What is an axiom? The first step to thinking straight.
It is the ground on which all logics and mathematics rest. No axiom, no certainty. Reasoning your way until first principles will grant you certainty in knowledge. Finding the axiomatic base of a discipline is precisely that: searching the principle, the origin. No mathematical proposition is firm unless it is set on axioms, for these little fellas will give you a firm fulcrum to develop any posterior thought. Aristotle said that the more you know about the origin of things the more you are able to get to know them as they are.
Axiom is an obvious truth, self-evident, that neither calls for proof nor cannot be disproven, because it simply is. It is; and if it were not, then nothing else would be too.
The word axiom comes from the Ancient Greek ἀξίωμα (axioma), which means “worthy”, i.e., it has value in itself, it sustains itself, it is the very essence, the very truth and dispense crutches.
Let us see one example with the three main axioms in logic:
Identity.
‘a’ is equal to ‘a’. Something is always equal to itself (and therefore cannot be equal to another.)
Non-contradiction
No object can be itself and not be itself at the same time.
