Friday, 25 December 2015

Quine's Poor Tom Revisited: Against Sayward

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 'pis 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. 

Monday, 21 December 2015

Modal Realism

This is just an expository post, but I hope to make some original points in subsequent posts which will consider objections to modal realism.

Central to modal realism are the Leibnizian biconditionals,

(Leib­NEC) A proposition is necessary iff it is true in all possible worlds.
(Leib­POSS) A proposition is possible iff it is true at some possible world.

These tie attributions of necessity and possibility to quantificational statements about possible worlds. Different philosophical accounts which use these sentences accounts differ over what sorts of things possible worlds are taken to be, and over the role given to the Leibnizian biconditionals. (With typical forms of modal fictionalism, the biconditionals are typically augmented with an 'According to F' operator, where 'F' names a fiction.) The distinctive marks of modal realism, setting it apart from other philosophical uses of the Leibnizian biconditionals, are that it takes possible worlds to be of the same kind as the actual, concrete world we live in, that it takes the Leibnizian biconditionals to be true all by themselves (no fiction operator required), and that it takes these to constitute analyses of the modal notions appearing on the left hand sides.

The chief proponent and developer of modal realism, David Lewis, intends it to be a reductive account of modality – so his theory of possible worlds must be spelled out non­modally. Accordingly, the 'possible' in 'possible world(s)' on the right hand sides of the biconditionals is not supposed to be taken as anything more than part of a conventional, historically familiar way of referring to the worlds which do the work in his account. 

Such is the theory of modal realism in broad outline. Its characteristic commitments may be summed up in one sentence as 'There are other worlds, and every way our world might have been is a way some world is' (cf. Lewis 1986, p. 2).

In future posts I want to consider some objections to modal realism, but first let us consider in a preliminary way three finer points about the theory.

One finer point concerns the individuation of worlds. As Lewis phrases the question, 'What makes  two things worldmates? How are the worlds demarcated one from another? Why don't all the possibilia comprise one big world? Or, at the other extreme, why isn't each possible neutrino a little world of its own?' (Lewis 1986, p.70). Lewis's answer to this is: spatiotemporal relatedness. '[W]henever two possible individuals are spatiotemporally related, they are worldmates. If there is any distance between them – be it great or small, spatial or temporal – they are parts of one single world.' (This gives rise to an objection – the island universes objection – based on the idea that we should not in our analysis of modality rule out the possibility of a world with multiple spatiotemporally unrelated “universes”. I will not consider this objection at length, but cf. Lewis 1986, p. 71, Bricker 2001 and Vacek 2013.)

The second finer point concerns the treatment of propositions about particular individuals, and how they are to be evaluated with respect to worlds other than our own (or more generally, worlds other than the one from which the propositions in question are being evaluated). To begin with, note that general statements pose no corresponding difficulty. Going along with the modal realist's doctrine that there are other worlds, a question like 'Is “All swans are white” true at all worlds?' seems to have a straightforward meaning (at least given the familiar point that we want to hold fixed the meaning of the sentence in question when evaluating the proposition with respect to other worlds). But if we ask 'Is “John is white” true at all worlds?', where John is some actual swan, the question arises: does John himself exist at any of the other worlds?

The two different answers we might give to this question correspond to different forms of modal realism. If we answer in the affirmative, we get what is called modal realism with overlap. If we answer in the negative, get what is called modal realism without overlap. The canonical form of modal realism, David Lewis's as developed in his (1986), is of the latter sort. In order to enable us to evaluate propositions about particular individuals with respect to other worlds in the framework of modal realism without overlap, Lewis developed a theory of counterparts. To evaluate 'John is white' at some world W, we as it were look at that world and select the closest counterpart to our this-­worldly swan John, and then consider whether that swan is white. If so, we say that 'John is white' is true at W. This approach has been felt to be damagingly counterintuitive, giving rise to an objection originated by Saul Kripke called the Humphrey objection, which we will consider in a futute post.

The third and final finer point I want to note concerns the issue of what, if anything, modal realism has to say about the extent or range of the worlds – what worlds are there, and what are they like? As Lewis saw the matter, it was incumbent on him to provide principles which so to speak “generate” sufficient worlds, so that there is one for every possibility. To this end he proposed a principle of recombination, but he admitted that this was inadequate (Lewis 1986, p. 92). More recently, it has been questioned whether any such principles are needed for the theory qua analysis of modality (cf. Cameron 2012).

Note that modal realism is obviously free of the chief defects of pre-Kripkean analyticity approaches – the modal realist analysis does not push us toward the conclusions, implausible ever since Kripke, that necessary truths are true in virtue of meaning, or that they are all a priori. This is one of the things which, together with the boldness and clearness (at least in a certain sense) of the theory, makes it such a serious contender given the present state of play.

In future posts I will consider objections to modal realism, some of which we have just alluded to. My ultimate conclusion will be that the most serious objections are very serious indeed, and devastating when taken together. (General methodological qualms about certainty in philosophy aside, I believe that the theory is certainly incorrect. But it is profoundly incorrect and cannot be discussed too carefully. This series of posts will necessarily fall short of plumbing the full depths of the matter.)

References

Bricker, Phillip (2001). Island Universes and the Analysis of Modality. In G. Preyer & F. Siebelt (eds.), Reality and Humean Supervenience: Essays on the Philosophy of David Lewis. Rowman and Littlefield.

Cameron, Ross P. (2012). Why Lewis's analysis of modality succeeds in its reductive ambitions. Philosophers' Imprint 12 (8).

Lewis, David K. (1986). On the Plurality of Worlds. Blackwell Publishers.

Vacek, M. (2013). Modal Realism and Philosophical Analysis: The Case of Island Universes FILOZOFIA 68, No 10, p. 868-876.