Wednesday, 23 August 2017

Notes on Counterfactual Scenario Descriptions, Sources of Modal Error (or Uncertainty), and Deep Puzzles of Modality

One interesting thing about my account of subjunctive necessity is the way it separates two kinds of things that we could be wrong or confused about in our judgements of subjunctive modality: the truth of what we're holding true for the purposes of a counterfactual scenario description (CSD) and the genuineness of that CSD.

For example, I might think 'Hesperus is not Phosphorus' is subjunctively possible because I falsely believe that Hesperus is Phosphorus. Or I might be acquainted with some strange animals I call Toves and then not feel sure whether 'Toves are animals' is necessary simply because I am not sure whether the things I am acquainted with are animals.

By contrast, there are modal questions which do not centre - at least not in any definite way - on the truth or otherwise of what is being held true. For example, granting that I am human, could I have been an animal? Or how about a Neanderthal? Or a bank account?

And cosmic questions about whether there could have been less matter or energy, or perhaps just one atom in a void? And here the question arises: how do you know what you have to know in order to know whether something is necessarily the way it is or not? (In some cases, that seems clear. E.g. you have to know whether Hesperus is in fact Phosphorus in order to know whether it necessarily is. But in others it really doesn't.)

Another puzzling thing stems from the way, in my account, you can have CSDs which aren't possible, since the things held true for them aren't true. For instance, if I think wrongly that Hesperus isn't Phosphorus (or even just grant that for the sake of argument), I will be prepared to produce CSDs involving Hesperus not being Phosphorus, and these may be perfectly genuine. This strikes me as an important virtue of my account - i.e., that it is some sort of advance, giving us a fruitful way of talking and thinking philosophically about modality. It is hard to say exactly why. One thing is that it enables us to bracket off distracting sources of modal uncertainty and error, perhaps allowing us to focus better on the stuff which really bothers us philosophically about modality. 

In any case, this thing - about there being genuine CSDs which, despite being genuine, aren't possible because false things are held true for them - gives rise to some puzzlement in its own right. When we can go different ways on the question of whether Hesperus is Phosphorus or Clark Kent is Superman - questions of the identity or distinctness of things - it seems like our underlying way of thinking about things, our conceptual apparatus, is basically the same. And to a fair, but perhaps lesser extent, going different ways on the question of the underlying nature of cats, or Toves, or water also seems to leave our conceptual apparatus largely the same. (There may be something wrong or lacking in this description.) We get the sense that we can flip the switch either way on these things quite readily, and continue in much the same way in either case when it comes to grasping a range of genuine CSDs which arise on the assumption that things are the one way or the other. On the other hand, what of things which are - in a conceptual sense, I want to say - far from true? 

Things get puzzling very quickly once such questions come into view. If I somehow hold it true that humans are cats, can I then produce genuine CSDs according to which that is true? It is hard to know what to say. One thing is that there might be an issue about whether we can really hold such things true, or perhaps better, whether it makes sense to talk of holding such things true. But to that it may always be replied - OK, but we can sometimes do something here, in these cases where you might worry about whether we can really hold the things in question true or not.

Are there two ways, then, of getting out of the sphere of genuine CSD-hood? One by holding things true which are either true, or not a big deal or problematic to hold true, and then going further and further away from actuality, so to speak, until you say things we might hesitate to call CSDs (e.g. holding it true that I am human, but then talking about a scenario where I'm a cat), and another by holding far-out things true?

Another worry concerns what might be called modal encroachment. The idea that, if we learn more about some things, we might realise that some things aren't possible that we thought were. And there is a question here about whether that could affect what we think about genuineness of a CSD, or whether what we formerly thought were not only genuine CSDs but possibilities (i.e. that the things being held true for those CSDs are the case) can always be retained as genuine CSDs by holding the right false things true.

I feel that with these issues my account, which could seem merely logic-choppy and perhaps trivial in a way, begins to make contact with some of the deeper puzzles surrounding modality. 

