"An axiom is proposition more general than the propositions or the science in which it employed as an axiom; or, an axiom is a proposition which is true of more subjects than the subject or the science in which it is quoted as an axiom. Hence. Geometry ought to admit as axioms all Algebraic truths. The simple truths of this kind, which are commonly called axioms, ore corollaries from the definitions of such terms as equal, whole, part, sum, etc." (The Pennsylvania School Journal, 1856)
"The logical axioms are the principle of all truth." (Otto Weininger, "Sex and Character", 1903)
"An axiom is a self-evident truth, the statement of which is superfluous to the conclusiveness of the reasoning, and which only serves to show a principle involved in the reasoning. It is generally a truth of observation; such as the assertion that something is true." (Charles S Peirce, "New Elements" ["Kaina stoiceia"], 1904)
"The mathematical axioms are therefore neither synthetic nor analytic, but definitions. [...] Hence the question of whether axioms are a priori becomes pointless since they are arbitrary." (Hans Reichenbach, "The Philosophy of Space and Time", 1928)
"Axioms are instruments which are used in every department of science, and in every department there are purists who are inclined to oppose with all their might any expansion of the accepted axioms beyond the boundary of their logical application." (Max Planck, "Where Is Science Going?", 1932)
"An axiom is common to all sciences, whereas a postulate is related to a particular science; an axiom is selfevident, whereas a postulate is not; an axiom cannot be regarded as a subject for demonstration, whereas a postulate is properly such a subject; an axiom is assumed with the ready assent of the learner, whereas a postulate is assumed without, perhaps, the assent of the learner." (Howard Eves, "Foundations and Fundamental Concepts of Mathematics", 1958)
"Whenever we write an axiom, a critic can say that the axiom is true only in a certain context." (John McCarthy, "Generality in Artificial Intelligence", 1987)
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