If you know only a little bit about Plato, what you know is probably that he had some very silly (sounding?) ideas. For example, that he believed in Forms: thing such as Beauty, Virtue, Justice, and The Good (always capitalized in English discussions of Plato), things that are supposed to be in some mysterious sense out there in the world. It is easy to argue that Plato’s interest in Forms was misguided. As Aristotle pointed out (Nichomachean Ethics II.2) knowing Virtue doesn’t seem to do you any good unless you know how to be virtuous. Plato’s doctrine of the Forms also leads to some awfully fascistic-sounding doctrines: in The Republic, Plato argued that we should be ruled by philosopher-kings because only they can know the Form of Justice. And then there’s the fact that Plato apparently believed in reincarnation.

However, the justifications for Plato’s views often come from philosophical problems that philosophers haven’t stopped discussing. Here are three examples:

A priori knowledge

It seems like there are some things we know a priori. That is, we can discover some things just by thinking about them–mathematics, for example. But how could this be so? In his dialog Meno, Plato gives the crazy-sounding answer that we’re really just remembering things that we knew before we were born. But since Plato’s time, lots of philosophers have tried to give better explanations of how a priori knowledge is possible. There’s been talk of innate ideas (in a sense that doesn’t require reincarnation), Descartes’ “clear and distinct perceptions,” and more empiricist accounts where a priori knowledge really just comes from reflecting upon our own ideas (that’s a very crude summary of the history I just gave, it’ll do for my purposes, but don’t quote me on it).

On the other hand, if you read contemporary discussions of the a priori, there doesn’t seem to be much concern for explaining how a priori knowledge is possible, in the sense that Plato or Locke would have understood the question. Reactions to previous theories of the a priori often take the form of noticing some apparent problems, and then dismissing the theory, without worry about what else might be put in its place. Contemporary philosophers might worry a bit more if they came in at least able to appreciate the mind set this is such a big puzzle we might need reincarnation to explain it!

The Indefinite

If you’re reading this post (i.e. alive today and fluent in English) you’ve probably heard the phrase “well, yes and no” quite a few times. Probably some of these times the answer seemed appropriate. But it would be completely insane to answer every “yes or no?” question this way. At some point, either a straight “yes” or a straight “no” has to be sufficient. It would be nice to say something about when “yes and no” can be an appropriate answer, what makes it an appropriate answer when it is, and what we’re really saying when we say it.

Furthermore, lots of philosophers have felt the appeal of the idea that every claim about the world is either true or false, not both (that part is the logical law of noncontradiction) and not something in between (that part is the law of the excluded middle). Aristotle argued that anyone who claims to reject the law of noncontradiction will refute themselves as soon as they open their mouth, and if they avoid this problem by refusing to say anything, they will be “no better than a vegetable” and not worth talking to. William of Ockham went further: people who deny the law of noncontradiction, he said, should be beaten and burned until they realize that there is a difference between being beaten and burned and not being beaten and burned.

The common way of talking, though, remains, and even Aristotle seems to fall into it at times. Worse, to take the common way of talking at face value can be especially tempting when faced with philosophical paradoxes where both a straightforward “yes” and a straightforward “no” seem to get us into trouble. It inspired another surprising conclusion on Plato’s part: since all the things of ordinary experience can be, for example, beautiful from one perspective and not beautiful from another perspective, they must not be fully real. It is only things like Beauty itself that are fully real and proper objects of knowledge. This theory, like Plato’s theory of a priori knowledge, seems silly, but it’s a testament to how seriously he took the problem.

Change

The problem of change, as understood by the ancient Greeks, may be the least inutitive to modern philosophers. Some ancients, you see, appear to have been awfully worried about the question “how can a thing change and remain the same thing it once was?” Plato’s answer, again, is that this is a serious challenge to the reality of familiar, perceptible objects, but the Forms are unchanging and fully real. Here, though, the initial question sounds a bit silly. A quick answer is that it chances in some respect but remains the same in another respect.

Perhaps the original question can be touched up a bit to show that that response is too quick, but there’s another question in this vicinity we might shift to instead: “how much can a thing change and remain the same thing it once was?” This, in forms like the sorites paradox, Ship of Theseus, and so on, gets surprisingly large amounts of attention in current anglophone metaphysics. It also can turn into the problem of the indefinite if we’re at any point tempted to answer the relevant questions with “yes and no.”

I could say quite a bit more about any of these three problems, but this post is just an introduction. Anyway, understanding the longevity of these problems, and the weird doctrines they’ve motivated, makes me more willing to take the problems seriously, and want to try to consider them from more angles than they’ve generally been considered from in any one time period.