Friday 25 December 2015

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. 
(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.

- 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.)


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.

Friday 20 November 2015

Skepticism About Metaphysical Modality and Unclear Cases

Some philosophers are skeptical of the notion of metaphysical or subjunctive modality isolated by Kripke. They may think for instance that the notion of necessity de dicto is coherent but nothing falls under it, or they may think that isn't even a coherent or legitimate notion. This post is more about the latter.

One cause of such skepticism, I suspect, is that some of the canonical cases Kripke adduces in Naming and Necessity are not particularly clear cases. That is, they are borderline or disputable cases. In addition, the attitude Kripke seems to take to these cases may not be completely appropriate. With these cases, he sometimes gives the impression that the way to know how it is with them is to use intuition - and here the intuiting has a different character than in clear cases. It seems like a kind of hearkening or special receptivity is supposed to be needed. All this may seem, so to speak, occult. And if this doesn't put us off the notion altogether, it may yet mislead us about what sort of account we should look to give of it.

The sorts of cases I have in mind are those of the table - could it have been made of ice? (Kripke intuits that it couldn't.) And the Queen: could she have been born of different parents? (Kripke intuits that she couldn't.) 

(One thing about the Queen case which has troubled me for years is what I call the fish argument. This argument works by iterating the supposed necessity of origin; if the Queen is necessarily the child of her actual parents, and they are necessarily the children of their parents, then we seem to be forced to conclude that the Queen is necessarily the descendant of some fish which she is in fact descended from - call him Colin. That is, there is no possible world involving the Queen where Colin isn't also around. This seems dubious.)

To all this, my suggestion is that we shouldn't get hung up on such cases when it comes to the question of whether the notions of metaphysical or subjunctive modality are legitimate, and when it comes to understanding those notions. Just as, when trying to give someone a grasp of the notion of tallness, it is better to work with examples of people who are definitely tall, or definitely not tall. To start insisting on certain judgements about more borderline cases is not to the point, and may make the whole business seem dubious. I think that following my suggestion may help us both explain and legitimate the notions in question, and may help us account for them in the proper way.

Sunday 1 November 2015

What is Necessity De Dicto?

I recently posted an account of necessity de dicto. The purpose of this post is to pin down exactly what this topic is. The notion in question of course looms large in contemporary analytic philosophy, but it will serve us well and keep us grounded to furnish in as clear a way as possible a basic characterization of it. In a future post, I will turn to specifying the problem or task which my account is addressed to with respect to the topic. In another future post, I will state some of my assumptions and guiding ideas.

The key source for the notion of necessity de dicto is of course Kripke's Naming and Necessity. It was there that our topic was (to the best of my knowledge) first clearly isolated and characterized. Priority aside, Kripke's characterization is not easily improved upon and has been very influential. (Regarding the notion itself, not its characterization: it is a very interesting historical question to what extent this notion was present in earlier thinking. Or to what extent similar notions were, and how they may relate to the present notion. I will make no attempt here to answer this.)

Kripke's starting-point in characterizing the notion of necessity de dicto is to remark that, while many (at the time he was speaking) seem not to differentiate between a priority and necessity, he certainly will not use 'a priori' and 'necessary' in the same way (p. 34). He then, after emphasizing that the notion of a priority is an epistemological one and mentioning some issues which might arise with that notion, gives the following characterisation of necessity:

The second concept which is in question is that of necessity. Sometimes this is used in an epistemological way and might then just mean a priori. And of course, sometimes it is used in a physical way when people distinguish between physical and logical necessity. But what I am concerned with here is a notion which is not a notion of epistemology but of metaphysics in some (I hope) nonpejorative sense. We ask whether something might have been true, or might have been false. Well, if something is false, it's obviously not necessarily true. If it is true, might it have been otherwise? Is it possible that, in this respect, the world should have been different from the way it is? If the answer is 'no', then this fact about the world is a necessary one. If the answer is 'yes', then this fact about the world is a contingent one. (pp. 35 – 36.)

This should go a long way to giving us an acceptable grasp of the notion of necessity de dicto. Kripke also says some things about the extension of the notion which may be of further help to this end. Before proceeding to that, however, I want to tighten up Kripke's characterization in a couple of ways, as well as emphasizing and de-emphasizing certain parts of it.

For one thing, note that Kripke moves freely here between talking of 'facts about the world' as well as things which can be called true or false, as the bearers of necessity. Later, he speaks also of 'states of affairs' and 'statements'. This is fine, but I want to make it clear that the topic I am addressing in my account is the notion of necessity as it applies to things which can be called true or false: statements – or as I say, propositions. This is what I mean by 'de dicto' in 'necessity de dicto'. To be still more precise about what propositions are – for a start, whether they are or involve sentences themselves, or just their meanings – is not necessary, but see this post for an approach I favour.

