[FOM] The Provenance of Pure Reason (II)

[Eray Ozkural]

On 5/29/06, Gabriel Stolzenberg <gstolzen at math.bu.edu> wrote:
>    1.  Bill's argument that the basic concepts of constructive math
> "belong to" classical math seems to work equally well with the law
> of excluded middle replaced by a version of Church's thesis that
> implies the negation of the law of excluded middle.  Does this mean
> that the basic concepts of constructive math belong both to classical
> math and to this other system that is inconsistent with it?

I would like to know more about this version of Church's thesis.
How does this implication occur?

I think that the view that classical mathematics is a restricted
subset of constructive mathematics, in analogy with non-Euclidian
geometry and Euclidian geometry, may be more relevant from
a logical point of view. Of course, I say that only because I think that
the semantic notions of "existence" and "function" hardly matter.
(When you say that empty set exists, how many people take that literally?)
What seems to matter more is that abstract concepts are
defined formally and communicated without error from individual
to individual (the idea of a friend named Bhupinder S. Anandh). [*]
After one observes this logical relation between the two schools,
one may go further and observe how a mechanical explanation is sufficient
to give semantics to constructive math, a situation which I believe
to be fulfilling from a physicalist point of view.

Regards,

[*] It now occurs to me that "without error" could be interpreted
as that there is no probability of error in this communication, if
we want to understand it mathematically.

-- 
Eray Ozkural (exa), PhD candidate.  Comp. Sci. Dept., Bilkent University, Ankara
http://www.cs.bilkent.edu.tr/~erayo  Malfunct: http://www.malfunct.com
ai-philosophy: http://groups.yahoo.com/group/ai-philosophy
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