Conjunction and Contradiction

A contradiction consists of a pair of sentences, one of which is the negation of the other. 1 From now on I shall settle on statement, but this decision will be of no consequence. 2 Intuitively, the first type of contradiction arises if we assert and deny the same thing in the same breath, whereas the second type of contradiction arises if we end up denying (perhaps unwittingly) something we have already asserted. We could plausibly generalize these formulations by construing in each case one of the two conjuncts, or statements, not as the negation of the other but as a conjunct or statement that is equivalent to the negation of the other. However, the notion of equivalence calls for a logic, and since Im going to be concerned with the logical status of LNC it will be safer to stick to narrow formulations such as (1) and (2). Somewhat more formally, these can also be put thus: (1') A contradiction is a statement of the form