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QuoteRef: daviPJ3_1972
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references c-d
Topic:
mathematics as a formal system
Topic:
limitations of formalism
Topic:
program source as truth
Topic:
mathematics by proofs and refutations
Reference
Davis, P.J., "Fidelity in mathematical discourse: Is one and one really two?", American Mathematical Monthly, 79, 3, March 1972, pp. 252-263. Google
Other Reference
reprinted p. 163-175 Tymoczko, T. (ed) New directions in the philosophy of mathematics, Boston: Birkhauser 1985
168 ;;Quote: a proof is like a program: the axioms are input, finding a proof is writing a program, verification is running the program
172 ;;Quote: the program itself is the only complete description of what the program will do
172+;;Quote: even if a complete description of a machine is unavailable, run a program and you will see what it does
175 ;;Quote: a derivation or proof has only probabilitistic validity; mathematics is somewhat like experimental sciences with repeatable experiments and widespread usage
ThesaHelp: references c-d (337 items)
Topic: mathematics as a formal system (30 items)
Topic: limitations of formalism (92 items)
Topic: program source as truth (17 items)
Topic: mathematics by proofs and refutations (31 items)