On 13 Sep, 18:12, Bruno Marchal <[email protected]> wrote:
> Marty,
>
> > Could you please clarify to a non-mathematician why the
> > principle of excluded middle is so central to your thesis (hopefully
> > without using acronyms like AUDA, UD etc.).
>
> Without the excluded middle (A or not A), or without classical logic,
> it is harder to prove non constructive result. In theoretical
> artificial intelligence, or in computational learning theory, but also
> in many place in mathematics, it happens that we can prove, when using
> classical logic, the existence of some objects, for example machines
> with some interesting property, and this without being able to exhibit
> them.
What you are proving is only existence in the mathematical sense.
The philosophical quesiton of whether backwards-E should be taken
literally (Platonism) or only metaphorically (formalism) is left
unadresses
by the PEM.
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