Williamson on indicatives and suppositional heuristics

Abstract

Timothy Williamson has defended the claim that the semantics of the indicative ‘if’ is given by the material conditional. Putative counterexamples can be handled by better understanding the role played in our assessment of indicatives by a fallible cognitive heuristic, called the Suppositional Procedure. Williamson’s Suppositional Conjecture has it that the Suppositional Procedure is humans’ primary way of prospectively assessing conditionals. This paper raises some doubts on the Suppositional Procedure and Conjecture.

Williamson’s Abductive Case for the Material Conditional Account

“…She even repeats them to herself. She then reasonably and correctly concludes (6) from ( 4) and ( 5): (6) The detector is not working.…”

“…Our second comment is that while Williamson is to be lauded for attending, not only to "linguistic data" distilled from the kind of vignette stories commonly used in analytic philosophy, but also to real data documented in the psychological literature on conditionals, he still gets the data to be accounted for badly wrong (as also pointed out in Berto, [6]). As Spohn [78] may have been the first to observe, psychological experiments using realistic materials tend to take for granted that, in conditionals, the antecedent is positively probabilistically relevant to the consequent, meaning that the materials of such experiments tend to consist of conditionals whose consequent is more probable on the supposition of the antecedent than it is unconditionally.…”

“…Williamson uses this story to argue for a conclusion rather different from Gibbard's, to wit, that conditionals express context-independent propositions and, more specifically, that they should be analyzed as material conditionals. His main argument is that a hearer who learns conditionals (4) and ( 5), which-note-are of forms A ⇒ C and A ⇒ ¬C , can and should conclude (6), which is of form ¬A . And indeed, on the MCA, this follows immediately.…”

“…De Finetti [14] and others following him (e.g., [3,5,31]) have proposed that "if" does express a binary truth-conditional connective, but that instead of a two-valued semantics, we need a three-valued semantics to state its meaning. 6 With V w (A) giving the truth value (1, 0, or undefined) of A at world w, the proposal is that…”

Williamson on conditionals and testimony

“…In fact, Williamson appears to endorse a ''large gap between theory and observation'' as a purported feature of modern, sophisticated scientific methodology (p. 116). For insightful critiques of, among other things, Williamson's fast-and-loose approach to data, seeBerto (2022) andRothschild (2022).5 As an anonymous referee remarked, while Williamson will not object to our reliance on abduction in this paper, others might well do so. In particular, Bayesians tend to reject abduction as a rational mode of inference.…”