Peirce's challenge to material implication as a model of ‘if’
Suppose there is a sweepstake in which only one thousand people are eligible to participate. Tickets are sold for ?1 each. No participant is permitted to buy more than one ticket. And the winner will take the total of the stakes. Then, intuitively, (3.1) is true while (3.2) is false. Read concludes (p. 6) that classical quantificational logic does not have the resources to express adequately the lack of entailment of the second sentence in (1) or (3) by the first. Moreover, he ascribes this inadequacy to the translation of 'if' by the implication sign of classical quantificational logic (p.10). What I wish to take issue with here is Read's ascription of the source of the observed inadequacy. Consideration of a broader range of data, however, makes clear that the inadequacy noted by Read does not reside in the translation of 'if' as classical material implication. For Peirce's puzzle can be reproduced without any occurrence of the subordinating conjunction 'if', or any occurrence of any of its lexical or syntactic counterparts. Consider the following pair of