David Bourget (Western Ontario)
David Chalmers (ANU, NYU)
Rafael De Clercq
Ezio Di Nucci
Jack Alan Reynolds
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Noûs 47 (3):453-466 (2013)
We argue that a semantics for counterfactual conditionals in terms of comparative overall similarity faces a formal limitation due to Arrow’s impossibility theorem from social choice theory. According to Lewis’s account, the truth-conditions for counterfactual conditionals are given in terms of the comparative overall similarity between possible worlds, which is in turn determined by various aspects of similarity between possible worlds. We argue that a function from aspects of similarity to overall similarity should satisfy certain plausible constraints while Arrow’s impossibility theorem rules out that such a function satisfies all the constraints simultaneously. We argue that a way out of this impasse is to represent aspectual similarity in terms of ranking functions instead of representing it in a purely ordinal fashion. Further, we argue against the claim that the determination of overall similarity by aspects of similarity faces a difficulty in addition to the Arrovian limitation, namely the incommensurability of different aspects of similarity. The phenomena that have been cited as evidence for such incommensurability are best explained by ordinary vagueness.
|Keywords||counterfactual conditionals comparative overall similarity Arrow's impossibility theorem ranking functions incommensurability|
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References found in this work BETA
David K. Lewis (1973). Counterfactuals. Blackwell Publishers.
James Woodward (2003). Making Things Happen: A Theory of Causal Explanation. Oxford University Press.
Timothy Williamson (2007). The Philosophy of Philosophy. Blackwell Pub..
Timothy Williamson (1994). Vagueness. Routledge.
Jonathan Bennett (2003). A Philosophical Guide to Conditionals. Oxford University Press.
Citations of this work BETA
Wolfgang Spohn (2013). A Ranking‐Theoretic Approach to Conditionals. Cognitive Science 37 (6):1074-1106.
Franz Huber (2014). New Foundations for Counterfactuals. Synthese 191 (10):2167-2193.
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