On 14 Sep 2009, at 19:02, Flammarion wrote:
>
>
>
> On 13 Sep, 18:12, Bruno Marchal <marc....domain.name.hidden> 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.
Indeed.
> The philosophical quesiton of whether backwards-E should be taken
> literally (Platonism) or only metaphorically (formalism) is left
> unadresses
> by the PEM.
Of course. that is why there is the MGA.
Bruno
http://iridia.ulb.ac.be/~marchal/
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Received on Tue Sep 15 2009 - 09:34:33 PDT