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Thursday, October 04, 2007

Lewis Conference, Day 2 (Salerno)

[cross posted from Knowability]

The talks today were on the semantics for conditionals. John Cantwell proposed a branching-time framework that aimed to unify our understanding of indicative and subjunctive conditionals. The variation in truth-value of corresponding indicative and subjunctive "Oswald sentences" is, on John's view, to be explained without positing a plurality of conditionals. The job can be done by tense and our understanding of open futures.

Hannes Leitgeb offered a probabilistic semantics for subjunctive conditionals. His very precise proposal (which I won't go into here) is a version of the thought that subjunctives are true just in case the consequent is sufficiently likely (in some objective sense) given the antecedent. By default Hannes rejects the strong and weak centering assumptions---respectively,

(A & B) --> (A []--> B), and

(A []--> B) --> (A --> B)

What this means is that, unlike the standard semantics, we get the desirable outcome that the truth of A and B is not sufficient to imply a counterfactual dependence between A and B, and that the truth of A and ~B is not sufficient to undermine a counterfactual dependence between A and B. The actual world can be one of the exceptional worlds where what does occur is not highly likely to occur (and where what is highly likely to occur does not occur).

Hannes replaces the centering assumptions with weaker centering-like assumptions---viz.,
(T []--> (A & B)) --> (A []--> B), and

(A []--> B) --> (T []--> (A --> B))

I believe T is meant to be a tautology, and so, the following rough paraphrase can be given: the truth of A & B does entail A []--> B, when A & B is sufficiently likely on its own, and the truth of A & ~B entails the negation of A []--> B, when A & ~B is sufficiently likely on its own. Perhaps we can put it in something like Lewisian terms. The stronger of the two says that no world is as close to the actual world as are the very likely worlds; and the weaker thesis is that no world is closer to the actual world than are the very likely worlds.



Photos:

1. Statue

2. John Cantwell

3. Hannes Leitgeb

4. Niels Bohr Mansion

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