The Pre-Kripkean Puzzles are Back

Yes, but does Nature have no say at all here?! Yes.

It is just that she makes herself heard in a different way.

Wittgenstein (MS 137).

Modality was already puzzling before Kripke - there’s a tendency for the potted history of the thing to make it seem like just before Kripke, philosophers by and large thought they had a good understanding of modality. But there were deep problems and puzzles all along, and I think many were alive to them.

There is a funny thing about the effect of Kripke’s work which I have been starting to grasp lately. It seems like it jolted people out of certain dogmas, but that the problems with those dogmas were actually already there. The idea of the necessary a posteriori sort of stunned those ways of thinking. But once the dust settles and we learn to factor out the blatantly empirical aspect from subjunctive modality - two main ways have been worked out, more on which in a moment - the issue comes back, and those ways of thinking and the problems with them are just all still there.

(When I was working on my account of subjunctive necessity de dicto, I thought of most pre-Kripkan discussions of modality as irrelevant and boring. Now that I have worked that account out, they are seeming more relevant.)

What are the two ways of factoring out the aposterioricity of subjunctive modality? There is the two-dimensional way: construct “worlds” using the sort of language that doesn’t lead to necessary a posteriori propositions, and then make the truth-value of subjunctive modal claims involving the sort of language that does lead to them depend on which one of the worlds is actual.

This is currently the most prominent and best-known approach. However, it involves heady idealizations, many perplexing details, and various questionable assumptions. I think the difficulty of the two-dimensional approach has kept us in a kind of post-Kripkean limbo for a surprisingly long time now. Except perhaps in a few minds, it has not yet become very clear how the old pre-Kripkean problems are still lying in wait for us. I have hopes that the second way of factoring out will move things forward more powerfully (while I simultaneously hope for a clearer understanding of two-dimensionalism).

What is the second way? It is to observe that the subjunctively necessary propositions are those which are members of the deductive closure of the propositions which are both true and C, where C is some a priori tractable property. (On my account of C-hood, the closure version of the analysis is equivalent to the somewhat easier to understand claim that a proposition is necessary iff it is, or is implied by, a proposition which is both C and true. On Sider’s account of C-hood this equivalence fails.)

My account of subjunctive necessity explains condition C as inherent counterfactual invariance, which in turn is defined using the notion of a genuine counterfactual scenario description. And it is with these notions that the old-style puzzles come back up. Sider’s account has it that C-hood is just a conventional matter - something like an arbitrary, disjunctive list of kinds of propositions. (Here we get a revival of the old disagreements between conventionalists and those who were happy to explain modality semantically, but suspicious of conventionalism.)

What are these returning puzzles all about? They are about whether, and in what way, meaning and concepts are arbitrary. And about whether, and in what way, the world speaks through meaning and concepts. Hence the quote at the beginning, and the quote at the end of this companion post.

On Warren's 'The Possibility of Truth by Convention'

Recently I read Jared Warren's 'The Possibility of Truth by Convention'. Sometimes when I read a paper, I strongly suspect I will end up finding it wrong-headed, and accordingly go in with a spot-the-fallacy attitude. I confess I did this in this case, but as I read it my attitude changed. Having read it, I now think I have had a prejudice against conventionalist ideas. And this makes sense: I have been trying to develop an analysis of subjunctive necessity de dicto, and an explanation of apriority, which appeal crucially to considerations I have been thinking of as broadly semantic. And one important defensive point for me has been that this does not entail conventionalism of any kind. I still think that's true, and still think it's important to point out since many philosophers are dead against conventionalism, but I think getting used to making that defensive point has led me to underestimate conventionalism. I may not agree with it (I suppose I'm agnostic now), but Warren's paper has helped me to see that there is more to it than I had been willing to allow.

Still, there is a point late in the argument that I have an issue with. In this post I will briefly summarize the key moves in Warren's argument and then raise this issue.

Warren discusses a widely adhered-to 'master argument' against conventionalism which runs as follows. The basic idea behind it is that truth by convention is a confused idea because, while conventions may make it the case that a sentence expresses the particular proposition is does, conventions cannot make the proposition itself true (unless it's itself about conventions).

