An Axiom, Postulate Or Assumption Is A Statement That Is Taken To Be True, To Serve As A Premise Or Starting Point For Further Reasoning And Arguments. The Word Comes From The Greek AxΓΕma (αΌΞΎΞ―ΟΞΌΞ±) 'That Which Is Thought Worthy Or Fit' Or 'That Which Commends Itself As Evident.'The Term Has Subtle Differences In Definition When Used In The Context Of Different Fields Of Study. As Defined In Classic Philosophy, An Axiom Is A Statement That Is So Evident Or Well-Established, That It Is Accepted Without Controversy Or Question. As Used In Modern Logic, An Axiom Is A Premise Or Starting Point For Reasoning.As Used In Mathematics, The Term Axiom Is Used In Two Related But Distinguishable Senses: "Logical Axioms" And "Non-Logical Axioms". Logical Axioms Are Usually Statements That Are Taken To Be True Within The System Of Logic They Define And Are Often Shown In Symbolic Form (E.G., (A And B) Implies A), While Non-Logical Axioms (E.G., A + B = B + A) Are Actually Substantive Assertions About The Elements Of The Domain Of A Specific Mathematical Theory (Such As Arithmetic).
When Used In The Latter Sense, "Axiom", "Postulate", And "Assumption" May Be Used Interchangeably. In Most Cases, A
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20
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