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If we wish to express our ideas in terms of the concepts synthetic and analytic, we would have to point out that these concepts are applicable only to sentences that can be either true of false, and not to definitions. 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, in 'The Philosophy of Space and Time (1928), as translated by Maria Reichenbach (1957), § 14 | ||