Counterfactual Dependence and Arrow

Noûs 47 (3):453-466 (2012)
  Copy   BIBTEX

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.

Similar books and articles

Analytics

Added to PP
2012-03-21

Downloads
906 (#14,333)

6 months
91 (#40,139)

Historical graph of downloads
How can I increase my downloads?

Author Profiles

Franz Huber
University of Toronto, St. George Campus
Thomas Kroedel
Universität Hamburg

Citations of this work

Multidimensional Adjectives.Justin D’Ambrosio & Brian Hedden - forthcoming - Australasian Journal of Philosophy.
Two Conceptions of Similarity.Ben Blumson - 2018 - Philosophical Quarterly 68 (270):21-37.
A Ranking‐Theoretic Approach to Conditionals.Wolfgang Spohn - 2013 - Cognitive Science 37 (6):1074-1106.
Social Choice Theory.Christian List - 2013 - Stanford Encyclopedia of Philosophy.

View all 15 citations / Add more citations

References found in this work

Counterfactuals.David K. Lewis - 1973 - Malden, Mass.: Blackwell.
The Philosophy of Philosophy.Timothy Williamson - 2007 - Malden, MA: Wiley-Blackwell.
Vagueness.Timothy Williamson - 1994 - New York: Routledge.
Causation.David Lewis - 1973 - Journal of Philosophy 70 (17):556-567.

View all 42 references / Add more references