In a future post I want to try to explore how our ideas might be prone to shifting and slipping without our realising it when we philosophize about modality. For instance, the obscure way the stakes can seemingly be raised in some way by the question of 'But could that really have happened?'. I also hope to make some progress on puzzles concerning 'whether the ground of modality is in us or the world', by trying to better uncover the thought processes underlying that unsatisfactory question. Perhaps then we will see better what the real issues are in this thicket of philosophy.

Postscript (or seedling for next time):

Dim hypothesis re. Kripkean showing of necessity of identity: it shows that things couldn't have been otherwise in a deep way by showing that they couldn't have been otherwise in a shallow way. 

I.e. in a certain frame of mind, we might think 'What do we know about how, and the extent to which, things really might have been different?'. A frame of mind with a sense of cosmic mystery, open to underlying system we have little or no inkling of. Then the Kripkean arguments come along and say 'Well, whatever the truth is about that, things certainly couldn't have been such that Hesperus isn't Phosphorus'.

It is notable that Kripke's results are necessities, or denials of possibility. This leaves it open that we have a way of thinking, or a concept of modality, on which all the Kripkean necessities are necessary as required, but where there is leeway which then disappears on some deeper view.

Friday, 18 August 2017

Scholarly Attention for the First Ever Sprachlogik Post!

It recently came to my attention that the first ever post here, from back in 2011, is the subject of a journal article by Matheus Silva, a Brazilian philosopher and logician.

Silva has also recently engaged with my argument against the Brogaard-Salerno Stricture, a principle about when it is OK to reason using conditionals.

Tuesday, 1 August 2017

An Adventure in Linking Necessity to Apriority

There is an important link between necessity and apriority which can shed light on our knowledge of the former, but initially plausible attempts to spell out what it is fall victim to counterexamples. Casullo (2003) discusses one such proposal, argues that it fails, and suggests an alternative. In this post, I argue that Casullo’s alternative also fails, suggest another, argue that that fails too, and then suggest another which I hope is correct.

First proposal

Kripke (1980) showed that it is not always knowable a priori whether a proposition is necessarily true. But, you might think, perhaps it is always knowable a priori whether a proposition has whatever truth value it has necessarily or contingently. To use Casullo’s (2003) terminology, while Kripke showed that knowledge of specific modal status (necessarily true, contingently false, etc.) is not always possible a priori, this leaves open the possibility of apriori knowledge of general modal status (necessary or contingent - and on this usage of ‘necessary’ and ‘contingent’, truth value is left open). Perhaps that is the link we are after between necessity and apriority.

The claim that general modal status is always knowable a priori entails the following:

(1) If p is a necessary proposition and S knows that p is a necessary proposition, then S can know a priori that p is a necessary proposition.

(The second conjunct of (1)’s antecedent sidesteps the worry that some necessary propositions may be such that it is unknowable that they are necessary.)

Casullo, following Anderson (1993), argues convincingly that this is false. Consider:

(1X) Hesperus is Phosphorus or my hat is on the table.

This is a necessary proposition, but for all any S could know a priori, it could be necessarily true (if the first disjunct is true), contingently true (if the first disjunct is false but the second true), or contingently false (if both disjuncts are false). So (1) can’t be right.

Second proposal

In an interesting effort to avoid the problem affecting (1), Casullo introduces the notions of conditional modal propositions and conditional modal status:

Associated with each truth functionally simple proposition is a pair of conditional propositions: one provides the specific modal status of the proposition given that it is true; the other provides its specific modal status given that it is false. Associated with each truth functionally compound proposition is a series of conditional propositions, one for each assignment of truth values to its simple components. Each conditional proposition provides the specific modal status of the proposition given that assignment of truth values. Let us call these propositions conditional modal propositions and say that S knows the conditional modal status of p just in case S knows all the conditional modal propositions associated with p. (Casullo (2003), p. 197.)
His proposed link between necessity and apriority is as follows:

(2) If p is a necessary proposition and S knows the conditional modal status of p, then S can know a priori the conditional modal status of p.

