[FOM] FOM: What is a proof?
John Corcoran
corcoran at buffalo.edu
Thu Jan 22 11:29:59 EST 2009
FOM: What is a proof?
Aristotle's general TRUTH-AND-CONSEQUENCE CONCEPTION OF PROOF was meant to
apply to all demonstrations. According to him, a PROOF is an extended
argumentation that begins with premises known to be TRUTHS and that involves
a chain of reasoning showing by deductively evident steps that its
conclusion is a CONSEQUENCE of its premises; a proof is a [logical]
DEDUCTION whose premises are known to be [material] TRUTHS. Starting with
premises they know to be true, knowers demonstrate a conclusion by DEDUCING
it from the premises. It is essential to this conception that a proof
provides KNOWLEDGE of the truth of its conclusion to anyone for whom it is a
proof. Every proof produces (or confirms) KNOWLEDGE of (the truth of) its
conclusion for every person who comprehends the demonstration. Persuasion
merely produces OPINION.
Q1. Who are the prominent figures in foundations of mathematics that ACCEPT
this view, perhaps with qualifications? Please give quotes if possible, or
at least give traceable references.
Q2. Who are the prominent figures in foundations of mathematics that REJECT
this view, perhaps with qualifications? Please give quotes if possible, or
at least give traceable references.
Q3. What are the qualifications required by prominent figures in foundations
of mathematics that ACCEPT this view with qualifications?
Q4. What are the objections by prominent figures in foundations of
mathematics that REJECT this view?
John Corcoran, PhD, DHC
Professor of Philosophy
University at Buffalo
Buffalo, NY 14260-4150
corcoran at buffalo.edu
http://philosophy.buffalo.edu/people/faculty/corcoran/
http://www.acsu.buffalo.edu/~corcoran/
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