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. 

On Kripke's Intuitive Anti-Quinean Defence of De Re Modality

This is the second post in a series on de re modality and quantification into modal contexts. The first is here.

Immediately after the passage quoted at the beginning of the last post where Kripke introduces the problem of de re modality, he goes on to argue that de re subjunctive modal ascriptions, and the notion of necessary and contingent properties, have intuitive content. I will quote this influential passage in full, and make a criticism of it. I will then suggest a weaker argument from analogy which could be given in its stead, and finally indicate my own view on the matter.

Here is the passage:

It is even suggested in the literature, that though a notion of necessity may have some sort of intuition behind it (we do think some things could have been otherwise; other things we don't think could have been otherwise), this notion [of a distinction between necessary and contingent properties] is just a doctrine made up by some bad philosopher, who (I guess) didn't realize that there are several ways of referring to the same thing. I don't know if some philosophers have not realized this; but at any rate it is very far from being true that this idea [that a property can meaningfully be held to be essential or accidental to an object independently of its description] is a notion which has no intuitive content, which means nothing to the ordinary man. Suppose that someone said, pointing to Nixon, 'That's the guy who might have lost'. Someone else says 'Oh no, if you describe him as "Nixon", then he might have lost; but, of course, describing him as the winner, then it is not true that he might have lost'. Now which one is being the philosopher, here, the unintuitive man? It seems to me obviously to be the second. The second man has a philosophical theory. The first man would say, and with great conviction 'Well, of course, the winner of the election might have been someone else. The actual winner, had the course of the campaign been different, might have been the loser, and someone else the winner; or there might have been no election at all. So such terms as "the winner" and "the loser" don't designate the same objects in all possible worlds. On the other hand, the term "Nixon" is just a name of this man.' [Presumably the quote from the imagined "first" man should have ended one sentence ago, but this is how it is in the text. -TH] When you ask whether it is necessary or contingent that Nixon won the election, you are asking the intuitive question whether in some counterfactual situation, this man would in fact have lost the election. If someone thinks that the notion of a necessary or contingent property (forget whether there are any nontrivial necessary properties [and consider] just the meaningfulness of the notion) is a philosopher's notion with no intuitive content, he is wrong.

I do not want to be dogmatic about this, but I suspect that there may be a bit of a bait-and-switch going on here. Certainly, it seems everyday and intuitive for someone to point at Nixon and say 'That's the guy who might have lost'. But then what this 'first man' says in response to the 'unintuitive man' (the philosopher), is beginning to sound pretty philosophical itself, albeit sounder. It is true that what he says, especially if you're trained in philosophy, seems intuitively compelling. But I think it's quite arguably out of character for the first man.

One way of making good on this suspicion is to reflect that forms like 'could have' and 'might have' do not just signal talk about counterfactual scenarios and counterfactual possibility. They also commonly find a retrospective epistemic modal use. And it seems to me that this is the most natural way to interpret the everyday, non-philosophical remark of the 'first man' above, 'That's the guy who might have lost'. To say that Nixon might have lost, on this suggestion, means something like: at some former stage, things could have gone either way – it would have been unreasonable then to be convinced that he would win.

This seems to me like a fairly everyday thing to say. The meaning Kripke intends – where what is asserted means something like (ignoring the later Finean distinction between essential and necessary properties): it's not part of Nixon's essence that he won the election – seems less so.

We can also argue along Gricean lines that the first interpretation yields something which it might actually be good to say in the sort of conversation about contemporary events Kripke has in mind. But saying this thing about – speaking loosely – Nixon's essence seems pragmatically odd; if you know that, then presumably you know something stronger from which it follows (such as that winning some election can't be an essential property of anyone), rather than making it sound as if there's something special about Nixon here. (Consider an obscure bystander around Nixon's age: it seems, from an unabashedly philosophical point of view now, implausible that it is part of this bystander's essence that he didn't go into politics, get to run for Presidential office in the election in question, and lose. So it seems you could say of that guy too that he might have lost the election, in the sense in which Kripke has in mind.)

So, I find Kripke's story about the first man and the unintuitive, philosophical man unconvincing: if the first man were really not a philosopher, I'm inclined to think that his intuitive-sounding utterance of 'That's the guy who might have lost' is far more plausibly interpreted along epistemic lines. This is somewhat ironic, given Kripke's seminal insistence on carefully distinguishing epistemic modality and a priority on the one hand from subjunctive modality on the other.