Master Argument:

P1. Necessarily, a sentence S is true iff (p is a proposition & S means p & p is the case).
P2. It's not the case that linguistic conventions make it the case that p.
C. Therefore, it's not the case that linguistic conventions make it the case that S is true.

Warren points out that 'making it the case that' admits of different readings. One is metaphysical, as in truthmaker theory. Another is causal, as in 'causes it to be the case that'. But another is explanatory, as in 'explains why it is the case that'. This explanatory reading, Warren contends, is what real conventionalism should be understood as working with. And, Warren argues convincingly, the argument isn't valid on that reading, since explanatory 'makes it the case that' contexts are hyperintensional: if you take a sentence embedded in such a context and substitute for it a sentence which is intensionally equivalent, you sometimes change the truth-value of the sentence it was embedded in. Warren's illustrative example:

[I]t is true that God's decree of ‘let there be light’ made it the case that (in the relevant sense) light exists, but it is false that either 2 + 2 = 5 or God decreeing ‘let there be light’ made it the case that (in the relevant sense) light exists.

So, the Master Argument isn't valid on the explanatory reading of 'make it the case that'. But can't this be patched up? As Warren notes:

if proponents of the argument accept a special principle requiring that explanations of sentential truth must also explain why the proposition expressed obtains, then a modified version of the master argument can be mounted that doesn't assume the intensionality of explanatory contexts.

Warren considers the prospects of shoring up the Master Argument with the principle he calls Propositional Explanation:

Propositional explanation : If Δ (explanatorily) makes it the case that sentence S is true, then Δ (explanatorily) makes it the case that p (where p is a proposition and S means that p). 

But Warren argues that the conventionalist has no good reason to accept this, and that it comes out of a way of thinking about the philosophy of language - he uses the phrase 'meta-semantic picture' - which they 'can, do, and should reject' (which makes the anti-conventionalist argument pretty weak). On the way of thinking Warren has in mind, propositions are in some sense more fundamental, and the truth of sentences is in some sense derivative of the truth of propositions. 

Now, I am happy to agree that conventionalists 'can, do, and should reject' this sort of picture of the philosophy of language. But I am not so sure that they should therefore deny Propositional Explanation. Maybe they can (and even should) accept Propositional Explanation, not because propositions come first in the order of explanation, but because - on their picture - once you've explained the truth of a sentence, you get an explanation of the truth of the proposition it expresses "for free". They can still block the Master Argument, however, by denying P2.

(Note in this connection that we should arguably separate two uses of 'the case' in this discussion. In the first premise of the Master Argument - 

P1. Necessarily, a sentence S is true iff (p is a proposition & S means p & p is the case).

- 'is the case', for the argument to work against truth by convention, should be read as 'true'. But in the second premise - 

P2. It's not the case that linguistic conventions make it the case that p.

- the second 'the case' is part of the phrase 'makes it the case that' which, Warren argues, is intended by the conventionalist to pick out an explanatory relation. And here we're really talking about making it the case, in this sense, that a proposition is true - and this gets passed over if we just write 'makes it the case that p'.)

Now, on my suggestion, the conventionalist's reason for accepting Propositional Explanation would be anathema to the anti-conventionalist for whom propositions are more fundamental, just as the anti-conventionalist's reason is anathema to the conventionalist. But maybe they can (and even should) agree on Propositional Explanation itself. This doesn't leave the conventionalist in much of a pickle, since they can - instead of trying to deny Propositional Explanation - just hammer their explanatory reading of 'makes it the case that' and use that to deny P2, arguing that P2 may be right if 'makes it the case that' is read metaphysically or causally, but that it is false on their intended reading.

Why doesn't Warren suggest going this way? His reasons are suggested in these passages:

(...) a version of conventionalism about arithmetical truth might maintain that the truth of ‘2 + 2 = 4’is fully explained by our linguistic conventions while also thinking that a full explanation of why 2 + 2 = 4 is a matter internal to mathematics and therefore should appeal to mathematical facts rather than linguistic facts.