(At this point I should emphasize that that is all I mean by 'de dicto' in 'necessity de dicto'. The term 'de dicto', and the contrasting term 'de re', are used in various ways in philosophy. It it especially important to realize that I count all attributions of necessity to propositions as attributions of necessity de dicto, even when those propositions are “singular propositions” about individuals – i.e., propositions attributions of necessity to which David Lewis would deploy counterpart theory to understand.)

Something I want to emphasize in Kripke's characterization is the way it cashes out necessity in terms of counterfactual scenarios – to use the language of some two-dimensional semanticists, scenarios considered as counterfactual, rather than scenarios considered as actual. This could be emphasized by calling our topic 'counterfactual necessity de dicto' or 'subjunctive necessity dicto', but I avoid this for the sake of brevity.

(You may think that this is the same as the point that necessity is not to be understood epistemologically, but I'm not so sure. For one thing, I suspect there are notions of 'could actually be the case' and 'must actually be the case' which, even if 'a priori possible' and 'a priori true' may be good expressions for them, can be cashed out non-epistemologically. (Cf. this post.) For another thing, 'Could have been' talk can also be given an epistemological reading, along the lines of 'Was epistemically possible'. In any case, emphasizing that with the notion of necessity de dicto we are dealing with scenarios considered as counterfactual, can only help to avoid misunderstanding here.)

Something I want de-emphasize in Kripke's characterization, on the other hand, is the way he classifies the notion of necessity he wants to talk about as a notion belonging to metaphysics. I do not think this is essential to grasping the notion in question: that can be done without any recourse to a notion of metaphysics. Kripke's use of a category of metaphysics here may be slightly helpful in emphasizing that necessity de dicto is not an epistemological notion, but that point can be emphasized without a notion of metaphysics. Since we can easily get by here without invoking a notion of metaphysics, I think we ought to avoid doing so. I am not going to argue the point at length here, but I suspect that invoking a notion of metaphysics may lead to some unhelpful prejudice about how the notion is best to be understood and analyzed (if it is to be analyzed) – or more to the point, how it is not to be analyzed. In particular, I worry that it may cause prejudice against accounts which crucially involve semantic considerations, by promoting a vague idea that necessity de dicto is “all about” how things are in the world, as opposed to having anything to do with language and thought.

Finally, Kripke's characterization should be supplemented with something about the sense of 'necessary' being unrestricted or very broad. To see this, consider an utterance like 'It is true that I stayed home yesterday. This couldn't have been otherwise, as I had to be there to let the electrician in.' This utterance may be true, but in that case the 'couldn't have been otherwise' part is not about necessity de dicto in the sense I am interested in – we are dealing with a contextually restricted range of ways things could have been. For instance, we are probably ignoring ways things could have been in which I stop caring about having electricity, or in which I never made the appointment with the electrician, or in which the appointment was on a different day. This supplementation of the Kripkean characterization has become customary. Witness Timothy Williamson in an interview:

Something is metaphysically necessary if it couldn’t have been otherwise, in the most unrestricted sense. (Williamson & Antonsen 2010, p. 18.)

Or Daniel Stoljar, referring to:

(…) the completely unrestricted sense of possibility that philosophers sometimes call “logical” or “metaphysical” possibility (…) (Stoljar 2006, p. 34.)

Or this terminological stipulation made by van Invagen:

Modal terms will be used in their “metaphysical” or “unrestricted” sense (…). (van Invagen 2015, p. 35.)