We can get a better idea of how it might have happened by recalling the grammatical devices Kripke uses to isolate subjunctive modality: what could be the case for all we know a priori is to be distinguished from what could have been the case (given various things we know, and not always a priori). This may lead to an overconfidence in the subjunctive mood (or whatever you want to call it) as a signal of subjunctive modality proper, a signal of the thing Kripke isolated.

Still, this criticism doesn't imply that there is nothing in what Kripke says in this influential passage. Two things can be gleaned from the passage which do militate in favour of his main conclusion, which is that the notion of necessary and contingent properties makes sense.

One is a kind of argument from analogy: even when you interpret the first man's initial, everyday-sounding utterance along more appropriate, epistemic lines, it is clear that what is under discussion is not a statement: that is, de re epistemic modality makes sense. (For a recent study of that topic cf. Seth Yalcin's work.) And so, putting this consideration together with Kripke's compelling isolation of a concept of necessity applying to propositions which is distinct (intensionally and extensionally) from those of a priority and analyticity, we might naturally expect de re modal constructions where the modality is of this broad sort, having to do with alternative ways the world could have been in some non-epistemic sense, to be possible too.

Another is a direct philosophical appeal to our intelligence: forget guys on the street, forget questions about what they may or may not say without thereby becoming philosophers, and just think about it. What the first man is made to say in response to the unintuitive man, even though it just sounds like Kripke doing philosophy, seems awfully compelling. To quote it again: 'the actual winner, had the course of the campaign been different, might have been the loser, and someone else the winner; or there might have been no election at all. So such terms as "the winner" and "the loser" don't designate the same objects in all possible worlds'.

The situation, as I see it, is something like this: Kripke has clarified and isolated notions of necessity, contingency etc., which in the first instance apply to propositions and perhaps states of affairs. Now, by analogy with other expressions in our language, we are led to consider forms like 'a is necessarily F' and 'There is an x which is necessarily F' (or 'There is an x such that it is necessary that x is F'), where we have a vague idea that the terms 'necessarily' and 'necessary' here are, in some way, to express this same notion, which we know in the first instance in application to specific propositions. Consider the syntax of quantified modal logic, where modal operators are combined with first-order logic, in advance of any definite understanding of what these formulas are to mean.

Philosophers often behave like little children who scribble some marks on a piece of paper at random and then ask the grown-up "What's that?" — It happened like this: the grown-up had drawn pictures for the child several times and said "this is a man," "this is a house," etc. And then the child makes some marks too and asks: what's this then? C&V 17e

Our problem is, in a way, similar to that of making a game which is like an existing game, but different in some respects – but where the required similarities and differences are not completely spelt out (and how could they be, without thereby completing the task already?). For example, chess for three players, or with no queens.

In the present case, the task draws us in, since we feel we can already make some dim sense of these constructions. The question of whether this can be spelt out clearly, and the spelling out of it should this be possible, is of logico-philosophical interest. Furthermore, the issue is connected in many people's minds with difficult philosophical topics – with Aristotelian essentialism, with metaphysics, and with confused issues to do with whether modality is 'located' or 'grounded' in language and thought, or in other things.

Accordingly, in the next post in this series I will take up the challenge of de re modality, trying to adapt my account of necessity as an attribute of propositions so that it can be applied to de re modality. My main assumption in taking up this challenge is: there must be a connection here, and a tight one (e.g. not something you would have to describe using words like 'sometimes' or 'usually'), and we now have to make this clear. This will also take heat off the idea that de re modality makes no sense, but perhaps in a way which might look strange from the point of view of certain ways of thinking about analysis: the right hand sides of my analyses will in many ways be less simple, more problematic and more difficult than the left hand sides, the things to be analysed. But the problems are not the same ones as affect the left hand sides, and that is important. Roughly, I want to show that de re modal talk is not left hanging by itself, when we have a notion of necessity which applies to propositions. It may in a sense be more intelligible left as it is than when analysed along the lines I propose. But we must distinguish between the first-order intelligibility of a linguistic form on the one hand, and our philosophical conception of how that form works and what it does on the other. Connecting de re modal talk to de dicto can, I think, help a lot with the latter.

