Re: Foundations Of Mathematics Abscondita

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FOMA.  Note 7 : What Is A Proof?

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Re: http://www.cs.nyu.edu/pipermail/fom/2009-January/013315.html

John,

I hear your emphasis on deductive reasoning in speaking of mathematical
demonstration, and I think I hear echoes of what Aristotle (supposedly)
said about knowledge per se being of generals and not of individuals --
a theme that reverberates all through mathematics, computation, and the
empirical sciences generally -- but you know that Aristotle recognized
forms of inference that are not deductive, not demonstrative, but that
nonetheless have their roles to play in the cycles (and epicycles?) of
inquiry that lead on to knowledge.

For my part, I find that it helps to examine deductive reasoning
within the larger context of inquiry that involves abductive and
inductive inference -- especially, of course, when we're talking
about the problems of probating probable conjectures, hypotheses,
and other forms of likely reasoning.

Jon Awbrey

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