There is a wrinkle here, however. For some things philosophers say may seem to go against the propriety of characterizing our topic in this way. On the way of speaking I have in mind, there are necessities in the sense of our topic which are not necessary in some other sense – 'logically' or 'mathematically' or 'epistemically' for example. See, for instance, this passage in Nathan Salmon (where he is arguing that an objection made to something he has proposed – the details of which don't matter here – does not hold water):
Metaphysical modality is definitely not an unrestricted limiting case. There are more modalities in Plato’s heaven than are dreamt of in my critics’ philosophy, and some of these are even less restrictive than metaphysical modality. One less restrictive type of modality is provided by mathematical necessity and mathematical possibility. […] Another type of modality less restrictive than metaphysical modality is provided by what is sometimes called ‘logical necessity’ and ‘logical possibility,’ to be distinguished from genuinely metaphysical necessity and possibility, or necessity and possibility tout court. A proposition is logically necessary if its truth is required on logical grounds alone […]. Although there is a way things logically could be according to which I am a credit card account, there is no way things metaphysically might have been according to which I am a credit card account. (Salmon 2005, p. 136)
But notice the contrast at the end of this passage between 'could be' and 'might have been'. Salmon is concerned here with what he calls 'the confusion between the generic notion of a way for things to be and the modal notion of a way things might have been'. According to Salmon, this confusion
is very probably the primary source of the idea that metaphysical modality is the limiting case of restricted modalities, that metaphysical necessity and possibility is the unrestricted, and hence the least restricted, type of necessity and possibility. For metaphysical necessity is indeed truth in all ways things might have been (modal, not generic), and metaphysical possibility is indeed truth in at least one way things might have been (modal, not generic). (ibid, p. 136.)
So, since we are explicitly talking about ways things might have been, it seems that Salmon would have no real disagreement after all with Williamson's succinct characterization of our topic, quoted above (except perhaps for some pragmatic disagreement about what to emphasize, or how best to use language to avoid potential confusions).

In any case, one thing that should be clear is that we are not dealing with a notion where certain contextually relevant matters of fact may be held fixed, as in the electrician example above.

So much for the intensional characterization of the notion of necessity de dicto. Another thing which may help us grasp the notion is consideration of its extension – cases, and what types of cases there are. Most instructive in this way are cases lying outside the overlap of necessity and a priority. After giving his intensional characterization of the notion, Kripke goes on to say that he will be arguing that, in addition to being conceptually different, the categories of necessity and a priority are extensionally different: 'I will argue below that in fact they are not even coextensive—that necessary a posteriori truths, and probably contingent a priori truths, both exist.' (Kripke 1980, p.38.)

An aspect of the character of the notion of necessity de dicto is captured vividly in some of Kripke's intuitive appeals regarding the necessary a posteriori, in particular with the use of the phrase 'given that', and similar language. For instance, if I think some object I have encountered empirically, a, is the same object as I have encountered empirically in other situations, b, then – while I might conceivably turn out to be wrong, i.e. while it might turn out to be the case that a is distinct from bgiven that a is indeed b, then a couldn't have been distinct from b; 'a = b' is necessary.

Regarding the contingent a priori, perhaps the most straightforward and instructive type of case occurs when a name is stipulated to refer to whatever object satisfies some description, where the description is of a sort where an object satisfying it could have failed to satisfy it. So if I stipulate that 'a' is to refer to the inventor of the zip (if there was an inventor of the zip), then the proposition 'a, if there is an a, invented the zip' is a priori: in virtue of the way I have set 'a' up to work, it just can't turn out empirically that a exists and yet didn't invent the zip after all. Now suppose that there is an inventor of the zip. In that case, the proposition 'a, if there is an a, invented the zip', while a priori, is contingent: someone else could have invented the zip.

We have now characterized our topic, first intensionally, by taking and modifying slightly Kripke's famous characterization, and then extensionally, by pointing to two striking types of cases. The next question we must address is 'What is the problem or task in relation to the topic, to which your account is a response?' I will concentrate on this in a future post.  


Kripke, Saul A. (1980). Naming and Necessity. Harvard University Press. (First published 1971.)

Williamson, Timothy & Antonsen, Paal (2010). Modality & Other Matters: An Interview with Timothy Williamson. Perspectives: International Postgraduate Journal of Philosophy 3 (1):16-29.

Salmon, Nathan U. (2005). 'The Logic of What Might Have Been' in Metaphysics, Mathematics, and Meaning. Oxford University Press. Article originally published in 1989.

Stoljar, Daniel (2006). Ignorance and Imagination: The Epistemic Origin of the Problem of Consciousness. Oxford: Oxford University Press.

van Invagen, Peter (2015). 'Nothing is Impossible' in God, Truth, and other Enigmas, Szatkowski, Miroslaw (ed.),. De Gruyter.

Wednesday 21 October 2015

Thursday 1 October 2015

An Account of Necessity as an Attribute of Propositions

I hope to say more about this in future, making the account more perspicuous and better defending it, but it is high time I made a blog post about it. My view that this account is correct has been stable since 2012. It fits with my account of propositions and could also be adapted to various other conceptions of propositions and meaning (but not all).

(Added October 2016: my most up-to-date treatment of this topic can be found in Chapters 1 and 5 of my PhD thesis. This is an early, undeveloped attempt.)

Some related posts:

A proposition is necessary iff it is, or is implied by, a proposition which is both inherently counterfactually invariant and true.