(Contrast, for example, Kit Fine's approach of taking essence as something basic – I get the sense of a wall having been erected to keep out trouble, but which also leaves us hapless and isolated. It is similar with his metametaphysical ideas: we must distinguish how things really or metaphysically are from how they are simpliciter, or something like that – and if you don't understand that, too bad: we're up against a wall. The difference, I think, is that in the first case the talk (essence talk) does make some sense, but has been walled off from things which may shed light on it in a way that can make this hard to believe, and hard to grasp, whereas in the second case, you have at most a degenerate, affect-charged sense, and the walls are merely there in a vain attempt to stop this from becoming glaringly apparent.)

Granularity and Quine

In a former post I introduced the idea that meanings and the like can be carved up at different granularities. This was motivated using Kripke's famous puzzle about belief, and introduced as offering the key to a solution.

I plan to develop this doctrine of semantic granularity further, adding detail and removing certain possible misconceptions, in future posts. For the time being, however, I will defer that and outline a further application of the doctrine (the original one being to Kripke's puzzle). Several more applications have occurred to me since arriving at the doctrine, each time bringing great joy and encouragement, since they seem to suggest that it really is a good idea. Accordingly, this will in all probability be the first of a series of posts which as a whole may be called 'Applications of Granularity'.

The application I want to outline this time is to Quine's famous skepticism about meaning and propositions. Quine's position is not so much that there are no such things as meanings or propositions (where these latter are construed as sentence-meanings) - although he does sometimes seem committed to that too - but rather that semantic notions such as that of meaning are somehow second-rate, badly-behaved, and not worthy of serious thought.

(Quine's peculiar conception of serious thought, first-rate concepts, real scientificality and the like - which could be called a scientistic conception, but is, to be fair to science, really much narrower than that; what we really have is a bias in favour of notions which Quine for his own peculiar reasons thinks of as first-rate scientific ones - is a very interesting matter which I would like one day to scrutinize here at some length. But this will have to wait till another time.)

Now, the application of the idea of semantic granularity I want to outline here is not to the refutation of Quine's position, although it may go some way toward breaking its grip. Rather, my focus is the explanation of Quine's position; what was going on with him when he came to it, and secondly, what is going on when other thinkers feel his arguments to have force.

Quine's skepticism focuses on the, to him, confusing individuation-behaviour of intuitive notions of meaning. To give a sense of his position, I will first quote from a section of McGrath's Stanford Encyclopedia of Philosophy entry on propositions, a section called 'The Individuation of Propositions', and then give a couple of illustrative quotes from Quine himself.

Some Quotes Illustrating Quine's Position

This section can be skipped or skimmed depending on how much of a sense one wants to get of Quine's position, or how much reminding one needs. To skip it, just scroll down to 'The Diagnosis'.

Probably needless to say, these quotations by themselves, to a reader unfamiliar with Quine's writings on the subject, will not give the full picture of what he had to say; it was an issue he picked up again and again and said a lot about.

Here is McGrath in the SEP:

Some philosophers, notably W.V.O. Quine, recognize the existence of certain sorts of abstract entities but not others at least partly on the basis of concerns about identity conditions. Quine granted the existence of sets, in part because they obey the extensionality axiom: sets are identical iff they have the same members. When it came to properties, relations and propositions, however, he found no such clear criterion of identity. The property of being a creature with a heart, he noted, is distinct from the property of being a creature with a kidney, even if all the same things exemplify the two properties. 

It is a controversial matter whether Quine was right to demand such rigorous criteria of identity as a condition for acceptance of a class of entities. However, even if Quine asks too much, any good theory of propositions ought to have something to say about when propositions are identical and when they are distinct. Developing theories which give such accounts in a way that fits well with intuitive data concerning propositional attitude ascriptions would enhance our reasons to accept propositions.

Now a few illustrative Quine quotes.

From 'Two Dogmas of Empiricism' (1951 edition):

For the theory of meaning the most conspicuous question is as to the nature of its objects: what sort of things are meanings? They are evidently intended to be ideas, somehow -- mental ideas for some semanticists, Platonic ideas for others. Objects of either sort are so elusive, not to say debatable, that there seems little hope of erecting a fruitful science about them. It is not even clear, granted meanings, when we have two and when we have one; it is not clear when linguistic forms should be regarded as synonymous, or alike in meaning, and when they should not.

This paragraph from a section of Philosophy of Logic boldly entitled 'Propositions Dismissed':

The uncritical acceptance of propositions as meanings of sentences is one manifestation of a widespread myth of meaning. It is as if there were a gallery of ideas, and each idea were tagged with the expression that means it; each proposition, in particular, with an appropriate sentence. In criticism of this attitude I have been airing the problem of individuation of propositions.

