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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.

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    Thanks, sadly Yablo does not specify a definition of "world closest to w".
    – PwNzDust
    Mar 26 at 8:42
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    Well, it's Yablo's (MIT) course on modal logic :D That particular lecture is probably not based on the textbook (Hughes and Cresswell) though, because the latter don't get to such applications in their book IIRC. So it probably comes from other works. As far as I can tell from SEP plato.stanford.edu/entries/counterfactuals/#TrutCondSimi Stalnaker did not actually try to define a "closest", "most similar" or the like, but Lewis did. So Yablo might be using a similar notion.
    – Fizz
    Mar 26 at 9:36
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    I've looked through Yablo's paper you mention now. For someone who doesn't work in that area it creates a lot of "huh?" moments. Even the appendix to the paper, which is supposed to be more technical, does the same for me. I'm not sure e.g. if there is a formalization of "worlds and situations"; it seems to be referring to jstor.org/stable/30226345 but Yablo doesn't actually cite that paper (although it cites a bunch of others from Stalnaker.)
    – Fizz
    Mar 26 at 11:47
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    Since the Yablo paper is included in a volume dedicated to Stalnaker, you can assume it's more or less a commentary on the latter's theories. Unfortunately, it's hard to find a precis of these. The last paper I linked to is alas "math free", so it doesn't help with any formalization.
    – Fizz
    Mar 26 at 11:53
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    plato.stanford.edu/entries/logic-conditionals is probably useful to read up to section 4 or so. (It's a separate article from counterfactuals.) Alas it's not clear in which of those systems from section 3 there Yablo is working (if any of those).
    – Fizz
    Mar 26 at 12:18
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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.

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  • I had not considered that interpretation. Thanks a lot , seems mine was just a problem of correctly understanding the conditional at use
    – PwNzDust
    Mar 26 at 20:13
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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.

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  • Thanks. The point I do not understand is why if p>q is true in w, then p->q is true in w and why if p->q is true in w then the counterfactual is, too.
    – PwNzDust
    Mar 26 at 7:40
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    The conditional logics based on Stalnaker / Lewis semantics for counterfactuals have it that counterfactuals imply material implications.. To see this informally consider Stalnaker's truth conditions. In Stalnaker's semantics, the similarity relation between worlds obeys the following restriction: If a proposition p is true in a world w, then w is the nearest world to w, where p is true. Assume p > q is true in w. If p is false in w, p->q is true in w. If p is true in w, w is the nearest world to w where p is true. So, since p > q is true in w, q is true in w. So, p->q is true in w.
    – sequitur
    Mar 26 at 22:57

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