LudovicoVan
Posts:
2,971
From:
London
Registered:
2/8/08
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Re: The computable reals are uncountable (?)
Posted:
Jun 3, 2012 4:45 PM
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"Dick" <DBatchelo1@aol.com> wrote in message
news:f5054fdf-9163-4096-8c5f-cc01ac4f5110@eh4g2000vbb.googlegroups.com...
> On Jun 3, 1:46 pm, "LudovicoVan" <ju...@diegidio.name> wrote:
>> "Dick" <DBatche...@aol.com> wrote in message
>> news:be754217-4b30-47e2-9c22-b86e14eb1a42@a16g2000vby.googlegroups.com...
>>
>> > It's interesting - but even Constructivists will admit that it may not
>> > be worth the trouble involved.
>>
>> Not really: in my searches so far I have seen that detractors of
>> constructive approaches claim that constructive analysis is clumsy, but
>> promoters claim that it is "only slightly" more clumsy, while
>> dramatically
>> gaining on the epistemological strength of the theories... Namely, I am
>> not
>> competent enough to take side here, yet there doesn't seem to be that
>> much
>> consensus as you seem to imply.
>
> I have a book: "Varieties of Constructive Mathematics" by Bridges &
> Richman.
One book only?
> It states:-
> "Since classical mathematics, as practised by all but a tiny minority
> of mathematicians, appears to offer a much less arduous route to
> discovery, and a far greater catalogue of successes, than its
> constructive counterpart, onr may well ask: Why should anyonr, other
> than a devotee of a constructivist philosophy, be interested in
> learning abour constructive mathematics?"
> He goes on to give reasons. However, I think the best reason is that
> you do have a constructivist philosophy; you find non-constructive
> arguments unsettling.
Your presumptions are uninteresting, not unsettling.
-LV
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