Source: Notre Dame J. Formal Logic
Volume 51, Number 3
In his "From classical to constructive probability," 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), (b)
unconditional bets with graded payoffs (Milne), or (c) unconditional bets with
ungraded payoffs(Dietz), 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.
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