This passage from the 'Meaning' entry in the playful Quiddities:

[...] what is it for two expressions to have the same meaning? They cannot have exactly the same use, for when we use one we are not using the other. One wants to say rather that they have the same meaning if use of the one in place of the other does not make any relevant difference. The question of sameness of meaning, then, comes down to the question what to count as relevant difference.

I see no prospect of a precise answer, nor any need of one. Everything real and objective having to do with our use of expressions, and hence with their meaning, can be said without positing any relation of full synonymy ofexpressions, or sameness of meaning. In describing ways in which an expression is used we may be said still to be explaining its meaning, but there is no lingering trace of a museum of labeled ideas nor of any clear and simple relation of paraphrase or translation.
[...]
I urged at the end of the entry on IDEAS that there is no place in science for ideas, and under KNOWLEDGE that there is no place in the theory of knowledge for knowledge. Now we find me urging that there is no place in the theory of meaning for meanings, commonly so called.

Finally, if a bit more detail is wanted, here are selections (kept in order) from a more nuanced discussion in section 42 of Word and Object, 'Propositions as Meanings':

A large part of learning 'apple' or 'river' was learning what counts as the same apple or river reexposed and what counts as another. Similarly for 'proposition': little sense has been made of the term until we have before us some standard of when to speak of propositions as identical and when as distinct.
[...]
If we are content to define identity of propositions by synonymy of sentences, there is no evident objection to calling propositions meanings of eternal sentences. Misgivings as to what sort of object such a meaning might be could be allayed, if one pleases, by identifying it with the very class of all those mutually synonymous sentences that are said to have it. The worry that remains is the worry over a suitable notion of synonymy of eternal sentences. If propositions are to serve as objects of the propositional attitudes, then the broad sort of sentence synonymy talked of in § 14 [Details of that don't matter here - TH] would be unsatisfactory as a standard of identity of propositions even if adequately formulated. It would be too broad. For it would reckon all analytic sentences as meaning an identical proposition; yet surely one would not want to regard all analytic sentences as interchangeable in contexts of belief or indirect quotation, especially if all mathematical truths are regarded an analytic. Hence Lewis and Carnap have resorted to narrowed derivative relations of synonymy, or intensional isomorphism in Carnap's phrase, as better suited to interchange in contexts of propositional attitude.
[...]
Mates, Church, and Scheffler have argued that Carnap's intensional isomorphism (and Lewis's earlier construction of similar character) is still too broad for interchange in contexts of propositional attitude. Putnam and Church have responded with proposals for further tightening the relation. Scheffler still finds loopholes, but part of his criticism can be annulled [...]
We do have our analyticity intuition, but it grades off. [...] Now there is no objection to a graded notion of synonymy or of analyticity, supposing it made reasonably clear; but it is unlikely to contribute directly or indirectly to a standard of identity of propositions. For propositions have to be the same or distinct absolutely; identity, properly so-called, knows no gradations.
These reflections count only against hoping to base identity of propositions on some sort of intensional isomorphism derived from the broad sort of sentence synonymy which is interdefinable with analyticity. We might still hope to construct some approximation to intensional isomorphism suitable for identity of propositions, in some other way than from the elusive broad notion of sentence synonymy.
[...]
This last point [No need to worry about what that was - TH] has the germs of an argument not only against our specific plan of a structural synonymy concept as a standard of propositional identity, but against the whole idea of positing propositions. For, insofar as we take such a posit seriously, we thereby concede meaning, however inscrutable, to a synonymy relation that can be defined in general for eternal sentences of distinct languages as follows: sentences are synonymous that mean the same proposition. We would then have to suppose that among all the alternative systems of analytical hypotheses of translation (§§ 15, 16) which are compatible with the totality of dispositions to verbal behavior on the part of the speakers of two languages, some are "really" right and others wrong on behaviorally inscrutable grounds of propositional identity. Thus the conclusions reached in § 16 may of themselves be said implicitly to scout the whole notion of proposition, granted a generally scientific outlook. The difficulties cited earlier in the present section are merely by the way. The very question of conditions for identity of propositions presents not so much an unsolved problem as a mistaken ideal.

