Non catastrophic presupposition failure

Question

In a previous question, I asked something similar but without explicitely referring to the source material of my doubt. Now I try to state it here with more precision: In "Non-catastrophic presupposition failure" Yablo tries to argue why sometimes, even if a presupposition is false, some statements strike us as true or false, and not undefined.

For instance: "The king of France is Bald & the Queen of England is bald" strikes us as false, even though there is no king of France. A possibile reason might be that the statement would be false, even if there was a king of France. In order to illustrate this possibility, Yablo writes:

The real asserted content S of a sentence, when a presupposition is false, is true(false) iff the simple sentence S is true(false) in the closest possibile world where the presupposition P holds.

From the paper: "S is true (false) in w iff S is true (false) in the world closest to w where π holds."

Given the previous example, "KoF is balde and QoE is bald" strikes us as false because, in the closest possibile world in which there is a king of France, that sentence is false, due to the fact that the Queen of England is not bald.

then Yablo goes on and says:

"This simplifies matters, because for S to be true (false) in the world closest to w where π holds is, on standard theories of conditionals, precisely what it takes for a conditional π → S to be true (false) in w."

"S is true (false) in w iff π → S is true (false) in w." "Note 22: I assume that π→S is false iff π→~S is true."

This looks to me as Yablo is putting forth the fact that "being true in the closest possible world where π is true" can be identified with π → S being true in the world of interest (where the evaluation takes place, so to speak) - but it is not clear to me why it should be so.

Answer 1

I think you are simply mistaking Yablo's nomenclature here. He is using the arrow symbol → to denote a counterfactual conditional, or perhaps some general conditional, not material implication.

For example, note that in footnote 22, p. 176, he says "I assume that π → S is false iff π → ~S is true." This would not be true of material implication, since A ⊃ B and A ⊃ ¬B can both be true. But with counterfactual conditionals, typically "if A were the case, B would be the case" contradicts "if A were the case, B would not be the case". And, "if A had been the case, B would have been the case" contradicts "if A had been the case, B would not have been the case".

Also, at the top of p 177 he expressly says that π → S should be read as "if it were the case that π, it would be the case that S". Note also that the paper contains no instances of the > symbol.

We seem to have run afoul of the general problem that there is no universally agreed upon nomenclature. Material implication is sometimes represented using ⊃, → or ⇒. Counterfactuals are sometimes represented using >, → or □→. Sometimes ⇒ is reserved for meta-level conditionals.

Answer 2

Your question is not entirely clear to me. Yablo claims that the truth conditions of simple sentences s containing definite descriptions may change depending on whether or not the presuppositions triggered by the descriptions are satisfied or not. If they are not satisfied, then the sentence s is true iff the counterfactual p > s is true, where p is the conjunction of s's presuppositions. As Yablo uses Lewis-style conditional logic it's a truism that p > s is true in a possible world w iff s is true in every nearest world to s, where p is true.

I've to reread Yablo's paper, but one of the problems I see with Yablo's proposal is that it makes counterintuitive truth assignments when conjunctions are concerned, where one of the conjuncts triggers necessarily false presuppositions.

Consider

(1) The round square is round and the Queen is bald.

As there are no round squares the uniqueness presupposition triggered by (1) is not satisfied in the actual world. So (1) is true iff in every nearest world, where a unique round square exists, the Queen is bald. But as there are no possible worlds where there is a unique round square the truth conditions of (1) are vacuously fulfilled. So (1) is true according to Yablo's proposal. But intutively, (1) is not true.