Nested conditionals and genericity in the de Finetti semantics

Abstract

The trivalent, truth-functional theory of conditionals proposed by de Finetti in 1936 and developed in a scattered literature since has enjoyed a recent revival in philosophy, psychology, and linguistics. However, several theorists have argued that this approach is fatally flawed in that it cannot correctly account for nested conditionals and compounds of conditionals. Focusing on nested conditionals, we observe that the problem cases uniformly involve generic predicates, and that the inference patterns claimed to be problematic are very plausible when we ensure that only non-generic (episodic and stative) predicates are used. In addition, the trivalent theory makes correct predictions about the original, generic counter-examples when combined with an off-the-shelf theory of genericity. The ability of the trivalent semantics to account for this complex interaction with genericity thus appears as a strong argument in its favor. 1 The trivalent semantics for indicative conditionals An extensive theoretical and experimental literature supports ‘Stalnaker’s thesis’, the equation between probabilities of conditionals and conditional probabilities (Stalnaker 1970; Edgington 1995; Bennett 2003; Hadjichristidis, Stevenson, Over, Sloman, Evans & Feeney 2001; Over & Evans 2003; Fugard, Pfeifer, Mayerhofer & Kleiter 2010; Douven & Verbrugge 2010, 2013 and many others). Stalnaker’s thesis: P(If A, C) = P(C ∣ A). Lewis’s (1976) proof is widely thought to show that this equation cannot hold. However, Lewis’ proof tacitly assumes bivalence, as do a wide range of other triviality proofs for Stalnaker’s thesis (Lassiter 2019). In fact, a trivalent, truth-functional semantics that supports Stalnaker’s thesis while avoiding triviality results was provided more than 3 decades before this thesis was proposed, in de Finetti 1936 (English translation in de Finetti 1995). According to de Finetti, the indicative conditional If A, C is true if A∧C, and false if A∧¬C, and otherwise undefined (here noted ‘#’). Most crucially, the indicative conditional is always undefined when its antecedent is false.1 1 For de Finetti, the third truth-value represents an epistemic relation of “doubt” between an agent and a sentence (de Finetti 1995: 182). Other interpretations are possible: for example, Hailperin (1996) interprets the # value as ‘don’t care’. For our purposes, it is not the meaning of the # value that is critical but its formal role in the semantics of conditionals, and so we will not take a stand on this interpretive question.