Richard Dietz

RAMSEY’S TEST, ADAMS’ THESIS, AND LEFT-NESTED CONDITIONALS

Adams famously suggested that the acceptability of any indicative conditional whose antecedent and consequent are both factive sentences amounts to the subjective conditional probability of the consequent given the antecedent. The received view has it that this thesis offers an adequate partial explication of Ramsey’s test, which characterizes graded acceptability for conditionals in terms of hypothetical updates on the antecedent. Some results in van Fraassen (1976) may raise hope that this explicatory approach to Ramsey’s test is extendible to left-nested conditionals, that is, conditionals whose antecedent is itself conditional in form. We argue that this interpretation of van Fraassen’s results is to be rejected. Specifically, we provide an argument from material inadequacy against a generalization of Adams’ thesis for left-nested conditionals.

On Generalizing Kolmogorov

In his “From classical to constructive probability” (2003), Brian Weatherson offers a generalization of Kolmogorov’s axioms of classical probability that is neutral regarding the logic for the object-language. Weatherson’s generalized notion of probability can hardly be regarded as adequate, as the example of supervaluationist logic shows. At least, if we model credences as betting rates, the Dutch-Book argument strategy does not support Weatherson’s notion of supervaluationist probability, but various alternatives. Depending on whether supervaluationist bets are specified as (a) conditional bets (Cantwell (2006)), (b) unconditional bets with graded payoffs (Milne (2008)) or (c) unconditional bets with ungraded payoffs (Dietz (2008)), supervaluationist probability amounts to (a) conditional probability of truth given a truth-value, (b) the expected truth-value, or (c) the probability of truth respectively. It is suggested that for supervaluationist logic, the third option is the most attractive one, for (unlike the other options) it preserves respect for single-premise entailment. 1 Weatherson’s generalized calculus of probability According to Kolmogorov’s classical axioms of probability, any function defined on sentences of a given language L of propositional logic is a probability function just in case it (i) takes non-negative real numbers as values, (ii) it takes for tautologies the

Vagueness and probability: introduction

This introduction provides some background to the contributions to this volume.