In a fairly opaque passage in his commentary on Aristotle's Categories Peter Abelard denies both directions of a biconditional sentence very much like a Tarski biconditional: "A man exists" is true iff a man exists. "A man exists" is taken to be a sentence token and the right hand element is taken to be the existence of a man. Neither Abelard's argument nor his reason for making the argument is clear. It at first appears that Abelard may be claiming that (...) each of the corresponding conditionals is false. Such a claim could amount to a rejection of the correspondence theory of truth and would naturally have serious repercussions for the study of Abelard's logic. In this paper I argue that Abelard does not deny the truth of the biconditional only its necessity. Abelard makes this argument in response to Boethius and certain twelfth-century masters , who argue that there is a logically necessary connection between words and things, and hence between sentence tokens and what is the case in the world. Abelard is not expressing any serious reservations about the correspondence theory of truth. He is demonstrating the logical importance of the conventionality of language. Arguing against authorities, and twelfth-century peers, he shows that there is no logically necessary connection between words and things, hence the Tarski biconditional is not necessarily true. (shrink)