Quine's Poor Tom Revisited: Against Sayward

UPDATE (Nov 2019): I have recently published a paper on this topic, 'Quine's Poor Tom', in the European Journal of Analytic Philosophy.

I have recently come back to the argument in section 31 of Quine's Word and Object. In a post just over four years ago I criticized the argument for a use-mention shift with regard to a principle which, on an opaque reading of 'believes', is a reasonable thing to require of a good logician, but which, on a transparent reading of 'believes', is not a reasonable thing to require of a good logician.

In Quine's argument as he stated it, the principle is introduced in terms of belief in sentences, which all but forces an opaque reading. But then when it is applied in the argument, Quine has semantically descended to a 'believes that' construction, and applies the principle in such a way as would only be legitimate if it is given the transparent reading.

The principle as originally stated runs as follows:

(Acumen) [P]oor Tom, whatever his limitations regarding Latin literature and local philanthropies, is enough of a logician to believe a sentence of the form ‘δp = 1’ when and only when he believes the sentence represented by ‘p’. (Quine 1960, p. 148.)

In that-clause form it runs as follows:

(AmbigThatAcumen) Tom believes that δp = 1 when and only when Tom believes that p

(For the definition of the 'δp = 1' construction see my original post, but it can be read as 'The truth-value of "p" = 1' without going far wrong.)

Sleigh's (1966) objection makes the same point that I made towards the end of my original post, namely that the (AmbigThatAcumen) is only a reasonable assumption on an opaque reading, whereas its transparent reading is needed for the argument. He did not note that Quine's originally stating the principle in terms of belief in sentences all but forces us to give it an opaque reading at that point in the argument.

Widerker (1977) and Sayward (2007) criticized Sleigh's objection. I did not engage with these papers in my original post. In this post, I would like to refute Sayward's criticism. I think this can be done more or less conclusively.

Widerker's objection is less easily dealt with, and leads us into some interesting territory. I am currently working on a paper where I try to sort out the whole mess, and try to draw a metaphilosophical lesson.

One of the most important things I did not appreciate earlier is that Quine in his argument does give us what is needed for a good argument for his ultimate conclusion, namely that it will not do to treat belief transparently always. Once we see this, what is so objectionable about his argument may start to look more like a matter of presentation.

The way Quine presents things, I would like to say, is not perspicuous, and cultivates an air of paradox. (Quine makes it look like he has shown that if we treat belief transparently always, and if Tom has good logical acumen and believes one true thing and one false thing, then he believes everything.) I think this is philosophically bad, and so presumably did Sleigh. But it is interesting to note that what originally looked more like a dry, logical error (so to speak) may be more effectively criticized in this way - as a matter of non-perspicuous, philosophically bad presentation, rather than the commission of a definite logical error which flouts a principle we could get the supporter of Quine's argument to agree to. (Compare on the one hand the attempts of "cranks" to show that Cantor's diagonal proof was unsound, and on the other hand Wittgenstein's more sophisticated criticisms. I have blogged about this matter elsewhere.)

Sayward's criticism is simply that Sleigh has left it unargued that (AmbigThatAcumen) on its transparent reading is an unreasonable thing to require of  a logician - put differently, the criticism is that Sleigh has left it unargued that (AmbigThatAcumen) on its transparent reading does not express a form of logical acumen. He writes:

So if Sleigh’s point is to carry much weight it must take the form of a claim that no logical acumen, or at least none at all widely shared, is expressed by [(AmbigThatAcumen) read transparently]. But so far as I can see that simply goes unargued in his paper. Indeed, so far as I can see the paper contains no argument that the logical acumen to which Quine referred is not expressed by [(AmbigThatAcumen) read transparently]. It is simply and baldly asserted. (Sayward (2007), pp. 57 – 58.)

This objection can be convincingly rebutted. Firstly, it gets the dialectic wrong. Quine, for his argument to be plausible, needs his hypothesis about Tom's logical acumen plausibly to be about some genuine kind of logical acumen. I think it is perfectly fair to point out that this only seems to be so if we take the hypothesis opaquely, in which case it doesn't support the argument. This is already a good objection, in my judgement, without any further argument that it is not the case that (AmbigThatAcumen) read transparently – contrary to appearance – does express logical acumen after all.

Admittedly, this appearance may not be universal. This leads us to a second, stronger, point against Sayward's objection: Sleigh does give an argument that no logical acumen is expressed by the transparent reading! Sayward's claim that he does not do so is a sheer mistake. The argument comes at the end of Sleigh's note and runs as follows (except I have, for ease of reading, removed the subscript notation which he applies to singular terms to disambiguate between transparent and opaque, and simply put bracketed specifications of the intended reading next to 'believes' instead):

Obviously, (4') does not express the idea of Tom's acumen. Consider: 

(9) Tom believes [transparent] that [δp] = 1. 

and 

(10) Tom believes [opaque] that [2­ - 1] = 1. 

Given (10), (9) is true provided the sentence represented by 'p' is true. But we cannot infer from this that Tom believes the sentence represented by 'p' even if every singular term in 'p' is taken transparently and even if Tom is overflowing with logical acumen. (Sleigh 1966, p. 93.)

Clearly this is an argument, so Sayward is just wrong in saying that Sleigh doesn't offer one. I think it's a perfectly good argument, too – although I think it was unnecessary to make 'believes' in (10) opaque and (as I hope to make clear in the paper I am working on and perhaps a future post here) this makes Sleigh more vulnerable to Widerker's criticism.

Finally, I think we can give a more straightforward argument that the transparent reading does not express any sort of logical acumen. To rewrite the principle with an explicit disambiguation:

(TransparentThatAcumen) Tom believes [transparent] that δp = 1 when and only when he believes [transparent] that p.

Now, let us plug in some truth for 'p' which not everyone with logical acumen knows – say, 'Quine was born in 1908':

Tom believes [transparent] that δ(Quine was born in 1908) = 1 when and only when he believes [transparent] that Quine was born in 1908.

Now, substituting '1' for the co­extensive 'δ(Quine was born in 1908)', we get

Tom believes [transparent] that 1 = 1 when and only when he believes [transparent] that Quine was born in 1908.

This is plainly not something we should require of a reasoner. Using 'of' language to induce a transparent reading, so that the point reads more intuitively: a reasoner may not believe, of Quine, that he was born in 1908. They may not have any beliefs about Quine at all. Obviously, they should not in that case – by the 'only when', which is essential to Quine's argument – fail to believe, of 1, that it is equal to 1. But we obtained this wrong result just by substituting co-extensive terms in an instance of (TransparentThatAcumen). Therefore (TransparentThatAcumen) does not express any sort of logical acumen. Rather, it seems like something we definitely shouldn't conform to.

The above, I think, completely diffuses Sayward's criticism.

References

- Quine, W. V. (1960). Word and Object. The MIT Press.

- Charles Sayward (2007). Quine and his Critics on Truth-Functionality and Extensionality. Logic and Logical Philosophy 16:45-63.

- R. C. Sleigh (1966). A note on an argument of Quine's. Philosophical Studies 17 (6):91 - 93.

- David Widerker (1977). Epistemic opacity again. Philosophical Studies 32 (4):355 - 358.