.g. observed that none of the trials contradicted your causal understanding – you never got results out of line with your mental model like going way higher or lower than expected. your mental model has some approximations, estimates, etc., instead of being totally precise. in the context of having an explanatory understanding of what's going on and what data is relevant, then having a several data points helps you improve those estimates.
As well as multiple data points helping me improve the accuracy of my mental model, they have also importantly told me that this technique works at all. Before I try such a technique I may only have a vague intuition that it might help, but I wouldn't say "I know it works" until I have tried it multiple times.
>>> However, In all cases it seems that we rely on our background knowledge to judge (deduce) the randomness of a sample.
>> This is a concession that we don't and can't learn by induction and that CR is right.
> I do not see how you conclude this.
It contradicts the claim that we induce theories from data by saying that we rely on [something other than data] in order to deal with data.
>>>> However, In all cases it seems that we rely on our background knowledge to judge (deduce) the randomness of a sample.
>>> This is a concession that we don't and can't learn by induction and that CR is right.
>> I do not see how you conclude this.
> It contradicts the claim that we induce theories from data by saying that we rely on [something other than data] in order to deal with data.
I disagree.
There are premises involved in an inductive argument (e.g. the sample is practically random) as there are in a deductive arguments too. The background knowledge I'm talking about are speaking to these premises.
For example. In the deductive argument.
1) All dogs bark
2) Spot is a dog
3) Therefore, dog barks
It would be our existing background knowledge that we use to judge whether premises 1 and 2 exist.
BTW, there was a question I didn't really get an answer to, but I would like one.
> Do you know of anywhere in Popper's writing where he demonstrates the impossibility of performing an induction?
#16821
>For example. In the deductive argument.
>1) All dogs bark
>2) Spot is a dog
>3) Therefore, dog barks
??????????????????????
This doesn't seem like a deductive statement. This just seems like all dogs bark therefore all dogs bark. It's just tautology and and it doesn't use the Spot is a dog premise in the conclusion. Did you mean:
P1) All dogs bark
P2) Spot is a dog
C1) Therefore, Spot barks
#16823
Yes, error in the conclusion. It should be:
3) Therefore, spot barks.
#16821 You said induction relies on the background knowledge necessary to figure out how representative a sample is. That means major, prior understanding of the field before you even try to use induction to do anything. Understanding what's representative in the field is basically the whole ball game that induction deals with. That's basically the thing induction is claiming to offer. Induction is supposed to tell us that the sun rising tomorrow is highly representative, rather than use that as a premise to say "given that we already non-inductively figured out that the sun rising tomorrow is highly representative, it's likely to happen".
And induction further alleges that it does its job without creative, critical or intelligent thought because it's supposed to explain how those work rather than rely on them. By allowing such major background knowledge, which comes from prior rational thinking, you're violating this and ruining induction as an explanation of how thinking works. You're changing induction into a mere thinking technique that intelligent beings can use sometimes, which gets rid of its claimed fundamentalness.
Again, you aren't familiar with either side of the debate and what the rival positions are, and that's our main problem.
This proposed (by you) use of background knowledge for induction doesn't compare with the background knowledge used by deduction. I can evaluate deductive arguments about singing, dogs or suns without having background knowledge about singing, dogs or suns. Deduction doesn't require field-specific prior knowledge.
#16822 For example in:
Realism and the Aim of Science
PART I. THE CRITICAL APPROACH
Chapter 1. Induction
Section 2. The Critical Approach: Solution of the Problem of Induction.
Sub-section VI
To help search for it, that section starts with:
> The critical approach which I have described here leads almost immediately to a straightforward solution of Hume’s problem of induction (1739).[11]
> Let us remember what Hume tried to show (in my opinion successfully, as far as logic goes).
Another one is
The World of Parmenides: Essays on the Presocratic Enlightenment
ESSAY 10
CONCLUDING REMARKS ON SUPPORT AND COUNTERSUPPORT
How induction becomes counterinduction, and the epagōgē returns to the elenchus
---
One can also state the refutation of induction in a sentence, e.g.: All finite data sets can be generated from infinitely many different functions.
In other words, the idea that we learn by spotting the patterns in our data is wrong because all data sets fit infinitely many patterns.
