Issue 41, March 2011
On the Triviality Results and the Restriction on Conditionalization
Lewis’s arguments for the triviality results are considered as a powerful rejection of the truth-conditional accounts of conditionals: the absurd consequence
that for any propositions A and C, p(C/A) = p(C) is derived from the classical probability calculus, conditionalization, and Stalnaker’s semantics for conditionals.
In this paper, it is argued that the triviality results need not be a threat to Stalnaker’s semantics, for we can derive a generalized triviality result from the classical
probability theory and any thesis about conditional probability. The lesson, I suggest, is that we should reconsider the classical probability theory or set a restriction on the rule of conditionalization such that the triviality results may be avoided.