The Diagnosis

As we can see, Quine's objection to meanings, propositions, etc. was based on the idea that there is no single, clear criterion of identity for them. Given the doctrine of semantic granularity, this is no surprise and no objection. The individuation of these things differs at different granularities. In the grip of preconceptions about how language must properly work, Quine mistook a feature for a bug.

(I say that 'the individuation of these things differs at different granularities', but that form of expressing the point could be misleading and sound like some kind of antirealism - I will address that at length in a future post. For now: the point could be more carefully put in terms of the truth-values of synonymy or non-synonymy sentences, or of identity or distinctness statements about meanings, propositions etc.

This is connected with Quine's point in the Word and Object selection above, 'For propositions have to be the same or distinct absolutely; identity, properly so-called, knows no gradations.' On my approach, it is not that identity needs to have gradations, rather that identity statements with meaning- or proposition-designating phrases come out with different truth-values when operating at different granularities.)

It is instructive here to see how I, with my doctrine of granularity, can and indeed must agree with a lot of the things Quine says on the way to his hostile position, and how with the doctrine of semantic granularity on board, we can see that the hostile position doesn't follow.

For example: 'The very question of conditions for identity of propositions presents not so much an unsolved problem as a mistaken ideal' from the Word and Object selection. Indeed, if the question is construed as asking for a single, all-purpose set of conditions, it does present a mistaken ideal. What the doctrine of granularity says is that the conditions are different at different granularities, and that is part and parcel of the power and flexibility of semantic notions as bundlers and separators of linguistic items and occurrences.

And from Quiddities, 'The question of sameness of meaning, then, comes down to the question what to count as relevant difference. I see no prospect of a precise answer, nor any need of one.' Note the 'one'; the whole point of the doctrine of granularity is that there is no one answer here.

I hope I have conveyed in outline how the doctrine of semantic granularity can explain and perhaps help break the grip of Quine's hostility towards meanings, propositions and the like. This application will, if I am right, only become clearer and seem stronger with the development of the doctrine I intend to pursue in future posts.

Note finally that despite the focus here (especially in the Quine quotes) mostly being on propositions construed as sentence-meanings, all this applies just as much to sub- and super-sentential meanings as well, for instance with names and the individuation of their "meanings", which I construe as name-uses or individual concepts, or with the meanings of larger things like arguments or speeches or books.

References

McGrath, Matthew (2008). Propositions. Stanford Encyclopedia of Philosophy.

Quine, W.V.O. (1986). Philosophy of Logic. Harvard University Press.

Quine, W.V.O. (1987). Quiddities: An Intermittently Philosophical Dictionary. Belknap Press of Harvard University Press.

Quine, W.V.O. (1951). Two Dogmas of Empiricism. Philosophical Review 60 (1):20–43.

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

Quine on Facts: A Case-Study in Projective Fallacies

Quine was famously skeptical about facts. As I said in the last post, Quine can be seen as resolutely maintaining something which Strawson seems to suggest at his most objectionable moments. This will enable us to give a sharp diagnosis of one particular skeptical confusion about facts.

What on the part of true sentences is meant to correspond to what on the part of reality? If we seek a correspondence word by word, we find ourselves eking reality out with a complement of abstract objects fabricated for the sake of the correspondence. Or perhaps we settle for a correspondence of whole sentences with facts: a sentence is true if it reports a fact. But here again we have fabricated substance for an empty doctrine. The world is full of things, variously related, but what, in addition to all that, are facts? They are projected from true sentences for the sake of correspondence.

But let us ponder this last maneuver for a moment. The truth of 'Snow is white' is due, we are told, to the fact that snow is white. The true sentence 'Snow is white' corresponds to the fact that snow is white. The sentence 'Snow is white' is true if and only if it is a fact that snow is white. Now we have worked the fact, factitious fiction that it is, into a corner where we can deal it the coup de grace. The combination 'it is a fact that' is vacuous and can be dropped; 'It is a fact that snow is white' reduces to 'Snow is white'. Our account of the truth of 'Snow is white' in terms of facts has now come down to this: 'Snow is white' is true if and only if snow is white.

This nicely illustrates the attitude about fact-talk we were arguing Strawson had, and which Quine shares. All but the thinnest, most eliminable uses of fact-talk, such as prefacing propositions with 'It is a fact that', are cast out as bad philosophy. But this doesn't at all follow from the explanatory failure, if such there be, of attempting to account for truth in terms of correspondence with facts; why would dubious theories of truth be the only other thing you can do with fact talk, besides these most eliminable uses? We haven't been given a shred of evidence to suggest that they are.

