Paradox

202 A BRIEF HISTORY OF THE PARADOXThe sophism prompts students to distinguish between themain connective of a sentence and subordinate connectives.If “and” is the main connective, then A means A1. If “or” isthe main connective, A means A2.In addition to logical sophisms, there are grammaticalsophisms. Linguistics began with puzzle sentences such as“Love is a verb.” Twentieth-century linguists continued thepractice with counterexamples to increasingly sophisticatedgrammatical generalizations. For instance, one natural theoryof how pronouns work is that they borrow the referenceof an earlier referring phrase (unless the meaning is suppliedfrom outside the sentence, as when we point). Thus, “Francistouched the beggar and cured him” is solved as “Francistouched the beggar and cured the beggar.” In 1967, EmmonBach and Stanley Peters pointed out that this theory leads toan infinite regress when applied to cross-referential sentencessuch as “The pilot that shot at it hit the Mig that chased him.”In the Mig sentence “it” means “the Mig that chased him”and “him” means “the pilot that shot at it.” Substituting onephrase for the pronoun always leaves the other pronoun.Since we are finite beings, we cannot go round and roundsubstituting forever. Do we understand the sentence byleaving some pronoun ungrounded? Or is the Mig sentencemeaningless? Buridan would have loved the Bach-Petersparadox.As sophisms became more challenging, their solutionsbecame controversial. Writers of logic manuals would thenreview past solutions, present their own, and finally show theadvantages of their proposal. The insolubles lie at the extremeend of this continuum of difficulty.But how did the medievals come by the insolubles? Inthe previous chapter, I argued that they were unable to