Sunday, June 11, 2006


Tales of the Inexpressible

When Jason Stanley was here for the UT Grad Conference in April, I took the chance to talk to him about his draft 'Philosophy of Language in the Twentieth Century'. Now, I haven't managed to finish the paper, but it's an impressive survey of a stupidly large field, and Stanley manages to include nice accounts of the contributions made by Tarski and Carnap and other figures who we all acknowledge as a vital part of the story of our subject, but who often get somewhat glossed over in these kinds of overview pieces.

However, one figure who is really noticeably absent is the later Wittgenstein. Moreover, Stanley's assessment of the contribution of the Tractatus to 20th Century philosophy is surprisingly negative:

'The Tractatus impeded progress in philosophy, because it led philosophers (in particular the Logical Positivists) to expend their energies in the pursuit of developing and honing a criterion of meaningfulness, and using the criterion to argue that traditional philosophical theses failed to satisfy it, and were hence meaningless [...]. ' (p10)

Now, Stanley doesn't deny that the Tractatus did some good; in particular, he notes that the connections the early Wittgenstein saw between modality and meaning turned out to yield insights when studied more systematically by later philosophers (p10). But my own assessment of the Tractatus is overall much more upbeat, and I wanted to say a little bit about why.

Firstly, and most germane to Stanley's topic, the Tractatus contains one of the earliest and clearest statements of the thought that the meaning of a sentence is its truth-conditions:

4.024 'To understand a proposition means to know what is the case, if it is true.

(One can therefore understand it without knowing whether it is true or not.)

One understands it if one understands its constituent parts.'

Stanley takes the idea that the proper form a theory of meaning should be truth-conditional to have been 'extraordinarily fruitful, perhaps the most fruitful insight in the long history of the study of meaning' (p18). As David Wiggins presents the history of that insight (in 'Meaning and Truth Conditions: From Frege's Grand Design to Davidson's' in the Hale and Wright Blackwell Companion), the Tractatus marks the first important development of the idea after Frege. From this perspective, the Tractatus should be a integral part of Stanley's story.

I also have a more positive view of the saying/showing distinction. It would be hard not to agree that it provided inspiration for some philosophical wild-goose chases (though I'm not sure how to assess the claim that such failed projects were a symptom of philosophical progress being impeded). On the other hand, I think the distinction led to some geniune insights in maths and logic. Wittgenstein originally introduced the distinction to offer a response to Lewis Carroll-style worries about the system of logic in Principia Mathematica. Those concerns are evident on the first page of the Notes on Logic (1913), where Wittgenstein writes that '[d]eductions only proceed according to the laws of deduction but these laws cannot justify the deduction.' (Notebooks 1914-18: p108). We find the saying/showing distinction first unveiled as the solution to this problem in the opening sentence of the Notes dictated to Moore in Norway in 1914:

'Logical so-called propositions shew [the] logical properties of language and therefore [the] Universe, but say nothing.' (Notebooks: p108).

That one can infer B from A and A -> B is not to be justified by appeal to a further rule of inference. Rather, anyone who understands the symbols involved can see that B follows from these premises. This difficult thought received its mature statement in 5.132 of the Tractatus:

'If p follows from q, I can conclude from q to p; infer p from q.
The method of inference is to be understood from the two propositions alone.
Only they can justify the inference.
Laws of inference, which - as in Frege and Russell - are to justify the conclusions, are senseless and would be superfluous.'

Tricky stuff. But the passage forms part of a pretty deep critique of the universalist conception of logic coming from Frege and Russell. The issue here is not just how inference is to be justified, though that's obviously a central and important part of Wittgenstein's concerns. In the background here is the issue of how the logical propositions are to be demarcated. For the universalist the mark of the logical is unrestricted validity and their self-evidence; from his earliest recorded philosophical remarks it is clear that Wittgenstein is starkly opposed to universalism. Logic 'must turn out to be a totally different kind than any other science' (Letter to Russell 1912, Notebooks: p120).

I should get to the point. The saying/showing distinction is the centrepiece of Wittgenstein's critique of the universalist conception of logic, and this critique had a number of really interesting and important consequences. For example, it provided grounds on which Wittgenstein could check Russell's tendency to claim that the axioms he needed to adopt to try to get his logicism to fly were logical; a crucial moment in the history of set theory, and its demarcation from logic.

Of course, as I noted above Stanley doesn't claim that the Tractatus didn't have positive influence. But here I wanted to say a little about why I disagree with his overall assessment; the Tractatus certainly has its flaws, particularly stylistic flaws, but ultimately I think it was an impressive, at times poignant, and overall beneficial contribution to 20th Century Philosophy. In any case, I strongly recommend reading Stanley's paper; I've learned a lot from it, and from thinking through these points of disagreement.

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Nice post, Aidan.

One might also mention in this connection that the TLP contains a very early formulation of a semantic notion of logical consequence, which is significantly absent from the universalist conception. In the TLP, the conception is roughly that one
proposition q is a logical consequence of another p iff every assignment of truth-values to the elementary constituents of p and q which makes p true, also makes q true (ยงยง 5.11-5.12).

This is of course tied up with the famous introduction of the truth-tables.

Wittgenstein presents the tables as "propositional signs" (4.442), which is indicated by the fact that the tables are put in inverted commas. The intention, I believe, is to deliver an alternative notation to Frege and Russell's which involved individual symbols for logical constants. These signs were misleading for Wittgenstein since the material implication could not be a relation (5.42).

Anyway, one very nice paper about all this is Ricketts, T: 'Pictures, Logic, and the Limits of Sense in Wittgenstein's Tractatus', in Sluga & Stern (eds.), The Cambridge Companion to Wittgenstein, Cambridge: Cambridge University Press, 1997, p.p. 59-99.

Thanks Andreas, good point. I'm familiar with the Ricketts piece, though I do remember it as one of the many recent good pieces of Tractatus scholarship that randomly announces comradeship with Diamond and Conant on Wittgenstein's early philosophical method on the very last page.

I also found Juliet Floyd's paper on this stuff in Shapiro's Oxford Handbook extremely rich and informative.
I somehow thought it was "Tales from the Inexpressible".

Anyway, when I first read Jason Stanley's thing, I thought some bits (mainly the last sentence) were fairly polemical. But then rereading those bits, I realized he was actually making a point I'd generally agree with, but putting it more forcefully than I would.

I had always taken it as platitudinous that meaning is use, or something like that, while he came down very harshly on that position. But I think in the end I agree with him, that the biggest contributions to the theory of meaning (and as I see it, to the theory of use) have been from a truth-conditional perspective.

As for Wittgenstein, I was quite surprised when I found out recently how much many people dislike him, countering those who worship him. No one seems to be able to treat him just like any other influential philosopher.
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