Consider the argument in the second paragraph. It can be resisted from the point of view of the correspondence theory. Furthermore, we can put the correspondence theory to one side and show that, in any case, it does not even begin to show facts to be 'fictions'.

First of all, consider the point of view of a fact-based correspondence theory: the truth of propositions can be explained in terms of a relation of correspondence and certain relata, facts. Quine's transformation, which he just blandly performs without a word of explanation or justification, of the 'corresponds to the fact that' formulation into the 'if and only if it is a fact that' formulation, from this point of view, could justly be said to rather obscure the explanation. And the next step, of declaring 'it is a fact that' to be vacuous and dropping it, is completely indefensible. One thing is the fact that you can drop that phrase in many ordinary contexts – it does not at all follow that you can further mutilate the philosophical explanation in question in the same way.

In Strawson's case, the “elimination” was of a different sort, effected by imagining a counterfactual scenario in which we speak a language consisting only of simple commands. In the present case, the "elimination" is effected by transforming sentences of our language so that reference to facts disappears. It fails triply:

Firstly, the transformations are unjustified from the point of view of the correspondence theory.

Secondly: no evidence has been given that there are not other occurrences of fact talk which Quine cannot eliminate.

Thirdly: even if fact-talk were always eliminable, that doesn't eliminate facts, doesn't show them not to exist – that would be a use-mention confusion. (This point was made by my former teacher Adrian Heathcote.)

(Quine, or a good Quinean, however, may object that this third objection misses the point, and that there is something lying behind this argument: Quine's conception of ontology. I will not get into that possibility here.)

These three problems with Quine's “elimination” aside, we still have the contention in the first paragraph that facts are 'projected from true sentences'. This suggestive idea, particularly in light of our considerations about the role of concepts (or internal meanings, or modes of presentation) in the individuation of facts, could give independent support to the idea that facts are fiction, so it requires separate treatment. To this end, we shall now consider the idea of a projective fallacy in general, and go on to show that it is Quine, not the person who speaks of facts, who is guilty of one here.

Projective Fallacies (or Confusions) in General

There is a general idea, which seems to me to be important and useful in philosophy, that we sometimes get led into error or confusion by reading features of our language or thought into the world – or alternatively, projecting them onto the world.

Before considering some (hopefully relatively uncontentious) examples of such confusions or errors, let us review some classic philosophical expressions of the general idea.

Hume, in A Treatise of Human Nature: “The mind has a great propensity to spread itself on objects.” [Book 1, Part 3, §XIV]

Russell, in his Logical Atomism lectures: 'There is a good deal of importance to philosophy in the theory of symbolism, a good deal more than one time I thought. I think the importance is almost entirely negative, i.e., the importance lies in the fact that unless you are fairly self-conscious about symbols, unless you are fairly aware of the relation of the symbol to what it symbolizes, you will find yourself attributing to the thing properties which only belong to the symbol. That, of course, is especially likely in very abstract studies such as philosophical logic, because the subject-matter that you are supposed to be thinking of is so exceedingly difficult and elusive that any person who has ever tried to think about it knows you do not think about it except perhaps once in six months for half a minute.'

Wittgenstein, in the Investigations 104: 'We predicate of the thing what lies in the method of representing it.'

I will speak of 'projective fallacies' to refer to instances of this sort of thing, with the caveat that 'confusion' may be more appropriate in many cases, since there need not be any definite fallacious inference drawn, in the sense of a transition from proposition to proposition forming part of a chain of reasoning.

Examples of Projective Fallacies

Here I will try to give some examples of projective fallacies which aren't very philosophically loaded, in order to give a better idea of what they are.

Bands in the rainbow: looking at rainbows in relative scientific ignorance, it would be natural to think that the bands of colour we perceive in them correspond to intrinsic structural features of them. We might expect that bits of the rainbow near the end (width-wise) of band are more intrinsically different from those near the same blurry boundary on the other side, than are two equally distant bits which fall within one band. But this would be a projective fallacy.

Illusory failures of homophony: Taking two words with the same pronunciation but different spellings in isolation, and saying them one after the other by themselves, we might persuade ourselves that we ordinarily pronounce them very slightly differently, when this is not in fact the case. A difference which lies only in our mode of representing speech has been projected into our speech.

