This wrote this on an Objectivist discussion forum in 2013.
Observe what? There are always many many things you could observe. Real scientific observation is selective.
Perform which action? There are many many actions one could perform. Real scientific action is selective.
Which patterns? There's always many many patterns.
In each case, being selective requires complex (critical) thinking. Ideas come first. Induction is supposed to explain how thinking works, but actually presupposes it.
Merlin Jetton replied:
Okay. Give us your answer to these questions. Please give us simple methods that cover all possible cases. How do we delimit those infinitely many possible conjectures?
(Following Popper.) We don't run into all the same problems because we use different methods in the first place.
We don't start with observation, scientific experiment, or finding patterns. All of those come later, after you already have various ideas. Then you do them according to your ideas. This is not problematic in general. It is a problem when you say stuff is "step 1" that actually presupposes ideas, and then claim your set of steps is a solution in epistemology and is how we get ideas.
We have a different approach that is not like induction and avoids many of induction's problems. By using different methods some problems never come up. We never have the problem of figuring out what to observe before having ideas, for example, because we say ideas come first before observations.
How are ideas learned then? Not from observations. Ideas come first. That's not to say observations are excluded. Observations are very useful. But first you need some ideas. Then you can observe (selectively, according to your ideas about what is important, what is interesting, what is notable, what is relevant to problems of interest, what clashes with your expectations, etc, etc ... and if your way of observing doesn't work out you can improve it with criticism, you can change and adjust it) and use the observations to help with further ideas (in a critical role – they rule things out).
Now this is a hard issue and you haven't read the literature and don't be too ambitious about how much you expect to learn from a summary. But anyway, because it's hard I'm going to split it up. First we'll consider an adult who wants to learn something. Then we could talk about how a child gets started after. I'll save that for later if the adult explanation goes over OK. The child is the harder case. I think it's too much to do the child first, all at once.
So, one of Popper's insights is that starting places aren't so important. I'm guessing this sounds dumb to you, because you're a foundationalist and think you have to start with the right foundations/premises/basis and then build up from there, step by step, making sure not to introduce errors or contradictions as you go. And Popper criticized and rejected that approach and offered a significantly different approach.
So let me try to explain what Popper's approach is like. People make mistakes. People are fallible. Errors are common. People mess up all the time. This isn't skepticism. People also get things right, learn, acquire knowledge, make scientific progress, etc, etc... But it's important to understand how easy it is to make mistakes. Knowledge is possible but hard to come by. To get knowledge you have to put a ton of effort into dealing with the problem of mistakes. I think if you read this the right way, you could agree with it. Objectivism recognizes that lots of philosophies go wrong and using the right methods is important and makes a big difference and some stuff like that.
So, OK, error is common and a big part of epistemology and philosophy is how you deal with error. What are you going to do about it? One school of thought tries to avoid errors. You use the right methods and then you get the right answers. That sounds very plausible but I don't think it's the right approach. I'll try to talk about Popper's approach instead. Popper's approach is you do try to avoid errors but you're never going to avoid all of them in the first place. That's not the primary most important thing. Whatever you do, some errors are going to get through. What you really have to do is set up mechanisms to identify and correct errors.
Popper applied this approach widely. Take politics and political systems. One of Popper's big ideas about politics is that trying to elect the right ruler is the wrong thing to focus on. Electing the right guy is trying to avoid errors. Yes you should put some effort into that but you can't do it perfectly and it's not the most important issue. What is the most important issue? That errors can be identified and corrected. In politics that means if you elect the wrong guy you find out fast, and you can get rid of him fast and you can get rid of him without violence. Popper called the wrong approach the "Who should rule?" problem and said most political philosophy argues about who should rule, when it should be focussing a lot more on how to set up political systems capable of correcting mistakes about who gets to rule.
What about epistemology? "Which ideas should we start with?" is a bit like "Who should rule?" You're never going to get it perfect and it shouldn't be the primary focus of your attention. Instead you want to set things up so if you start with the wrong ideas you can find out about the mistake and fix it quickly, easily, cheaply.
error correction is (a lot) more important than starting in a good place. look at it another way. if you start in a bad place but keep making progress, after a while you'll get to a good place and keep going. but if you start in a good place but aren't correcting errors, there is no progress, things never get better, long term you're doomed. so error correction is the more crucial thing that you really need.
so how can adults be selective? how can they decide what scientific experiments to do or which actions and results to investigate? how can they decide what patterns to look for? answer: they already have ideas about that. they can use the ideas they already have. that's ok! they don't need me to tell them some perfect answer. i could give them some advice and there could be some value in it, but it doesn't matter so much. they should start with the ideas they already have, use those, and then if something goes wrong they can make adjustments to try to do something about it. (and they can also philosophically examine their ideas and try to criticize instead of waiting for something noticeable to go wrong.)
in one sense, we're both advocating the same thing. people can and do use the ideas they already have about how to be selective, what issues to focus on, which patterns are notable, and more. but we Popperians know that is what's going on, and know how to keep making progress from there even if people aren't great at it. inductivists on the other hand think they have this method from first principles that is how people think but actually it smuggles in all sorts of common sense and pre-existing ideas as unexamined, uncriticized premises. and that's a really bad idea. those premises being smuggled in are good enough to start with, but what you really need to do is examine and criticize them!
i have not addressed how children/infants get started. i also haven't explained how thinking works at a lower level. (being able to criticize and correct errors requires thinking. how is that done?). we can get to those next if what i'm saying so far goes over ok. also the very short answer for how thinking works is that evolution is the only known theory for how knowledge can be created from non-knowledge. human thinking, at a low level, uses an evolutionary process to create knowledge. (i mean thinking literally uses evolution, not metaphorically. and no i'm not saying you consciously do that).