A proposition is inherently counterfactually invariant iff, if it is held true, it is held fixed across counterfactual scenario descriptions, i.e. its negation does not appear in any counterfactual scenario descriptions.

(I say 'its negation does not appear in any' rather than 'it appears in all' because counterfactual scenario descriptions don't normally deal with everything - are not normally maximal.)

Whether or not a proposition is inherently counterfactually invariant is a matter of the internal meaning of that proposition.

When I speak of 'counterfactual scenario descriptions', I mean not just those actually produced, but those which can be produced. Thus there is an unreduced modal element in my analysis of de dicto necessity.

Not everything which we could call a description of a scenario, where the scenario in question does not in fact obtain, counts as a counterfactual scenario description. If we say, for example, 'Perhaps things are actually such that ...', what goes in the blank is not to be counted as a counterfactual scenario description, even if it is a description of a scenario which does not obtain. Rather, I am talking about descriptions which, so to speak, describe a scenario as counterfactual - e.g. 'Things could have been such that ...'. This is like the distinction two-dimensional semanticists emphasize, between considering a scenario as actual vs. considering it as counterfactual. When a description is made of a scenario which is being considered as counterfactual, then that is a counterfactual scenario description.

We must distinguish between genuine and non-genuine counterfactual scenario descriptions. In the case of the latter, we may always say that the meaning of at least one of the expressions involved is being violated or departed from. For example, if we suppose that 'Cats are animals' is necessarily true, and yet speak loosely of a counterfactual scenario in which there are robot (and thus non-animal) cats. Here we can either say that we are using 'cat' in a different meaning entirely, in which case the counterfactual scenario description may be genuine, or are beginning with the primary meaning but, as it were, stretching it, in which case we have a non-genuine counterfactual scenario description. Another example: if Euler had squared the circle, he would have been famous for it. The description in the antecedent of what Euler does should be regarded as a non-genuine counterfactual scenario description. I take this notion as primitive, and think it is vague.

Note that it is not the case that a counterfactual scenario description is genuine iff the scenario it describes is metaphysically possible, and so it would be a mistake to think that counterfactual scenario descriptions play more or less the same role as "possible worlds" do in some other accounts. For instance, if I believe that Hesperus is not Phosphorus, then if I talk about a case in which 'Hesperus had been Phosphorus', this will be a non-genuine counterfactual scenario description, even though it is metaphysically possible, indeed actual, for Hesperus to be Phosphorus. Likewise, if I - again, believing Hesperus not to be Phosphorus - talk about a situation in which Hesperus and Phosphorus are distinct, this may be a genuine counterfactual scenario description, even though it is metaphysically impossible for Hesperus to be distinct from Phosphorus.

It cannot be denied that the notion of a genuine counterfactual scenario description, and in turn that of inherent counterfactual invariance, have much of the character of the notion of necessity de dicto. Still, as we have just seen, they behave quite differently. So it is anything but trivial to see that we can put these notions together with those of truth and implication to yield a statement of the conditions under which a proposition is necessary de dicto.

We may also delineate the inherently counterfactual scenarios in another way: they are those which are such that it is a priori that they are necessary if true. I do not think we should think of this as giving the content of the notion, however. It is another way to get a handle on the relevant class of propositions, which may help us to get the notion.

To see why closure under implication is required, consider any disjunction of a necessary truth with a contingently true or false proposition. Such a disjunction will of course be necessary, but it will not be inherently counterfactually invariant, since it can be held true by holding the contingent proposition true and the necessary one false.

My analysis gets the right answer on such a case, since the proposition will be implied by a proposition which is both inherently counterfactually invariant and true - in the simple disjunction case, the necessary disjunct. However, note that the relevant implier will not always be a part of the proposition in question: consider 'Everything is either such that it is either not a cat or is an animal, or such that it is either less than 100 kilograms in weight or not in my room'. This is in fact necessarily true, since all cats are animals and that is a necessary truth (or so I'll assume - the particular example doesn't matter). But you might hold it true if you disbelieve that all cats are animals, by believing that nothing in the speaker's room weighs more than 100 kilograms. If that is how you held it true, you would let its negation appear in counterfactual scenario descriptions - namely, descriptions of scenarios in which I have something heavy in my room.

Again, it is very important to see that counterfactual scenario descriptions do not act as "possible worlds" in my account. One easy way to see this is to consider someone who falsely believes a proposition whose negation is necessarily true a posteriori. Examples: 'Hesperus is not Phosphorus', 'Cats are robots', 'Hesperus is Mars'. Such a person will be in a position to produce counterfactual scenario descriptions involving these propositions, despite them being not only false but impossible. My account filters these out from being classed as necessary by means of the truth requirement.