Taking an “operator” for a representative: An extra-terrestrial who had correctly concluded that road signs sometimes depict objects to be found in their vicinity (such as speed-bump signs, signs indicating the presence of wildlife, etc.), might see a sign disallowing dogs and mistakenly infer that there are creatures nearby with large crosses attached to their bodies.

Incidental features of models: A boy makes a model of a boat he admires, and uses a piece of wood in which he had made, at another time and for some other purpose, a regular series of indentations. Years later, as a grown man, he finds the model he made, notices and remembers deliberately making the indentations, and forms the erroneous idea that the boat he admired bore indentations in the corresponding place.

Projection-Based Skepticism about Facts

Let us return now to Quine's formulation of projection-based skepticism about facts. He said:

The world is full of things, variously related, but what, in addition to all that, are facts? They are projected from true sentences for the sake of correspondence.

In other words, the idea that there are facts involves a projective fallacy. In the following two sections I want to show that this is completely wrong, and ironically so: it is Quine who is guilty of a projective fallacy here, in thinking that the believer of facts is guilty of a projective fallacy.

Something Which Is True: A Genetic Point about Ideas of Facts

We talk of particular facts – we have concepts, or ideas, of particular facts. How do we arrive at these? I think it is plausible to say that we derive them, in some sense, from true propositions. Think of how we form our ideas of particular propositions: first we formulate the propositions, then we produce an idea of that proposition. We might say these ideas of propositions are projected from the propositions themselves. Likewise with ideas of facts, although the projection is different.

This may be called a genetic point about ideas of particular facts, since it is not a piece of semantics or analysis, but rather a hypothesis about how certain cognitive structures come about.

It seems plausible, does it not, that in order to have an idea of a particular fact, you need to have some true propositions under your belt? The reason for this, we may say, is that our ideas of particular facts are – in some, if not all cases – derived from our representations that such-and-such is the case, when it is the case – that is, from true propositions.

The Irony of Projection-Based Skepticism About Facts

We are now in a position to see that Quine, in painting the idea that there are facts as guilty of a projective fallacy, is himself guilty of a projective fallacy: he has projected a property of our ideas of facts – namely, their being derived, or projected, from our true propositions – onto facts themselves, and concluded that, since facts are also meant to be mind- and language-independent, the whole idea of facts is bankrupt; facts are impossible fictions. But that is a mistake.

Reference

Quine, W. V. (1987). Quiddities: An Intermittently Philosophical Dictionary. Belknap Press of Harvard University Press.

Against Quine's Argument in Sect. 31 of Word and Object

ADDED: Here is a followup post from 26 December 2015.
UPDATE (Nov 2019): I have recently published a paper on this topic, 'Quine's Poor Tom', in the European Journal of Analytic Philosophy.

Section 31 of Quine's Word and Object contains an arresting fallacious argument. In 1966, R.C. Sleigh Jr. published an objection to it. In 1977, David Widerker published an objection to Sleigh's objection. More recently, in 2007, Charles Sayward has published a paper where Sleigh's objection is further criticized. (References below.)

I will not engage directly with these three papers, but rather aim to give a clearer objection to Quine's argument.

Here is Sayward's apt description of the argument's point:

To a first approximation, the argument purports to show that if Tom has a certain minimal level of logical acuity—a level many of us possess—then if ‘belief’ has a sense in which it is a transparent operator, then Tom, if he in that sense of the word believes anything, he in that sense of the word believes everything. (Sayward 2007, p. 54.)

Quine assumes that Tom believes at least one true sentence and one false one. In fact, he assumes something much stronger: that Tom believes the true sentence 'Cicero denounced Catiline' and the false sentence 'Tully did not denounce Catiline'. (Cicero is Tully.) That these sentences are are (in a sense) contradictories, and that they are about the same object, is not essential for Quine's argument. These features of Tom were needed for earlier, separate arguments in chapter IV of Word and Object. 
Here is the argument:

Where ‘p’ represents a sentence, let us write ‘#p’ (following Kronecker) as short for the description: 

     the number x such that ((x = 1) and p) or ((x = 0) and not p). 

[In place of '#', Kronecker and Quine used a different symbol, which I can't easily reproduce here. - TH.] 

We may suppose that poor Tom, whatever his limitations regarding Latin literature and local philanthropies, is enough of a logician to believe a sentence of the form ‘#p = 1’ when and only when he believes the sentence represented by ‘p’. But then we can argue from the transparency of belief that he believes everything. For, by the hypothesis already before us, 

     (3) Tom believes that # (Cicero denounced Catiline) = 1.

