[FOM] Certainity vs Boundedness
Timothy Y. Chow
tchow at alum.mit.edu
Tue May 6 19:31:11 EDT 2008
A. Mani wrote:
>I think it will help if your question(s) are narrowed
>down to aspects of specific theories.
I'm not sure exactly what kind of narrowing you are asking for. My
specific suggestion is that the fundamental difference between
justification in mathematics and justification in other areas of knowledge
is that a unit of mathematical knowledge (i.e., a theorem) can be
*definitively* justified by a *bounded* amount of evidence (i.e., a
proof), provided we assume that the evidence is error-free. In contrast,
no bounded amount of evidence can ever definitively justify, say, a law of
physics, even if we grant by fiat that the evidence is error-free.
Unboundedness can enter into the process of error detection, of course,
but that's a side issue.
Is my assertion not sufficiently narrow? Why not?
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