Consequences of the Suppositional Rule
This chapter argues that the Suppositional Rule is a fallible heuristic, because it has inconsistent consequences. They arise in several ways: (i) it implies standard natural deduction rules for ‘if’, and analogous but incompatible rules for refutation in place of proof; (ii) it implies the equation of the probability of ‘If A, C’ with the conditional probability of C on A, which is subject to the trivialization results of David Lewis and others; (iii) its application to complex attitudes generates further inconsistencies. The Suppositional Rule is compared to inconsistent principles built into other linguistic practices: disquotation for ‘true’ and ‘false’ generate Liar-like paradoxes; tolerance principles for vague expressions generate sorites paradoxes. Their status as fallible, semantically invalid but mostly reliable heuristics is not immediately available to competent speakers.