Consequences, Theory of

Abstract

The theory of consequence is a branch of logic that studies dependence relations between propositions as a separate subject. Thus it is, in a way, more general than syllogistics. It rests on old foundations, but as a distinct field it was born around 1300. Its most creative phase was 1320–1340 (Burley, Ockham, Buridan), but it was elaborated afterwards, and retained an established place in the logic books. A “consequence” from antecedent(s) to a consequent is probably best regarded as a valid inference. According to its standard definition, a consequence holds when the antecedent is incompatible with the opposite of the consequent. Logicians sought general rules for such relations. Some rules were “proof-theoretical,” that is, one consequence follows from others; some rules concerned the validity of a single inference type. A lot of theorems of propositional logic were proved in this connection, and modal qualifications were soon added. A large part of the discussion was about various distinctions of consequences. They could be ut nunc (under present conditions), or simply, without temporal qualifications. Simple consequences were either formal or material. Roughly, the earlier writers (Burley, Ockham) declare that formal consequences are valid because of the meanings of terms, but Buridan defines formal validity in the manner of modern logic, as the validity of all instances of the same logical form. This initiative was criticized, but finally many logicians utilized both definitions, one amounting to analyticity, the other to logical validity.