Casullo dubs this ‘a version of the traditional account of the relationship between the a priori and the necessary that is immune to Kripke’s examples of necessary a posteriori propositions’ (Casullo (2003), p. 199). It handles (1X) nicely. Calling (1X)’s disjuncts ‘Hesp’ and ‘Hat’, its associated conditional modal propositions will run as follows:

If Hesp is true and Hat is true, (1X) is necessary.
If Hesp is true and Hat is false, (1X) is necessary.
If Hesp is false and Hat is true, (1X) is contingent.
If Hesp is false and Hat is false, (1X) is contingent.

These are plausibly knowable a priori, as required by (2).

But consider:

(2X) Everything is either such that it is either not Hesperus or is Phosphorus, or such that it is either on the table or not my hat.

While it contains connectives, this is not a truth functional compound in the relevant sense, since it does not embed any whole propositions. So on Casullo’s proposal, (2X) will be associated with just a pair of conditional modal propositions. Which ones? A problem here is that there is no very clear positive case for any pair (the account, after all, was probably not formulated with (2X) in mind), but I think it is clear that the only candidate pair which could stand a chance is:

If (2X) is true, it is necessary.
If (2X) is false, it is contingent.

(After all, (2X) is true and necessary, so the other available choice for first member couldn’t be right, and the second member of the pair seems true and knowable a priori.)

Instantiating Casullo’s proposal (2) on (2X), we get:

If (2X) is a necessary proposition and S knows the conditional modal status of (2X), then S can know a priori the conditional modal status of (2X).

But it seems clear that the first conditional modal proposition for (2X), i.e. that if (2X) is true, it is necessary, could not be known a priori. So (2) can’t be right either.

Third proposal

What strikes one initially about the disjunctive counterexample to the first proposal is that it has a component whose general modal status is knowable a priori. But this isn’t true of the counterexample to the second proposal; it has no component propositions at all. What is true about both counterexamples is, not that they have cromponent propositions whose general modal status is knowable a priori, but that they are implied by such propositions.

Let us say that a proposition p possesses a priori necessary character iff it can be known a priori that p is a necessary proposition, i.e. that p has whatever truth value it has necessarily.

Now, I submit that if a proposition whose general modal status is knowable at all is necessarily true, then it is in the deductive closure of a set of true propositions possessing a priori necessary character.

How, though, to generalize this so that it covers all necessary propositions (i.e. necessarily false propositions as well as true ones)? For a few weeks, I thought this would work:

If a proposition whose general modal status is knowable at all is necessary, then it is either in the deductive closure of a set of true propositions possessing a priori necessary character, or it is in the deductive closure of a consistent set of false propositions possessing a priori necessary character.

To cast the point in a form similar to (1) and (2) above:

(3) If p is a necessary proposition and S knows that p is a necessary proposition, then p is either in the deductive closure of a set of true propositions which S can know a priori to be necessary, or it is in the deductive closure of a consistent set of false propositions which S can know a priori to be necessary.

But I have just recently realised that this is false as well.

The problem lies with necessarily false propositions. Requiring consistency of the set of false propositions that implies a putative necessary proposition rules out necessarily false propositions that contradict themselves. E.g. 'It is both raining and not raining' is, and can be known to be, a necessary proposition, but it is not implied by any consistent set of false propositions of apriori necessary character. On the other hand, removing the consistency requirement causes the account to overgenerate, at least on a classical conception of implication; 'I had toast for breakfast' is implied by the set of false propositions of a priori necessary character {'2 + 2 = 4', 'not-(2 + 2 = 4)'}, since that set implies any proposition whatsoever.

