Wittgenstein on Regularity Part 1

"If language is to be a means of communication there must be agreement not only in definitions but also (queer as it may sound) in judgments. This seems to abolish logic, but does not do so.--"
-Wittgenstein, Philosophical Investigations 242

Regularity is Wittgenstein's answer to a certain line of Socratic questioning. The question goes something like: "Very well, this is good and that is good, but in virtue of what do we call all these things good? What allows us to do so?" The concept "good" is a "universal," it is said in the same way of many things, and so it poses the question of unity in multiplicity: what grounds our using the same word to designate many things? What is "the same" in every case?

Plato's answer-- so rumor has it, at any rate, since I have not studied Plato-- is that the unity resides in and behind the things themselves: they really participate in something which is the same in all of them, the Idea of the Good. Our language reflects an actual unity, albeit through a glass darkly. We should not be too quick to criticize this position, since we obviously have no idea what it means ("participation"?--, but as a matter of fact we are quick to criticize it, because we have a ready answer to the question of unity in multiplicity. This answer is nominalist and, one might say, "psychological": the concepts exist in us, we say things are the same because we see something in them that is the same. We have a picture of a cat in mind, we compare an object with the picture of the cat, and if it is more or less the same as our picture, we call it a cat. (This theory is nominalist because there isn't anything outside of us which grounds "catness": if we one day decided to split animals up into "is brown" and "is black" instead of "meows" and "barks," there would no longer be catness, and of course the cats wouldn't have changed.) (1)

Note what has changed here: the locus of identity. No longer in the things but in us. Note what has stayed the same: identity itself. There is something that all cats share, in virtue of which we call them cats.

Wittgenstein just fucking destroys this model. That is, he refutes it on so many levels that it's hard to keep track of which is the essential one. (Once you realize that this model is wrong, it's obviously wrong for any one of a dozen reasons; the real question is how we dug ourselves into this hole in the first place.) Still, there is an order to his critique. Wittgenstein, famously, uses the example of "games," so I'll do the same. (2)

1. There is no essence of "game" which all games share. Board games, Tetris, tennis, the games people play-- there are relationships within this series, but there is no single thing that they share.

2. It is a poor phenomenological account of language use to say that you work by applying a concept. The labor you'd have to do to check my assertion in 1 is a good indication of this: Even if you could find something that all those "games" share, would it be accurate to say that this knowledge is somehow mysteriously "present" every time you use the word? (3)

3. Even if you had such a paradigm it wouldn't help, because you'd need a higher criterion of identity to check whether any given case of "game" was "identical" to your "picture" of "game." This is the fundamental issue. Suppose I do indeed have a picture of "game," and I compare actual objects with this picture in order to figure out if each of them is a game. How am I to know what counts as a "match" between my object and my picture? What degree of unity must I seek here? Clearly, to resolve this questions I would need a rule of some sort, another concept-- the concept of "cases in which I am to apply the concept 'game.'" But this leads to an infinite regress.

Essentially, Wittgenstein's point is an application of the Third Man Argument-- Plato's refutation of the theory of the forms or ideas-- to the "subjective" theory of concepts described above. The problem we sought to resolve initially was that of identity in difference: what do all cats share such that we call them all "cat"? We gave the answer: We call them all "cat" because they're all similar to our idea of a cat. But now we're faced with the same problem on a different level: "In virtue of what do we call our idea of a cat and a cat similar?" When do we do so, and under what criteria? The problem remains unsolved.

According to Wittgenstein, "identity" and "similarity" cannot resolve this problem. This is where regularity comes in, as I'll show in my next post.

(1) I claim that this is indeed the theory of concepts you would get if you left a bright high schooler alone in the room with the Theatetus for two minutes. It's an empirical claim, and I'd like to know if you disagree: I'm interested in figuring out what metaphysics comes naturally to people of our era.

(2) Wittgenstein's use of examples is extremely complex. In discussing games, he proves (a) that there is no single concept of "game," (b) that language is a lot like a game, and (c) that there is no concept (essence) of language. Often he's doing all three in one passage.

(3) The best possible proof of this is a note given under roughly passage 69 of the Philosophical Investigations: "Someone says to me: 'Shew the children a game.' I teach them gaming with dice, and the other says "I didn't mean that sort of game." Must the exclusion of the game with dice have come before his mind when he gave me the order?"[I don't know why he spells "show" that way either.]