"A recurring concern has been whether set theory, which speaks of infinite sets, refers to an existing reality, and if so how does one ‘know’ which axioms to accept. It is here that the greatest disparity of opinion exists (and the greatest possibility of using different consistent axiom systems)."
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Paul Cohen: (quote from p. 2410)
https://en.wikiquote.org/wiki/Axiomatic_system
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Axiomatic system
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