[FOM] Certainity vs Boundedness

[Mani A]

"Timothy Y. Chow" <tchow at alum.mit.edu> wrote:
>On this point of view, mathematical knowledge is not
>necessarily certain, 
>but the scope of uncertainty is carefully
>circumscribed: We just can't be 
>absolutely certain that the alleged proof *is a
>proof* because it might 
>contain a bug in it.

>I am wondering if this point of view has been
>developed in detail by any 
>philosophers of mathematics.

Yes, in fact any theory of intentionality is bound to
touch the issues mentioned and any proposed solution
must make use of such theories (either implicitly or
explicitly). Some references are Kit Fine's book
"Reasoning with Arbitrary Objects. Aristotelian
Society Series. Basil Blackwell, Oxford,
1985."
" J. H. Hardy. Instantial Reasoning, Arbitrary Objects
and Holey Propositions. PhD thesis,
 Indiana University, June 2001." 

Hardy deals with the proof of a simple theorem in
Euclidean geometry and adapts Anil Gupta's "Holey
proposition theory" to his version.

I have my own theories that involve dialectical
reasoning.
 
I think it will help if your question(s) are narrowed
down to aspects of specific theories. 


Best

A. Mani

--
A. Mani
Member, Cal. Math. Soc








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