Fourth proposal

Now, without wanting to rule out that we could specify a special implication-like relation which behaves as desired, I have nevertheless tentatively given up on bringing in consistency to get a general result which covers not only necessary true propositions but necessarily false ones as well. Instead, I think the thing to do is to exploit the idea that a necessarily false proposition's negation is necessarily true, giving us:

(4) If p is a necessary proposition and S knows that p is a necessary proposition, then either p or its negation is in the deductive closure of a set of true propositions which S can know a priori to be necessary.

Maybe this one is true! Please let me know, by comment or email, if you see a problem.

Thanks to Albert Casullo for helpful and encouraging correspondence on this topic.


Anderson, C. Anthony (1993). Toward a Logic of A Priori Knowledge. Philosophical Topics 21(2):1-20.

Casullo, Albert (2003). A Priori Justification. Oxford University Press USA.

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

Saturday, 8 July 2017

An Attempt to Diagnose the Disagreement over the Relational Explanation of Identity

Here is what I have to say in response to the schmidentity challenge as posed to the sui generis view of identity statements. (See also these two related posts from several years ago.)

OK, so we can grant that you can introduce a 'schmidentity' predicate in the way Kripke describes. We can also grant that this predicate could then get used to do what we do with identity statements. But can we, having granted these things, nonetheless deny that the meaning and function of identity statements is explained with the object-relation story?

I am strongly inclined to do all of this. Why? Because the characteristic function of informative identity statements and their denials - the way they get us to merge and separate mental files, or concepts of individuals - is passed over in this explanation. Going along with the object-relation explanation seems to render this incidental, instead of the main point. That explanation makes it look as though the main function of an 'a is b' statement is also fulfilled by the corresponding 'a is a' statement, which of course it is not.

But, someone may argue, does the object-relation explanation really create this false appearance? And here it would be easy to be dogmatic. There would be something silly about insisting that yes, this sort of explanation really does create this false appearance. After all, my opponent - the philosopher who wants to say that the object-relation story is perfectly adequate, and that there's no problem here, and that anyone who thinks there is is in a muddle - doesn't actually seem to be confused about the fact that 'a is b' statements are often useful in a way that the corresponding 'a is a' statements are not. They would happily admit that. So the difference between us seems to be in whether we are happy to leave this out in our primary explanation, so to speak, of identity statements.

And it is important that I allow that the object-relation explanation of identity statements does show something. It's not as if it is a sheer mistake. It shows that we can so to speak depict identity statements as a special case of relational statements, i.e. statements like 'John loves Mary'. I do not want to deny this, or deny that it is of philosophical interest.

There is something neat or cool about this sort of observation, too. It has a charm to it, similar to the charm possessed by clever hacks (in the sense of computer culture). I think that the philosopher who wants to defend the object-relation story lacks a proper place to put this. They feel the charm, the strikingness, of the explanation, and - not wanting this to elude them - wrongly place it in the "primary explanation" place in their thinking, instead of a place marked something like "striking and potentially instructive thing you can say". So long as we only focus on the "primary explanation" place, it looks like the defender of the object-relation story is missing something and proposing something maddeningly objectionable, but it also looks like the antagonist of the object-relation story is missing something. It is not until we consider other possibilities for the significance of the object-relation story that we are able to give both parties their due.

This, I now think, is a very important point (even though I may not have expressed it very well). I regret that I didn't manage to arrive at this point in my paper on this topic. I also think my predecessors were missing something in this regard.

So, we can grant the possibility of the schmidentity predicate, and the possibility of it coming to be used to do the characteristic work of identity statements, but nonetheless deny that the object-relation story should take pride of place in our explanation of the meaning and function of identity statements. A leftover question here is: should we also deny that the meaning and function of statements made with the 'schmidentity' predicate, if they are being used in the way we use identity statements, is explained by their stipulated semantics? And the answer, I think, is Yes. If they are being used in that way, then the object-relation story should not take pride of place in their explanation. But it is understandable that we should hesitate here, since 'schmidentity' was introduced and defined by means of the object-relation story, and this invites us to look at their use - when they are being used in the characteristic way we use identity statements - as a kind of secondary thing, a happy side-effect.

