In Logical Syntax, Carnap says that he has shown that one can talk about the logical form of language and that this is a counterexample to Wittgenstein’s dictum that you cannot talk about logical form, as it can only be shown. There is something that seems odd about this. From the little bit of secondary literature I’ve read, no one really seems to say much about this, although some of Carnap’s contemporaries seem to embrace Carnap’s claims. It seems like Carnap is talking past Wittgenstein. The problem with fleshing out this claim is that I have to flesh out one of the difficult doctrines in the Tractatus. (As opposed to the simple ones, I guess.) I’m going to attempt to sketch an answer.

Carnap says that we can talk about the logical form of a language within the language. He uses Goedel’s arithmetization of syntax as the justification for this claim. This technically works fine. It allows Carnap to talk about the syntax of a language within the language by talking about the numbers that represent the sentences, their formations, and their derivations. This is an entirely language internal feature.

Before getting to Wittgenstein, I need to write a disclaimer. I’m not sure at the moment how the resolute interpretation of this stuff would go, so I’m going to stick with a metaphysical reading of this. (This is compounded by not having the texts handy to flip through. I expect that Kremer’s recent paper on the cardinal problem of philosophy and Goldfarb’s on the saying/showing distinction will be relevant.) It shouldn’t really matter as I think Carnap gets things wrong from both the resolute and traditional readings of the Tractatus.

Wittgenstein’s view of logical form, at least before throwing away the ladder, is, roughly, that logical form is what language shares with reality. The passages that say this are likely what Carnap has in mind, and likely how he and others in the Vienna Circle understood it. Both language and reality, propositions and facts, share a form, their logical form. It is in virtue of this that there is a connection between language and the world. Carnap gets things wrong because trying to say what a sentence’s logical form is would be to describe a language external connection rather than a language internal feature, the geometry of finite, serial orders of symbols, to use Carnap’s phrase. There is then the further question of why Wittgenstein thinks that you cannot say, only show, what the logical form of a proposition is. I don’t think I can attempt that without spending some time with the Tractatus, which I do not have handy. In any case, Carnap has talked right past Wittgenstein. Carnap is talking about forms of signs in combination. This is something that I think Wittgenstein would have no problem agreeing with. You can describe the order or arrangement of concrete signs with your signs, but that doesn’t get at the logical form of the symbol, which is the sign in meaningful use.