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axioms



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In particular, I would say that virtually all professional mathematicians agree that questions of the form “Does Theorem T provably follow from Axioms A1, A2, and A3?” have objectively true answers.

From Scientific American • Sep. 15, 2019

These Axioms do not much influence our other Knowledge.

From An Essay Concerning Humane Understanding, Volume 2 MDCXC, Based on the 2nd Edition, Books 3 and 4 by Locke, John

All the inductions involved in all geometry are comprised in those simple ones, the formulæ of which are the Axioms, and a few of the so-called Definitions.

From A System Of Logic, Ratiocinative And Inductive by Mill, John Stuart

Still, the Law of Causation cannot be derived from the Mathematical Axioms, nor these from the Logical.

From Logic Deductive and Inductive by Read, Carveth

Inasmuch as Axioms of Uniformity are ultimate truths, they cannot be deduced; and inasmuch as they are universal, no proof by experience can ever be adequate.

From Logic Deductive and Inductive by Read, Carveth



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