And: 

Premise (2) will be justified by some argument to the effect that it would be extremely odd and implausible to think that our linguistic conventions could fully explain why 2 + 2 = 4 (e.g.), since this will be true in languages with markedly different linguistic conventions than our own and would have been the case even if our linguistic conventions had never existed. 

Wanting to allow for these points seems to make Warren think conventionalists should deny Propositional Explanation. But note that the above points are about 'why 2 + 2 = 4', i.e., not about why some proposition has some status. So for these points to support Propositional Explanation, propositions have to be thought of as having a very close metaphysical relationship to states of affairs (whose explanations, if they are mathematical states of affairs for instance, should be internal to mathematics). But it seems to me that that way of thinking about propositions is anathema to the conventionalist, who instead should see them as a kind of abstraction from sentences and our uses of them. That is why they can accept Propositional Explanation on the grounds that once you've explained the truth of a sentence you get an explanation of the truth of its expressed proposition "for free". And that is why they can deny P2.

So, the latter part of Warren's argument seems, if I'm reading him right, to be that the conventionalist, after defending themselves against the Master Argument by pointing out that they intend an explanatory reading of 'makes it the case that' on which that argument is invalid, should go on to respond to the modified Master Argument by protesting that it rests on a view, Propositional Explanation, which is anathema to their approach to the philosophy of language. But I suspect that it may be better for them to embrace Propositional Explanation - not because propositions are more fundamental in some way that their opponents think they are, but because if you explain the truth of a sentence, you get an explanation of the truth of the expressed proposition "for free" - and instead deny P2, which is anathema to their approach to the philosophy of language.

The conventionalist can hold that the Master Argument is invalid and that it rests on a false premise, and that the modified Master Argument, i.e. the Master Argument augmented with Propositional Explanation, is valid but unsound, not because Propositional Explanation is false, but because of the false premise that the plain Master Argument also contained.

This is of course not a fundamental disagreement with Warren's overall project here. In a broad sense, I am working alongside Warren and trying to give the conventionalist more options (something I am surprised to find myself doing!). If I have a disagreement with Warren here, it is about which option is best for them.

Reference

Warren, Jared (2014). The Possibility of Truth by Convention. Philosophical Quarterly 65 (258):84-93.

Sidelle and the Contingency of Conventions: An Objection Regained

This is a draft of a paper.

Alan Sidelle's conventionalism about modality is well-known, and only a bit less of a whipping-boy than the earlier positivistic views of Ayer (1936) and Carnap (1947). Published in his 1989 book Necessity, Essence and Individuation: A Defense of Conventionalism, it focuses on the problem of explaining the existence of the necessary a posteriori from a metaphysical standpoint according to which (in Sidelle's phrase) we, and not the world, are the source of modality. (I think this isn't very clear, but I don't want to press that here.)

I will not give a proper exposition of Sidelle's account here. I will just say that the basic idea is that a modal claim such as 'Necessarily, water is H20' follows from the a posteriori claim 'Water is H20' together with an a priori claim, such as 'If water is H20, then necessarily, water is H20'. The idea is that the a priori claim is somehow a matter of convention.

There are many problems with such a view – see Yablo's incisive (1992) review for a start. For example, can the a priori claim really be said to be a matter of convention? How doesn't this fall prey to the following argument?: it may be that what sentences mean is conventional, but we can't make the propositions they mean true by convention, except for the special case of propositions about conventions. (Yablo calls this the Lewy point, citing Lewy (1976). See also Quine (1936).) And even if this is somehow surmounted, aren't we still in the dark about what necessity is? (While Sidelle's aims, when stated carefully, do not seem to include saying what necessity is, some of his more impressionistic rhetoric does seem to try to say something about that. In any case, his account leaving us in the dark about the nature of necessity, if it does, is something worth taking due note of, since it is commonly taken to be addressing that issue.)

Here I will discuss another central objection (or type of objection) – that from the contingency of conventions. Or rather, Sidelle's recent response to it; in a 2009 paper called 'Conventionalism and the Contingency of Conventions', Sidelle defends his conventionlism about modality from this sort of objection. He carefully distinguishes two objections here, one focusing on truth-making, the other on necessity-making:

1. Truth-making version. If conventions were different, certain necessary truths would not be true. This seems to follow from conventionalism, catching it in a contradiction – since what it is to be a necessary truth is not failing to be true in any circumstances.
2. Necessity-making version. If conventions were different, certain necessary truths may have been contingent. This seems to follow from conventionalism, but seems wrong.

