Counterfactual Dependence and Arrow

Noûs 47 (3):453-466 (2013)
Authors
Thomas Kroedel
Universität Hamburg
Franz Huber
University of Toronto, St. George
Abstract
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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DOI 10.1111/j.1468-0068.2011.00855.x
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References found in this work BETA

Counterfactuals.David K. Lewis - 1973 - Blackwell.
Vagueness.Timothy Williamson - 1994 - Routledge.

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Citations of this work BETA

A Ranking‐Theoretic Approach to Conditionals.Wolfgang Spohn - 2013 - Cognitive Science 37 (6):1074-1106.
Two Conceptions of Similarity.Ben Blumson - 2018 - Philosophical Quarterly 68 (270):21-37.
New Foundations for Counterfactuals.Franz Huber - 2014 - Synthese 191 (10):2167-2193.
Metaphysical Necessity Dualism.Ben White - 2018 - Synthese 195 (4):1779-1798.

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