Informally, the implications of a proposition p (or set of propositions S) are those propositions which one would accept in the schema ‘if p then…’, (or, if each of S, then…). These will include things accepted only because of common sense, things which are common knowledge or presupposed in some context, or a sense of what regularly happens (‘if we go to London we will get caught in the crowds’). Logic tries to codify what is implied by sets of propositions in the more rigorous sense of what cannot possibly be false if they are each true. See also implicature.
Subjects: Philosophy — Mathematics.