Multidimensional Possible-World Semantics for Conditionals

Philosophical Review 121 (4):539-571 (2012)

Authors
Richard Bradley
London School of Economics
Abstract
Adams’s Thesis, the claim that the probabilities of indicative conditionals equal the conditional probabilities of their consequents given their antecedents, has proven impossible to accommodate within orthodox possible-world semantics. This essay proposes a modification to the orthodoxy that removes this impossibility. The starting point is a proposal by Jeffrey and Stalnaker that conditionals take semantic values in the unit interval, interpreting these (à la McGee) as their expected truth-values at a world. Their theories imply a false principle, namely, that the probability of a conditional is independent of any proposition inconsistent with its antecedent. But they also point to something important, namely, that our uncertainty about conditionals is not confined to uncertainty about the facts (what the actual world is like) but also expresses uncertainty about the counterfacts (what the world would be like if one or another supposition were true). To capture this observation, this essay proposes that the semantic contents of conditionals be treated as sets of vectors of possible worlds, not singleton worlds, with the coordinates of each specifying the world that is or would be true under the supposition that it represents. The probabilities of truth for conditionals will then depend on the joint probabilities of the facts and counterfacts, the latter in turn depending on the mode of supposition. The implication of this treatment is that the probabilities of conditionals are conditional probabilities whenever the mode of supposition is evidential.
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DOI 10.1215/00318108-1630921
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References found in this work BETA

Counterfactuals. [REVIEW]William Parry - 1973 - Journal of Symbolic Logic 44 (2):278-281.
Conditional Probabilities and Compounds of Conditionals.Vann McGee - 1989 - Philosophical Review 98 (4):485-541.
Two Recent Theories of Conditionals.Allan Gibbard - 1981 - In William Harper, Robert C. Stalnaker & Glenn Pearce (eds.), Ifs. Reidel. pp. 211-247.

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Citations of this work BETA

The Spectre of Triviality.Nate Charlow - forthcoming - Analysis:anz011.
Probabilities of Conditionals in Context.Justin Khoo - 2016 - Linguistics and Philosophy 39 (1):1-43.

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