Sidelle argues (convincingly, in my view) that (1) is wrong – the conventionalist isn't committed to that. (I refer readers to his paper for this.)

Sidelle acknowledges (2) to be more serious, and devotes his paper to responding to it. Here, I will argue that his response to (2) fails at an early step, for use-mention reasons.

Sidelle considers but rejects one possible avenue of response, a partly bullet-biting response which says: OK, so this shows that, at least sometimes, what is necessarily so may not have been necessarily so (and also that, at least sometimes, what is contingently so may not have been contingently so). Such truths, then, are contingently necessary and contingently contingent, respectively. This is tantamount to rejecting the characteristic axiom of S4 – that what is necessary is necessarily necessary.

Sidelle will not have this. It is simply too implausible that the S4 axiom fails for metaphysical modality. Indeed, there is reason to think that the appropriate system is S5 (since an unrestricted accessibility relation seems appropriate), which is stronger than S4. Furthermore, he says, conventionalists, in his opinion, ought to try to “save the modal phenomena” and not be highly revisionary.

He also has an argument to the effect that even biting this bullet wouldn't suffice, but I do not understand that argument (I think because it involves certain confusions bound up with Sidelle's form of conventionalism, but I won't try to go into that here).

Sidelle's strategy with (2) is to consider an example – that of 'bachelor', and what would be the case if our conventions governing it were different – and try to show that, if we are careful to stick to the proper mode of evaluating counterfactuals, namely where we keep our conventions, and the meanings of our terms, intact, we can see that the relevant (2)-like counterfactuals are not true.

Sidelle supposes for the sake of argument that our conventions make it that 'bachelor' applies to unmarried but eligible men, and not women, and then considers an alternative situation in which the conventions differed so that unmarried, eligible women fell in the extension of 'bachelor':

With such a convention, we would call unmarried Linda ‘a bachelor’, and so, ‘necessarily, bachelors are male’ would be false. However, how should we describe this situation? Is Linda a female bachelor? Of course not—someone counts as a bachelor only if they are male. Our rules for applying ‘bachelor’ tell us that one must be (give or take) ‘a never-been-married, but eligible male’ [footnote 14]—so ipso facto, the rules tell us that what rules the speakers in that world use is quite irrelevant to whether or not someone is a bachelor. They are no more relevant than the rules of Spanish if we are, in English, describing a situation in Mexico. And of course, this is perfectly general. Notice that this has nothing at all to do with Conventionalism—it is what anyone should believe about evaluating counterfactuals, when those counterfactuals contain words governed by certain semantic conventions—and of course, one doesn’t need to be a Conventionalist to believe there are at least some, or even many, such conventions. [footnote 15] And as the conventions in that situation are irrelevant to the truth of ‘Linda is a female bachelor’, so are they to the question of the necessity of bachelors’ being male there, and so, to whether our necessary truth is itself necessarily so (i.e. to whether or not it is necessarily necessary that bachelors are male). Thus, if the conventionalist story is correct, it will not be true that ‘had our conventions been different, what is necessary would (could) have been false’, or not necessary.

The first part of this quote is an unexceptionable rehearsal of how to evaluate counterfactuals dealing with situations where the meanings of words differ: don't get confused into using the words with those different meanings in describing the situation: it isn't the case that, if 'tail' meant 'leg', dogs would have four tails – although 'Dogs have four tails' would be true in such a situation, ceteris paribus. So while 'Dogs have four tails' would, in that situation, say something true, it does not actually say something true of that situation, i.e. about what happens in that situation.

Similarly with the sentence 'Linda is a female bachelor' – it would say something true in the situation in question, but it isn't – given what it actually means – actually true of that situation.