To get a better grip on the role the notion of inherent counterfactual invariance plays in my account, compare Sider’s account on which there is something list-like and arbitrary at the core of the notion of necessity de dicto. The account is given in Writing the Book of the World, but is also rehearsed briefly in ‘Symposia of Writing the Book of the World’ (which has the benefit of being freely available at

According to this account, for a proposition to be necessary is roughly for it to be a logical consequence of a certain class of propositions, the “modal axioms”. Modal axioms come in different sorts, including mathematical truths, analytic truths (under a certain conception of analyticity), “laws of metaphysics”, and “axioms of a metaphysical semantics”. The account is a highly “defl ationary” one in that no metaphysically deep condition is given to unite all the modal axioms. They are given by a mere list (mathematical truths, analytic truths, …), which is selected, so to speak, “by us rather than by the world”—perhaps by linguistic convention.
Once you realize that the “modal axioms” Sider is talking about are all truths, you can see that his account shares a structure with mine: a proposition is necessary if it is or is a consequence of a true proposition fulfilling come condition C. Realizing that something of that form is correct is an important step. And I think my account is preferable to Sider’s because I have something more substantive to say about what the condition C is, such that it is in not in any relevant sense arbitrary whether a proposition has it or not: it is inherent counterfactual invariance. (Of course, if the notion of necessity de dicto seems arbitrary or conventional to you, you might prefer Sider’s account. I discuss that account and offer objections to it here.)

One of the attractive things about my account, I think, is that it does not try to reduce necessity de dicto to non-modal notions. For one thing, that may not be possible. For another, it seems it isn't necessary for an informative analysis of necessity de dicto. By not trying to reduce the modal to the non-modal, my account has more of a chance of being true and insightful. Also, it seems to me to be attractively simple and elegant, while still having enough structure, and involving the hitherto unfamiliar but natural notion inherent counterfactual invariance, so that it is understandable why it was not immediately obvious once the notion of necessity de dicto was clearly isolated by Kripke.

Saturday 19 September 2015

Two Opposite Types of Granularity Difference

This is another post in my series on semantic granularity. The others so far, in chronological order, are:

John and Mary both use the word 'happiness', and understand each other perfectly in most conversations. They use it in propositions in such a way that we would say that they both attach the same meaning to the propositions used, are on the same page, etc. But in certain relatively peripheral regions of application, they differ systematically.

We want to be able to tie John's peripheral uses of 'happiness' together with his non-peripheral uses - we want to say he's using the word in the same sense in both cases, but we also want to bundle his non-peripheral uses with Mary's. However, we also want to be able to make a semantic distinction between Mary's peripheral use and John's.

The solution is two operate at two granularities. A relatively coarse-grained bundling can tie all John and Mary's uses together - roughly, by ignoring peripheral use features. But we can use a more fine-grained bundling to describe the linguistic difference between Mary and John - at this granularity, we say they mean slightly different things by 'happiness'.

But there is another sort of descriptive problem which we solve with granularity shifts. For example, consider the normal uses made of the word 'hard' in the phrases 'hard man' (meaning something like 'tough guy'), 'hard wood' and 'hard test' (meaning a difficult test). We can distinguish three different senses here - very roughly, (i) toughness, (ii) solidity and resistance, and (iii) difficulty. Or two, a literal sense ('hard wood') and a "metaphorical" sense ('hard man', 'hard test'). Or we can bundle all these together.

Visually, we can think of the first kind of fine-graining as a kind of broadening of considerations which go into bundling, and the second kind of fine-graining as a kind of narrowing.

This is perhaps one of the things which have made granularity considerations, although quite natural, seem difficult - or not even arise as a serious possibility - from the point of view of analytic philosophy. That two different, in a sense opposing, things can be going on in shifts toward finer granularity, can make the matter confusing. But once we see what is happening and master it, it just reveals the richness and power of the approach.

From these examples, it may look like the first, 'broadening' type of fine graining is concerned with intersystematic distinctions – distinctions between different sign systems (in the example above, John's and Mary's idiolects) – and that the 'narrowing' type is concerned with intrasystematic distinctions – between elements and uses of some given sign system.

But this doesn't generally hold. In the broadening case, for example, we may have spoken about two very similar but subtly distinguishable meanings of quite different words in, say, John's idiolect. 'Envy' and 'jealousy', perhaps. Or 'rage' and 'fury'. Likewise, in the narrowing case, where we, at finer grain, distinguish the meaning of 'hard wood' from 'hard test', we could instead make that distinction between these words as used by two different people, or two different words used by two different people.