The issue is the infinite ambiguity of data. So the inductive idea, that data guides us, is wrong, because data is infinitely ambiguous.
There's also Russel's chicken story as well as Hume.
I think the issue is you have no clear idea what induction is, so you take refutations like helpful comments about what not to include in your conception of induction. If you committed to any particular version of induction, it'd either be refutable or compatible with CR (and poor terminology). But without a clear target, one can't offer you a refutation that will work for you.
> This proposed (by you) use of background knowledge for induction doesn't compare with the background knowledge used by deduction. I can evaluate deductive arguments about singing, dogs or suns without having background knowledge about singing, dogs or suns. Deduction doesn't require field-specific prior knowledge.
Take my example then:
1) All dogs bark
2) Spot is a dog
3) Therefore, Spot barks
How do you evaluate the first or second premise without any background knowledge?
You would require knowledge of what a dog is in order to determine whether Spot is a dog.
#16832 You don't deductively evaluate whether the first premise is true. Deduction doesn't do that. Deduction tells you whether the conclusion follows from the premises, not whether it's true.
from https://www.iep.utm.edu/val-snd/
>>A deductive argument is said to be valid if and only if it takes a form that makes it impossible for the premises to be true and the conclusion nevertheless to be false. Otherwise, a deductive argument is said to be invalid.
>>A deductive argument is sound if and only if it is both valid, and all of its premises are actually true. Otherwise, a deductive argument is unsound.
So when we are checking if the first and second premises are true we are checking if the argument is sound. Here you require background knowledge.
#16834 Yes, what's your point?
I was replying to this.
>This proposed (by you) use of background knowledge for induction doesn't compare with the background knowledge used by deduction.
So if you're now in agreement with me that we use background knowledge to evaluate the premises of both inductive and deductive arguments then we are led back to this exchange.
>>> However, In all cases it seems that we rely on our background knowledge to judge (deduce) the randomness of a sample.
>> This is a concession that we don't and can't learn by induction and that CR is right.
> I do not see how you conclude this.
#16836 You're lost. Deduction doesn't make the same claims as induction, so trying to parallel them like this won't help you. You're trying to lead the discussion but you're doing it pretty incoherently because, again, you are familiar with the claims of neither side of the debate that you're trying to debate. Do you want to study and learn? Do you have questions or curiosity, or are you just going to keep trying to incompetently win debating points instead of trying to understand the issues?
You need to take a step back and consider what the problem(s) to be solved are, then what the candidate solutions are and how they solve those problems. Since you don't have a clear picture of this, the stuff you're saying is a mess.
You also didn't answer #16826
>You're lost. Deduction doesn't make the same claims as induction, so trying to parallel them like this won't help you.
Yes, deduction and induction are not the same things. I was only referring to the evaluation of their premises, which as you have now agreed, involves background knowledge (for both types of inference). My reason for bringing up deduction was to highlight how this is an uncontroversial aspect of arguments/inferences.
You had made the claim that the use of background knowledge is a concession that we can't learn by induction. That is what led us down this path. Please provide a new argument for your claim or retract it.
I will review the texts you have referenced. Thank you for providing them.
#16843 You're trying to logically debate me, but you're incompetent at it, which is boring and tedious for me.
Here you make another claim without providing an argument.
It is important for me to be provided an argument for your claims, especially when you boldly conclude things that I don't agree with like "This is a concession that we don't and can't learn by induction and that CR is right".
Yes, following arguments carefully and logically might seem tedious, but that is the nature of philosophy.
Hit me up on twitter/discord if you find renewed interest in continuing this discussion.
#16845 I already argued many things with you. I presented a problem in need of solving here. You aren't providing a way of continuing which makes sense, and offers value, from my perspective. You seem neither interested in learning nor in problem solving about this. Suppose I go into detail on this an explain it to you and you concede, and I was simply right that you were confused. What will I get out of it?
Some more relevant posts:
https://curi.us/2124-critical-rationalism-epistemology-explanations
https://curi.us/1579-objectivist-and-popperian-epistemology
https://curi.us/1582-induction-is-wrong-a-lot
https://www.curi.us/1450-new-induction-disproof
https://curi.us/1580-false-dichotomies-package-deals-and-karl-popper
Another relevant post:
https://curi.us/2466-fallible-justificationism