From my C. S. Lewis's Dangerous Idea
“It is often supposed that the laws of logic are true by convention. But this is clearly not a coherent idea. Before conventions can be established, logic must already be supposed. If logical laws are human conventions, then presumably it is at least possible for us to have different conventions. But the laws of logic are conditions of intelligibility; without them we could not say anything. Part of what it means to say anything is to imply that the contradictory is false. Otherwise, language simply does not function in a declarative way. So the reality of logical laws cannot be denied without self-refutation, nor can their psychological relevance be denied without self-refutation” (82).