Some Problems in Plato

I was reading Plato's Republic when I noticed the following logical errors and major points of disagreement:

1.) (False classification) Socrates often uses concrete examples of a certain class to make claims about abstract ideas without justifying how the abstract idea is a part of the given class. In other words, he appears to use a string of examples to justify a claim. But in so doing, he assumes that the idea is part of the class, and he therefore groundlessly ascribes all the features of that class to the abstract idea.

This pattern occurs at 332 c-e and 333a (not the greatest example, but it works). Socrates gives many examples of "crafts" and their beneficial functions. He then asks his interlocutor what benefit "the craft of justice provides." This implicitly identifies justice with the class of crafts, thereby assuming that justice has the same characteristic of any general craft. By answering the question, the interlocutor is duped into accepting this classification. This is not especially problematic until 342e and 343a, when Socrates uses the fact that, in all of his examples, crafts do not seek their own advantage, but the advantage of something else. He then applies this to justice: so justice must work to the advantage of something else. This contradicts his interlocutor's prior assertion that justice is to benefit oneself by helping friends and harming enemies.

The logic here is flawed because Socrates never defines what a craft actually is, and whether it is reasonable to say that justice is a craft. He uses a rhetorical slight of hand to make the interlocutor accept that justice is a craft. Socrates then forces the interlocutor to accept that justice must have the same characteristics as his hand-picked crop of examples of crafts.

2.) (Absence of existence arguments) Plato builds up magnificent structures of theoretical speculation throughout many works. The canonical example is in Republic: he devises his famous utopian society ruled by philosopher kings. The arguments are elegant and comprehensive, but the reader is left with the feeling that the society is oppressive and unnatural. While Plato would undoubtedly have some clever responses to these charges, he nevertheless ignores a crucial obligation. In mathematics, when one defines a mathematical object, before one can do anything with it, one must prove that it exists in a given context. In a similar manner, Plato can theorize endlessly, but it is all nonsense if he does not give a very detailed (given the size of his claims) account of existence.

Plato actually claims to give a proof of existence, but it has many flaws. When confronting the existence of his Republic, Socrates states: "Is it possible to realize anything in practice as it can be formulated in words or is it natural for practice to have a lesser grip on truth than theory, even if some people do not think so? Will you first agree to this or not? -- I agree" (472e). Here, Plato effectively assumes away the problem of existence asserting that anything that can exist theoretically can exist in reality. This is tantamount to the belief that all things can be shown to exist in reality by logical necessity alone--without resorting to any empirical or perceptive means at all. This is a very Cartesian view, and there is much evidence that it is logically unfounded. Whether things exist is a property of the space in which they exist, not the human mind.

3.) (Excessive reliance on the "forms") This is not a logical flaw of his, but a serious limitation of his philosophy. He repeatedly denigrates "practical" knowledge and reasoning as inferior to the theoretical. The historical success of empirical knowledge shows that this is unwise. This is ultimately a consequence of his excessive reliance on his "forms". By emphasizing their importance and perfection, he neglects the fact that reality and the "shadows" are one route to accessing the forms (and maybe the only route). It is only by studying and examining lots of empirical cases of justice that we can understand what justice is. But we can never know precisely what justice is because it is simply can't be precisely defined, so we must continue to learn about it by studying specific examples and experimenting.

In other words, I think speculation alone is typically not especially useful unless it can be made extremely precise (I belive only mathematics can ever do this). If I understand him correctly, I think Plato would disagree... or he would claim that all speculation can be made extremely precise like mathematics. It's not too hard to argue that human reality is (thankfully) not that mathematical.