Axioms

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We can not have, and do not need to have, proof for everything that we accept as being true. We accept some things as being true because they are self-evident to us, i.e. axioms. All proofs are ultimately based on such axioms. The ability to see self-evident truths is therefore essential for any kind of knowledge.

In the above argument the word axiom is used with the definition described for example in Webster's Revised Unabridged Dictionary (1913).

Axiom:
(Logic & Math.) A self-evident and necessary truth, or a proposition whose truth is so evident at first sight that no reasoning or demonstration can make it plainer; a proposition which it is necessary to take for granted; as, "The whole is greater than a part;" "A thing can not, at the same time, be and not be."