Philosophical basics: A process of reduction

All philosophy starts with axioms. The question is which ones are the most basic, the most essential, the most inescapable.
The first axiom appears to be logic. Or perhaps reason. Or perhaps most basically, the law of non-contradiction. There cannot be a round square.
The law of non-contradiction was the basis for the rejection of dogmatic scepticism. You cannot know for certain that nothing can be known for certain. Just as the statement ‘I am a liar’ is inherently meaningless.