The definition of an axiom is a self-evident truth that requires no proof. When someone says to you, “the sky is blue, the grass is green and there is light from the sun every day,” that is axiomatic. Speaking for myself, as a female, that is most of what I see and experience in my life. It’s common sense that comes through the body’s senses. I still love it and find mysterious levels but I have no desire to take an axiomatic or empirical truth and put it in a lab. It usually turns out to be synchronicity, but that is another intuitive subject.
It is first classified as instinct through the ancient subconscious mind and climbs the ladder to intuition from the unconscious mind that comes through in dreams. That has happened to me all of my life. An experience I’ve had has gone from instinct to intuition because of a dream or dreams I’ve had. It’s like breathing for me.
I hope it does for you too. It makes life more enjoyable and understandable.