Week 3 – Gillies on ‘if’ (part 2)

[Note: I don’t normally do the write up for the MLE seminar, so this is probably going to be a break from the normal format. In particular, I don’t remember what people said and who said what, and all I have are my notes from when I read the paper, so I’m going to base it on that. — Andrew]

Last week we read Gillies paper “On the truth conditions for ‘if’“. I had been meaning to work out what this view was about for a while so it was good to get an idea.

In the paper, Gillies argues that a dynamic view of conditionals can reconcile two apparently inconsistent claims. The first is that the English conditional does not have the truth conditions of material implication, and the second is the premises of Gibbards famous argument that the truth conditions of the English conditional must be that of the material conditional. Two notable premises are import-export, i.e., that the following two sentences are equivalent (where $\rightarrow$ represents the English conditional.)

• $(p \rightarrow (q \rightarrow r))$
• $(p \wedge q \rightarrow r)$

Since Gibbards argument is classically valid, either some classical laws must be rejected, or the step from mutual entailment to sameness of truth conditions must be bad. And, indeed, both of these lines are open – for example, Cian pointed out in the seminar the conjunction elimination fails on Gillies favoured account (see post below), and that the entailment relation displays some other rather odd behaviour (e.g., I don’t think it contraposes.) But also, it is not clear on the “information preservation” view of entailment, that you can infer sameness of truth conditions from mutual entailment. I expect this is how Gillies dodges the argument, but its not made clear.

But there were some things that still puzzled me about the paper, especially the stuff towards the end. The first was the central claim that the conditional could be given truth conditions. I wasn’t quite sure what the truth conditions were on the dynamic view; after all, all there is to the meaning of a sentence is its ‘context change potential’, or, the transformation it performs on information, and it’s not clear how one gets truth conditions out of this. You could, of course, define it in terms of idling on a singleton index, but that’s not a notion that plays any role in the entailment relation, which I thought was supposed to be a relation between the truth conditions of the relata.

On a related point, another issue I had with it was I couldn’t quite see how it engaged with the Gibbard argument. I guess you can consistently assign the conditional a non-extensional semantics, and retain import-export and other related inferences, but only at the cost of severing the tie between entailment and truth conditions.

That is, we seem to have two notions of entailment: entailment1, which is cashed out, roughly, in terms of preservation of truth, and entailment2 which is roughly preservation of information (if you assert the premises in the right order, then you’ll be in a context where the conclusion sounds good when you assert it.) Accepting the Gibbard premises, we get that $\rightarrow$ and $\supset$ mutually entail1 each other. But entailment1 involves necessary preservation of truth, so we get that $\rightarrow$ and $\supset$ have the same truth conditions. On the other hand, if we accep the Gibbard premises, $\rightarrow$ and $\supset$ may mutually entail2 each other (perhaps, I haven’t checked.) But this notion of entailment, as it were, abandons truth conditions altogether. So I can see there’s a precisification of the ‘It’s a truth conditional account where the Gibbard entailments hold’ on which Gibbards entailments hold, and a precisification with a thoroughly truth-conditional account of ‘if’, but I can’t get both claims together?

Finally two minor things I didn’t get: (1) what IS the material conditional on the (second) dynamic view? Is it $(\neg p \vee q)$ or $\neg(p \wedge \neg q)$ (which aren’t equivalent) or something else? Because we need to know this if we’re to evaluate the claim that the English conditional is not a material conditional. (2) On the first view, if c is a context, there’s no guarantee that c+P is a context, (it won’t be well behaved if P is false for example), in fact, this situation will be very common, so what should the view be?