I just listened to Peikoff's lectures on Aristotle. I also reread Popper's WoP introduction about Aristotle. some thoughts:
btw notice what's missing from the lecture descriptions: Parmenides and Xenophanes.
this is mostly Peikoff summary until i indicate otherwise later.
Aristotle is a mixed thinker. some great stuff and some bad stuff.
Part of the mix is because it's ancient philosophy. They didn't have modern science and some other advantages back then. It's early thinking. So Aristotle is kinda confused about God and his four causes. It was less clear back then what is magical thinking and what's rational-scientific thinking.
Aristotle is bad on moderation. He thought (not his original idea) that the truth is often found between two extremes.
Aristotle invented syllogism and formal logic. this is a great achievement. very worthwhile. it has a bad side to it which is causing problems today, but i don't blame Aristotle for that. it was a good contribution, a good idea, and it's not his fault that people still haven't fixed some of its flaws. actually it's really impressive he had some great ideas and the flaws are so subtle they are still fooling people today. i'll talk about the bad side later.
it's called formal logic because you can evaluate it based on the form. like:
All M are P.
S is an M.
Therefore, S is P.
this argument works even if you don't know what M, P and S are. (they stand for middle, predicate and subject.) (the classical example is M=man/men, P=mortal, S=Socrates.) Aristotle figured out the types of syllogism (there's 256. wikipedia says only 24 of them are valid though.)
Aristotle was apparently good on some biology and other science stuff but i don't really know anything about that.
Aristotle started out as a student of Plato but ending up rejecting many of Plato's ideas.
Aristotle didn't say a ton about politics. What he said is mixed. Better than Plato.
Aristotle – like the Greeks in general (as opposed to e.g. pre-modern Christians) – cared about human happiness and life on Earth. and he thought morality was related to human happiness, success, effectiveness, etc. (as opposed to duty moralities from e.g. early Christians and Kant which say morality means doing your duty and this is separate from what makes you happy or makes your life good.)
Aristotle advocated looking at the world, empirical science. he invented induction.
Aristotle was confused about infinity. (Peikoff and some other Objectivists today like Harry Binswanger roughly agree with Aristotle's infinity mistakes.)
Aristotle was generally pro-human and pro-reason. in a later lecture Peikoff says the dark ages were fixed because European Christendom got some copies of Aristotle's writing from the Muslims and Jews (who were trying to reconcile him with their religions) and then Thomas Aquinas attempted to reconcile Aristotle with Christianity and this made it allowable for Christians to read and think about Aristotle which is what got progress going again.
now Popper's perspective, which Peikoff basically agrees with most of the facts about, but evaluates differently.
Popper agrees Aristotle did some great stuff and got a few things wrong. like Peikoff and a ton of other people. But there's a major thing Popper doesn't like. (BTW William Godwin mentioned disliking Aristotle and Plato but didn't say why.)
Aristotle wanted to say I HAVE KNOWLEDGE. this is good as a rejection of skepticism, but bad as a rejection of fallibility. Aristotle and his followers, including Peikoff, equivocate on this distinction.
Part of the purpose of formal logic is an attempt to achieve CERTAINTY – aka infallibility. that's bad and is a problem today.
Objectivism says it uses the word "certain" to refer to fallible knowledge (which they call non-omniscient knowledge. Objectivism says omniscience is impossible and isn't the proper standard of something qualify as knowledge). and Ayn Rand personally may have been OK about this (despite the bad terminology decision). but more or less all other (non-Popperian) Objectivists equivocate about it.
this confusion traces back to Aristotle who knew induction was invalid and deduction couldn't cover most of his claims. (Hume was unoriginal in saying induction doesn't work, not only because of Aristotle but also various others. i don't know why Hume gets so much credit about this from Popper and others. Popper wrote that Aristotle not only invented induction but knew it didn't work.)
and it's not just induction that has these problems and equivocations, it's attempts at proof in general ("prove" is another word, like "certain", which Objectivists use to equivocate about fallibility/infallibility). how do you justify your proof? you use an argument. but how do you justify that argument? another argument. but then you have an infinite regress.
Aristotle knew about this infinite regress problem and invented a bad solution which is still in popular use today including by Objectivism. his solution is self-evident, unquestionable foundations.
Aristotle also has a reaffirmation by denial argument, which Peikoff loves, which has a similar purpose. which, like the self-evident foundations, is sophistry with logical holes in it.
Popper says Aristotle was the first dogmatist in epistemology. (Plato was dogmatic about politics but not epistemology). And Aristotle rejected the prior tradition of differentiating episteme (divine, perfect knowledge) and doxa (opinion which is similar to the truth).
the episteme/doxa categorization was kinda confused. but it had some merit in it. you can interpret it something like this: we don't know the INFALLIBLE PERFECT TRUTH, like the Gods would know, episteme. but we do have fallible human conjectural knowledge which is similar to the truth (doxa).
Aristotle got rid of the two categories, said he had episteme, and equivocated about whether he was a fallibilist or not.
here are two important aspects of the equivocation and confusion.
Aristotle claimed his formal logic could PROVE stuff. (that is itself problematic.) but he knew induction wasn't on the same level of certainty as deduction. so he came up with some hedges, excuses and equivocations to pretend induction worked and could reach his scientific conclusions. Popper thinks there was an element of dishonesty here where Aristotle knew better but was strongly motivated to reach certain conclusions so came up with some bullshit to defend what he wanted to claim. (Popper further thinks Aristotle falsely attributed induction to Socrates because he had a guilty conscience about it and didn't really want the burden of inventing something that doesn't actually work. and also because if Socrates -- the ultimate doubter and questioner -- could accept inductive knowledge then it must be really good and meet a high quality standard!)
I talk about equivocating about fallible vs. infallible because I conceive of it as one or the other, with two options, rather than a continuum. But Peikoff and others usually look at a different way. instead of asking "fallible or infallible?" they ask something like "what quality of knowledge is it? how good is it? how justified? how proven? how certain?" they see a continuum and treat the issue as a matter of degree. this is perfect for equivocating! it's not INFALLIBLE, it's just 90% infallible. then when i talk about fallible knowledge, they think i'm talking about a point on the continuum and hear like 0% infallible (or maybe 20%) and think it's utter crap and i have low standards. so they accuse me and Popper of being skeptics.
the concept of a continuum for knowledge quality – something like a real number line on which ideas are scored with amount of proof, amount of supporting evidence/arguments, amount of justification, etc, and perhaps subtracting points for criticism – is a very bad idea. and look at it that way, rather than "fallible or not?" and "there is a known refutation of this or there isn't?" and other boolean questions is really bad and damaging.
Peikoff refers to the continuum with his position that ideas can be arbitrary (no evidence for it. reject it!), plausible (some evidence, worth some consideration), probable (a fair amount of evidence, pretty good idea), or certain (tons of evidence, reasonable people should accept it, there's no real choice or discretion left). he uses these 4 terms to refer to points on the continuum. and he is clear that it's a continuum, not just a set of 4 options.
But there is no something more beyond fallible knowledge, before infallible knowledge. And the ongoing quest for something fundamentally better than unjustified fallible knowledge has been a massive dead end. All we can do is evolve our ideas with criticism – which is in fact good enough for science, economics and every other aspect of life on Earth.