(I feel like saying something more at this point, which may be more objectionable, about what other use (schm)identity statements may have, apart from their practical use which has to do with merging and separating. A metaphysical use, so to speak. And about what attitude we take to this use, or whether it might be a kind of illusion. And this relates to one of the old posts linked to at the beginning. But I won't do more than make this hint, since these are treacherous waters and I wouldn't want to abuse the goodwill of a differently-minded reader.)

Saturday, 10 June 2017

The Schmidentity Challenge (to the Sui Generis View of Identity Statements)

In my (2016) I defended the idea that identity statements are sui generis. More precisely, I defended the idea that identity statements involving proper names (e.g. 'Hesperus is Phosphorus') are not to be explained by the claim that they ascribe a relation which holds between all objects and themselves and in no other case, or for that matter by the claim that they ascribe a relation between names (this latter claim being false). In contrast to my predecessors who railed against the object-relation view, I did not insist that the object-relation claim is false - I decided this was not a very clear thing to insist on, and anyway not really the point - but just that it doesn't explain the meaning and function of identity statements. It may be "something you can say", but it doesn't do that explanatory job. I thought, and still do think, that this is the way forward for the philosopher who feels that there is something fishy about the object-relation view, something which remains even if we succeed in avoiding - most likely by means of senses or similarly-motivated semantic difference-makers - the absurd conclusion that 'Hesperus is Hesperus' and 'Hesperus is Phosphorus' mean the same.

I defended my negative thesis about the explanation of identity statements against some possible objections in the paper, but one unaddressed challenge I have been thinking about in the years since writing the bulk of the paper (it took a long time to get it published, and I stopped trying for a while) is Kripke's celebrated 'schmidentity' argument. Here it is:
Suppose identity were a relation in English between the names. I shall introduce an artificial relation called 'schmidentity’ (not a word of English) which I now stipulate to hold only between an object and itself. Now then the question whether Cicero is schmidentical with Tully can arise, and if it does arise the same problems will hold for this statement as were thought in the case of our original identity statement to give the belief that this was a relation between the names. If anyone thinks about this seriously, I think he will see that therefore probably his original account of identity was not necessary, and probably not possible, for the problems it was originally meant to solve, that therefore it should be dropped, and identity should just be taken to the relation between a thing and itself. This sort of device can be used for a number of philosophical problems. (Kripke (1980), p. 108.)
As you can see, the schmidentity argument is framed primarily as an argument against the name-relation view of identity statements, which I also argued against. But this argument also threatens my position. As I see it, the challenge is as follows. Kripke's schmidentity predicate is a term which is explicitly introduced - explained, it is natural to say - as ascribing a relation which holds between all objects and themselves and in no other case. So, whatever is true of identity statements, schmidentity statements can be - indeed have been - explained by means of the object-relation stuff which I wanted to say fails to explain the meaning of identity statements. But schmidentity statements could be used to do what we do with identity statements. So then what grounds have we for supposing that identity statements differ semantically from schmidentity statements? Perhaps none. But then if identity statements and schmidentity statements are semantically on a par, and the latter can (are) explained by the object-relation stuff, then so can the former. So now it looks like my position is wrong.

I think this is a serious challenge to my position (about the object-relation claim not being explanatory of identity statements), but I can't help feeling that it misses something and that my position is right in some way. I will try to respond to the challenge in my next post here.


Haze, Tristan (2016). On Identity Statements: In Defense of a Sui Generis View. Disputatio 8 (43):269-293.
Kripke, Saul A. (1980). Naming and Necessity. Harvard University Press.

Saturday, 6 May 2017

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.

Tuesday, 2 May 2017

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 & 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.
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.


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