But, whenever ‘p’ represents a true sentence, 

     # p = #(Cicero denounced Catiline). 

But then, by (3) and the transparency of belief,

     Tom believes that #p  = 1,

from which it follows, by the hypothesis about Tom’s logical acumen, that 

     (4) Tom believes that p. 

But ‘p’ represented any true sentence. Repeating the argument using the falsehood ‘Tully did not denounce Catiline’ instead of the truth ‘Cicero denounced Catiline’, we establish (4) also where ‘p’ represents any falsehood. Tom ends up believing everything. (Quine 1960, pp. 148–149).

First, to rehearse Quine's definition of referential transparency. (Familiar readers can skip this paragraph.) Quine defines transparency in terms of 'modes of containment ... of singular terms or sentences in singular terms or sentences'. Definite descriptions count here as singular terms. For Quine, a mode of containment M is referentially transparent iff, 'whenever an occurrence of a singular term t is purely referential in a term or sentence C(t), it is purely referential also in the containing term or sentence M(C(t)). ' (p. 144, schematic letters changed). For a singular term t to be purely referential in a term or sentence is for it to occupy a purely referential position there. Quine's 'criterion' for a position's being purely referential is that the position 'must be subject to the substitutivity of identity' (p. 142). That is, to the substitutivity of co-extensive singular terms salva veritate.

Let us begin by simply granting (3) for the sake of argument, ignoring its justification - Quine's 'by the hypothesis already before us'. (After we have identified a later fatal flaw in the argument, we will return to (3)'s justification briefly, since it seems to suffer from essentially the same flaw.)

Now, note that Quine's 'hypothesis about Tom's logical acumen' (hereafter 'the acumen hypothesis') and the steps of his argument are at different semantic levels. The hypothesis is framed in terms of belief in sentences, while in the argument, sentences appear unquoted as the contents of 'that'-clauses. Thus, the acumen hypothesis does not apply directly to 'Tom believes that #p = 1', since that sentence says nothing about Tom's belief in any sentence. Quine is, apparently, suppressing a quotational and a disquotational step here. An expanded version of this part of the argument, in which the acumen hypothesis could be applied directly, would have to run something like:

(i) Tom believes that #p = 1.

(ii) Hence Tom believes the sentence '#p = 1'. (Quotation step.)

(iii) Hence Tom believes the sentence 'p'. (Acumen hypothesis together with (ii).)

(4) Tom believes that p. (Disquotation step.)

Secondly, note that 'believes' in 'Tom believes that #p = 1' is to be taken in a transparent sense, as the piece of reasoning preceding it makes clear. (In case of any residual doubt about this: in the very next sentence after the argument as quoted, Quine summarizes it by saying 'Thus in declaring belief invariably transparent ... we would let in too much.')

Putting these things together, we can see the invalidity of Quine's argument: when (i) is taken in a transparent sense, it does not imply (ii).

To see this, consider that Delia Graff Fara believes (in the transparent sense) that Quine wrote Word and Object. We hereby introduce a new name for Quine, 'G6'. Now, since G6 is Quine - since 'G6' and 'Quine' are co-extensive - we may infer that Delia Graff Fara believes (in the transparent sense) that G6 wrote Word and Object. Plainly, we cannot infer from this that Professor Fara, who knows nothing of my convention (at the time of writing), believes the sentence 'G6 wrote Word and Object'.

The problem with Quine's argument as it stands, then, is in the first instance a use-mention confusion. (None of the papers cited makes anything of this point.) We have now seen that the problem cannot be fixed by expanding the argument to contain a quotational and a disquotational step; the quotational step is invalid. Can it be fixed by rephrasing the acumen hypothesis as a schema containing placeholders for unquoted sentences?

It cannot. Such a schema would run: 'John believes that #p = 1 when and only when he believes that p'. The dilemma here is that, if 'believes' is taken transparently, the schema is not a defensible principle of rationality (even for logicians), and if it is taken opaquely, the principle doesn't apply to Quine's argument.

Finally, to return to the first step of the argument, namely (3)'s justification. The 'hypothesis' Quine cites here is, as far as I can tell, the acumen hypothesis. And so this step is just as invalid as Quine's inference to (4). For the case where 'p' is true, however, (3) will be true anyway, so long as Tom believes that 1 = 1.

Tristan Haze
The University of Sydney

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.