The Review of Symbolic Logic

Research Article

AN ARGUMENT FOR CONJUNCTION CONDITIONALIZATION

LEE WALTERSa1 c1 and J. ROBERT G. WILLIAMSa2 c2

a1 Somerville College, Oxford

a2 University of Leeds

Abstract

Are counterfactuals with true antecedents and consequents automatically true? That is, is Conjunction Conditionalization: (X ∧ Y) ⊃ (X > Y) valid? Stalnaker and Lewis think so, but many others disagree. We note here that the extant arguments for Conjunction Conditionalization are unpersuasive, before presenting a family of more compelling arguments. These arguments rely on some standard theorems of the logic of counterfactuals as well as a plausible and popular semantic claim about certain semifactuals. Denying Conjunction Conditionalization, then, requires rejecting other aspects of the standard logic of counterfactuals or else our intuitive picture of semifactuals.

(Received March 23 2012)

Correspondence

c1 SOMERVILLE COLLEGE OXFORD, OX2 6HD, UK E-mail: lee.walters@philosophy.ox.ac.uk

c2 DEPARTMENT OF PHILOSOPHY UNIVERSITY OF LEEDS WOODHOUSE LANE, LEEDS LS2 9JT, UK E-mail: j.r.g.williams@leeds.ac.uk