So far, so good. The trouble is in the last two sentences, when Sidelle tries to conclude from his unexceptionable rehearsal that it's not the case that, if our conventions were different, which propositions are necessary might be different. The last sentence just gives the conclusion. The whole argument, really, is in the second last sentence, so we will concentrate on that. Here it is again, with two words capitalized by me: 

And as the conventions in that situation are irrelevant to the truth of ‘Linda is a female bachelor’, so are they to the question of the necessity of bachelors’ being male there, AND SO, to whether our necessary truth is itself necessarily so (i.e. to whether or not it is necessarily necessary that bachelors are male).

Firstly, there is an ambiguity in Sidelle's phrase 'the truth of “Linda is a female bachelor”'. The conventions in that situation are obviously not irrelevant to the truth, in that situation, of the sentence 'Linda is a female bachelor'. But it is true that they are irrelevant to whether or not that sentence is actually true of the situation: it isn't of course, because there can't be female bachelors in any possible situation. So we can accept this and move on to see what Sidelle is likening it to.

The way Sidelle has put the point, it is not easy to see what the similarity is. The conventions in that situation are irrelevant to the truth of some sentence here, and similarly, to the necessity of bachelors being male there? The points would seem more similar if Sidelle semantically descended for the first bit: just as the conventions in that situation are irrelevant to whether Linda is a female bachelor in that situation, so too are they irrelevant to whether the bachelors are necessarily male there.

In any case, the point can be accepted: bachelors are necessarily male, in all situations. So in a situation where the conventions were different, any bachelors would still need to be male.

But, and this is the crucial point, in saying this, we are using our language, with our conventions, and describing a counterfactual scenario. Our proposition 'Necessarily, all the bachelors are male' is true of that situation. Call the situation S – our more explicit proposition 'Necessarily, all the bachelors are male in S' is true. And you can substitute for 'S' the name of any possible situation.

To ask of that situation, of S, whether the bachelors are necessarily male there, is palpably not to ask whether the proposition that bachelors are male – the proposition now, or whatever thing bears modal statuses, not just the sentence – is necessarily true in that situation. That question just hasn't been raised.

And this is why 'AND SO' is capitalized – it is spurious. It just doesn't follow from all the bachelors in situation S necessarily being male – that's us describing the scenario from here, remember – that the proposition that bachelors are male is necessarily true in that situation – and so you can't conclude from it that some proposition of ours which is necessarily true is necessarily necessarily true. Of course, such a conclusion is itself plausible, but that doesn't mean Sidelle – a conventionalist about the modal statuses of propositions – is entitled to it! And his argument only gets there by means of a subtle, illicit use-mention shift.

Having established to his satisfaction that he is not committed to what is necessary varying with convention, Sidelle then faces the task of explaining why the following plausible constraint on explanation fails in this instance: if A explains B, it can't be that no change in B would ever come about if A changed.

I think there are serious problems with his attempt, and I hope to make this clear in future. My purpose here has just been to show that the previous step, which led Sidelle to having to face this question about explanation, is fallacious. Sidelle has slid from mention to use in the consequents of the counter-conventional, counterfactual conditionals at issue: he can agree with everyone else that, if conventions had been different, any bachelors would still necessarily be male, but this is not the same as being able to agree that, if conventions had been different, the proposition that any bachelors are male would still be necessary. His argument from common knowledge about how to evaluate counterfactuals does not succeed in earning him the right to the latter, only the former. We can conclude from this alone that Sidelle has not adequately responded to the (necessity-making focused) objection from the contingency of conventions. 

References 

Ayer, A.J. (1936). Language, Truth and Logic. London, V. Gollancz, Ltd.

Carnap, Rudolf (1947). Meaning and Necessity. University of Chicago Press.

Lewy, Casimir (1976). Meaning and Modality. Cambridge University Press.

Quine, W.V. (1936). Truth by Convention. In The Ways of Paradox and Other Essays.

Sidelle, Alan (2009). Conventionalism and the contingency of conventions. Noûs 43 (2):224-241.

Sidelle, Alan (1989). Necessity, Essence, and Individuation: A Defense of Conventionalism. Cornell University Press.

 Yablo, Stephen (1992). "Review of Alan Sidelle, Necessity, Essence and Individuation." Philosophical Review 101: 878-81.