For centuries many of Aristotle’s contributions to philosophy were considered sacrosanct. His truths were ‘eternal truths’ which could never be denied. But the advent of modern philosophy led to the gradual discarding of Aristotelian thought. Surely his most important contribution, logic, would last forever. Then came Nietzsche, and even this was called into question:
We cannot both affirm and deny the same thing. This is a subjective empirical law – nothing to do with logical ‘necessity’, only of our inability to do it.
In Aristotle’s view the law of contradiction is the most certain basic principle of them all. It is the ultimate and most fundamental principle upon which all demonstrative proof rests. The principles of every axiom depend upon it. Yet if this is really the case we should perhaps examine more thoroughly what presuppositions are already involved here. Either it says something about actuality, about being, as if we already knew it from another source; that is, as if opposite attributes could not be ascribed to it. Or it means: opposite attributes should not be ascribed to it. In which case, logic would not be an imperative to know the truth, as formerly supposed, but merely an imperative to organise a world that we could look upon as the true one.
Thus it remains an open question – Do the axioms of logic precisely match reality? Or are they simply a means and method for us to create a concept of ‘reality’ that suits us? As already indicated, to agree with the first question we would have to possess a previous knowledge of being (i.e., one prior to our use of, and in no way involved with, logic). And this is certainly not the case. The proposition (the one that forms the law of contradiction) thus involves no criteria of truth. It is simply an imperative saying what should count as true.
– Nietzsche, Will to Power, Sec 516