One thing we can say, perhaps, is that the 'broadening' type of fine graining is about considering how more ground is covered, factoring in more stuff about 'the lay of the land', where the 'narrowing' type is more about marking off different regions. The first involves making more distincions among expression-uses based on how the expressions cover the ground they cover, the second involves making more distinctions among expression-uses based on what ground they are covering in that use.

Tuesday 8 September 2015

Forthcoming in Logos & Episteme

(UPDATE 8 July 2016: See this post for some information and links regarding a debate brought about by this paper.)

My paper 'Two New Counterexamples to the Truth-Tracking Theory of Knowledge' is forthcoming in Logos & Episteme. It derives from this blog post. The final draft is available at PhilPapers.

An interesting point about its origin: I was originally playing with what I thought might be a type of counterexample to the truth-tracking account involving weird self-referential propositions. After investigating for a stretch I concluded that the approach was no good, at which point the counterexamples in the present paper (which have nothing to do with self-reference) came into my head. Something about the disappointment at the weird self-referential approach failing, together with the fact that I had during the investigation started to get used to the idea that I was able to refute the truth-tracking theory, caused me to think of the actual counterexamples.

For another recent counterexample to the truth-tracking theory (which also works against some other theories) see Neil Sinhababu and John Williams's paper 'The Backward Clock, Truth-Tracking and Safety' and Sinhababu's blog post about it.

Saturday 15 August 2015

The Principle of Compositionality and Semantic Granularity

This is another post in my series on semantic granularity. The others so far, in chronological order, are:

If meanings properly get carved up at different granularities, as I maintain, what are the implications for the 'the principle of compositionality'? I believe that granularity considerations can shed light on the status and application of this principle, and clear up much of the confusion surrounding it.

This confusion appears to be considerable. Witness Daniel Cohnitz ('Is Compositionality an A Priori Principle?'):

A superficial look at the literature on the principle of compositionality [...] could suggest that the discussion is as confused as a discussion can be.

I will now quote some classic and some typical formulations of the principle, and then indicate what we can say about it in light of granularity.

From the Tractatus:

I conceive the proposition—like Frege and Russell—as a function of the expressions contained in it. (3.318)

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. (4.024)

It is essential to propositions, that they can communicate a new sense to us. (4.027)

Frege, in a letter to P.F. Jourdain, probably written in 1914:

The possibility of our understanding [my emphasis] propositions which we have never heard before rests evidently on this, that we construct the sense of a proposition out of the parts that correspond to the words.

Theo Janssen, 'Compositionality':

The principle of compositionality reads, in its best known formulation:
The meaning of a compound expression is a function of the meanings of its parts.

But this omits something. The way the parts are put together, not just their meaning, goes into determining the meaning of the whole. ('John loves Mary' means something different from 'Mary loves John'.)

This is the point made by 3.141 of the Tractatus:
The proposition is not a mixture of words (just as the musical theme is not a mixture of tones). 
The proposition is articulate.

The following instances do not omit this:

B.H. Partee, handout for Ling 310 The Structure of Meaning, Lecture 1, February 20, 2006 p.1:

The Principle of Compositionality: The meaning of an expression is a function of the meanings of its parts and of the way they are syntactically combined.

'Compositionality', The Stanford Encyclopedia of Philosophy:

[T]he meaning of a complex expression is fully determined by its structure and the meanings of its constituents.

We have now seen the principle of compositionality stated in various ways.

One idea I want to suggest is that, at a maximally fine granularity, the principle of compositionality can be thought of as guaranteed to hold – a blanket, a priori principle.

However, once we relax the granularity, compositionality can begin to fail in many cases.

This would give us an avenue by which to approach the confusion about whether the principle of compositionality is just a conceptual truth about how all languages – everything we would call a language – must work, or an ideal which is sometimes met and sometimes not, or just something which occurs sometimes (i.e. for some languages, or parts of languages) and not others, without necessarily being an ideal: from a fine-grained point of view, it can be construed as something which applies without exception, but from courser-grained points of view, we can make distinctions between cases where it holds and cases where it doesn't. (The stuff about being an ideal versus not being an ideal can then be considered using this as a basis.)

