3 Axioms:

Existence exists - There is something, as opposed to nothing. Existence is axiomatic because it is necessary for all knowledge and it cannot be denied without conceding its truth. To deny existence is to say that something doesn't exist. A denial of something is only possible if existence exists.

A is A/The Law of Identity - Everything that exists has a specific nature. Each entity exists as something in particular and it has characteristics that are a part of what it is. Identity is the concept that refers to this aspect of existence; the aspect of existing as something in particular, with specific characteristics. An entity without an identity cannot exist because it would be nothing. To exist is to exist as something, and that means to exist with a particular identity.

Consciousness is the faculty that perceives that which exists. - To be a consciousness, it must be conscious of something external to itself. Only after it is conscious of something external can it identify itself. Descartes argued that consciousness is axiomatic because you cannot logically deny your minds existence at the same time as using your mind to do the denying. Because to be conscious is to perceive something, consciousness requires something outside of itself in order to function; consciousness requires and is dependent upon, existence.

Logic is the art of conforming one's thoughts to the Law of Identity. It is the art of non-contradictory identification.

Logic is used in integrating ideas as well. What this means in practice is combining information clearly, and without contradiction. It must be combined into a specific, identifiable package, that doesn't contradict itself.

These three axioms and logic form the basis of a rational and defensible epistemology.