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.