The proposal I just indicated – that at a maximally fine granularity, compositionality can be thought of as holding a priori and across the board – while it has a certain theoretical appeal, is problematic: it might seem straightforwardly false (in light of the existence of idioms, for example), but of course replies can be made to that (for example, that semantically, idiomatic phrases have less, or just different, parts or constituents than they would appear to have considered literalistically). I do not want to be dogmatic about this, and I suspect there is room for “having it both ways” by means of careful disambiguation.

Some of the points I want to make here can be made without any such strong principle (that is, without the proposal above – call it 'the blanket proposal'). I will therefore do that first, and then come back and reconsider the blanket proposal.

Compositionality Can Depend on Granularity

The proposal summed up in this heading is weaker than the blanket proposal (the proposal that granularity holds a priori across the board at maximally fine granularity but can fail in cases as the granularity is coarsened): all that is claimed is that some complex expressions are such that compositionality may be said to hold of them, given a certain granularity of individuation of their components' meanings, but also such that compositionality then fails to hold at a coarser granularity.

Consider this bit of dialogue from season 2 of Flight of the Conchords:

Murray: Now, we've known each other for quite some time in the professional realm. I'd like to push things forward in the friendship realm.

Jemaine: What's the friendship realm?

Murray: Well, you've heard of a realm?

Bret: Mm.

Murray: Yep?

Jemaine: Yes.

Murray: Well this is like a friendship one.

What makes this sequence is the way Murray's compositional "explanation" of 'the friendship realm' fails drastically. Is this, then, a “counterexample to compositionality”? Not really; or at least, to say that would not be to tell the whole story.

I think we can take two views of this case, and many others like it: a compositional/fine-grained view and a non-compositional/course-grained view.

On the first conception, we think: Murray means something here, he has put together a meaningful proposition. 'Friendship' and 'realm' here are clearly functioning in a way that is continuous with and related to a great many other occurrences of these words. Therefore, whatever this proposition means, that 'friendship' and 'realm' contribute in the way they do, or that they appear here in the way they do, in a proposition with this meaning, is part of – or an aspect of – the meaning, or the use, of these words (given fineness of grain).

Taking this viewpoint does not commit us to saying that these fine-grained component meanings were fully present before the phrase 'friendship realm' was ever used: depending on the details of the case, we could say that some people attached those meanings to the component terms already and some attached others (but that the difference never showed up, or slightly, but not in such a way as to prevent mutual understanding), or that no one used the words with exactly those meanings before the phrase was used, but that they were spontaneously arrived at when the phrase was coined (and understood, if we change the case and suppose it was understood by Jemaine and Brett, as would be more likely in real life) – that is, the meanings of 'friendship' and 'realm' were spontaneously and slightly extended.

On the second conception, by contrast, we think: 'friendship' and 'realm' are familiar words, and they were both presumably around for a long time before 'friendship realm' was ever used. Putting these two meaningful words together, however, doesn't all by itself yield one and only one possible meaning. There is room for going different ways here. ('The friendship realm', for instance, might be used differently from how Murray uses it, to mean some mythical realm in which everyone is friends.) Of course, when 'friendship realm' does end up meaning some particular thing, this will not be unrelated to 'friendship' and 'realm' – they guide the meaning, without determining it. The gap between what they provide and the meaning of 'friendship realm' must be filled by semantic developments pertaining to 'friendship realm'. But we needn't say that these developments affect the meanings of 'friendship' and 'realm' taken by themselves – we can maintain that they haven't taken on new meanings.

(It may be that compositionality doesn't necessarily fail according to this second conception: perhaps the gap between what the pre-existing meanings of 'friendship' and 'realm' and a meaning for 'friendship realm' can be thought of as being filled by a structure or mode of composition, if we construe this as going beyond surface syntax.)

Now, what does this get us, i.e. what does it get us to see that there is all this room for manoeuvring here?

One thing it gets us is a way of explaining a large class of putative counterexamples to the principle of compositionality, without denying any natural point of view. In fact, we have before us two ways of accounting for the idea that this is a counterexample to compositionality. Rather than two equally good ways of accounting for exactly the same thing, I think they cover different sorts of cases, different instances of the idea that this is a counterexample to compositionality; compositionality can be said to fail here in two senses:

(1) While compositionality may be said to hold at a very fine granularity, it can be said not to hold at a coarser one. So, one thing that might be going on when we think we have a counterexample to compositionality is that we are operating at a granularity at which it is a counterexample – and if someone disagrees, we might be talking at crossed granularities.

