The Plato Thread

[vulcanlogician]

The Republic is clearly a reaction to the execution of Socrates, preferring the Spartan model of government. Bleh.

I'm familiar with this narrative. And for all we know it's true, or at least true to some degree.

[I had some other analysis here, but it wasn't coherently expressed, so- delete]

I see the parable of the cave as a basic philosophical mistake that has had many bad consequences over the past couple millennia. Beautiful ideas, but ultimately a deep mistake.

@Brian37 mentioned this line of criticism. And, I have to say, there is merit to what Brian37 and Dawkins say on the matter. But I wouldn't call it a mistake.

I don't think rationalism is quite dead. It's probably the most underrated of modes to understanding reality. What's more, rationalism is constantly contrasted to empiricism. As if one contradicts the other. There is no principle contradiction between rationalism and empiricism. Many philosophers have pointed out that empiricism has something of a "rationalist skeleton." That empiricism itself depends on the primacy of logic to be true. I see the two approaches as complimentary, not contradictory.

If anything... even to one who wants to pronounce rationalism dead, you still have my "wrong idea being a sounding board for the right idea" notion I explained in the other thread to contend with. If anything the divided line and allegory of the cave were a hell of a sounding board for the right idea. Like I said before, gods, bigfoot, and UFOs are shitty ideas/explanations that don't help us get to the right idea. But with Plato's well-articulated vision, we learn something valuable when we knock it down. If some people in history took it as gospel, that's their fault. Socrates urged us to question everything and even admits in Book 1 of the Republic that he knows nothing. I take that as a genuine disclaimer for the ideas that follow, whether Plato intended it or not.

Meno has a very interesting argument, from mathematics, about the nature of knowledge and memory. it is interesting to see how the slave arrives at the correct answers, but only through leading questions.

There is also a dialog, I don't recall which one, in which Theatetus mentions that he has a proof that `square roots' are irrational unless the integer is a perfect square. This is interesting as part of the history of mathematical ideas. The discovery of irrational ratios was a blow to the Pythagorean philosophy and the investigation of the concept of irrational ratios by Theatetus was quite important. There is even a quote in Aristotle using Theatetus' definition as opposed to the more well-known definition by Eudoxus. In any case, that Theatetus claims to have a proof is interesting because the only natural proof at that stage would have been one using prime numbers and unique factorization.

There were plenty of blows dealt to mathematical realism in the 19th and 20th centuries: Bertrand Russell's criticism of Frege, and a few others that escape me right now. The thing about that is that while mathematical realism became much more dissatisfying of a theory after those revelations, mathematical fictionalism and other competing theories still remain as dissatisfying as, if not more dissatisfying, than mathematical realism.

I think the main point of the slave being taught to understand a mathematical principle is that there is a real principle that is kind of "there" to be discovered. It's kind of hard to dispute that. But if you want to claim that it is true that the principle is "there" waiting to be discovered, you are presented with all kinds of metaphysical puzzles. Some of these questions are things only philosophers care about. There are distinctions there that you can kind of gloss over or easily explain away. But you can't completely explain the issue away, and (for better or worse) philosophers have been chewing on that riddle for centuries.