(2) A dynamic, temporal sense. We make no bones about the fact that now we have some new complex expression, we can say that the meanings of its parts, plus its structure, determines the meaning of the whole. (Thus we are operating at the finer granularity.) But we insist that when it was introduced, its meaning wasn't so determined: rather, it induced spontaneous semantic development. So, we can call a use of language non-compositional in this sense if it involved such development – and we may relativize this to a thinker or speaker, a listener, etc. Something compositional for me might be non-compositional for you at first, but my saying it induces spontaneous semantic development on your side so that it becomes compositional after the fact. We might use 'dynamic compositionality' for this idea; when spontaneous semantic innovations occur involving complex expressions, we can say that those expression uses were dynamically non-compositional.

Neither sense conflicts with the claim that, at fine-grain and timelessly, 'friendship realm' and similar cases are perfectly compositional.

These considerations may also shed some light on the issue of whether, or in what circumstances, compositionality is to be regarded as an ideal to be striven towards, if not attained. In some cases, we may have as an ideal that no spontaneous semantic innovation – no guesswork, we might say, from an interpreter's perspective – be required for a certain language-game (use of language), for example in parts of science, certain personal encounters, or in parts of legislature. That is, dynamic compositionality may be desired. But it is just as clear that sometimes we want dynamic non-compositionality.

Or we might want a language, or a part of language, to be so simple that there is no room for granularity shifting: each expression has a couple of clear rules attached to it, and if you change any of them, it's just not natural to say that the meanings stayed the same. We might be able to ensure this by laying it down that compositionality must not fail. (If we're aware of granularity considerations, we might say 'must not fail at any reasonable granularity', but we need not be aware of them to pull off the trick.)

So, the above considerations get us a few things. What remains?

We have seen that many cases where compositionality seems to fail – such as Murray's use of 'friendship realm' – may be explained away by saying: if you individuate the components' meanings at a finer granularity, this is no longer a counterexample. But the question remains: can that be done in every case? That is, does the blanket proposal hold?

By getting clearer about the blanket proposal, we will get clearer about the nature or meaning of the principle of compositionality. In this connection, we should consider idioms, metaphors and similes, sarcasm and the like, and semantic “outgrowths” like 'Wednesday is fat' and 'The letter a is yellow'.

Such linguistic phenomena also suggest that there may be more to say about the notion of compositionality as an ideal.

The Blanket Proposal

A proponent of the blanket proposal might say that, when compositionality fails, we have decided to bundle together as having one meaning expressions, or possible occurrences of expressions, which on a more fine-grained conception would be regarded as having (perhaps only slightly) different meanings. But is this really plausible in every case?

Here are some difficult types of cases:

Idioms: Consider phrases like 'spitting image', 'dead ringer', 'nest egg', 'piece of cake', 'funny farm', 'loose cannon', 'no dice', 'from scratch', 'kick the bucket'.

Propositions like 'He is a loose cannon'

'Pull strings' a bit more flexible. Frozen metaphor.

Sarcasm and the like: A sarcastic utterance of 'That's just great' may seem to be a kind of counterexample to compositionality: what is meant is that something is terrible, but this depends not just on the meanings of the components and how they are put together, but also on the context: it might be meant non-sarcastically.

But we can invoke an intensional (internal semantic) analogue of Kripke's distinction between speaker's reference and semantic reference here, and insist that what this expression means, even in the sarcastic use, is that the thing in question is very good, even though what the speaker means by it is something else.

From the point of view of expression-meaning, then, sarcasm and the like do not threaten compositionality in the least. But there is nothing stopping us talking about compositionality in connection with speaker-meaning, and saying that it fails in this case ('That's just great').

Or, we may say that what the speaker means by the whole is determined by what the speaker means by the parts, together with their mode of composition, by maintaining that by 'great' the speaker means 'terrible'.

But other cases seem different. Suppose someone takes something to be very obvious, but, by way of parody of some other group who may doubt it, might sarcastically say, 'Of course, empirical studies may prove me wrong' (let's suppose they're quite nerdy). Here, the meaning is something like 'Come on, we know this!', but the sarcasm cannot be located, so to speak, in any particular phrase. The whole construction is bound up with the sarcasm – what is literally meant cannot aptly be stated using the same syntactic form, only negated (e.g. 'Of course, it's not the case that empirical studies may prove me wrong', or some other placement of negation).

For now I remain agnostic.

A Final Observation about Wholes and Parts and Granularity

Observation: Two propositions - or more generally, complex expressions - can be identical in meaning at one granularity, while none of their parts have the same meaning at any reasonable granularity. Or less extremely, while few of their parts, or none of their "key words", have the same meaning at any reasonable granularity. Or again, while their overall structure and arrangement of parts is quite different.

For example: 'Get out!' and 'Leave at once!'.