Re: Cardinality question

On Sun, 10 Apr 2005 15:29:49 +1000, "Peter Webb"
<webbfamily-diespamdie@xxxxxxxxxxxxxxx> wrote:

>
>> Of course there is, but the same difference exists wrt human
>> mathematicians.
>>
>> Or at least that's true of all the differences I can think of.
>>
>>
>> Exactly what is
>> it that a human can do which a computer cannot, regarding the question
>> of modelling uncomputable reals?
>>
>> David C. Ullrich
>
>You are right, of course. If we are all just Turing machines, then there is
>no difference. And the margins of Usenet are not big enough for me to prove
>that we are NOT just TMs.

I didn't claim we were all just TMs, just that computers can prove
anything people can.

>However, my point seems fair enough in context of the original post -
>essentially, what use is there for theories of infinite sets, beyond a few
>impossibility proofs in Computer Science that 95% of programmers would never
>have heard of ...

No, that most certainly was not your point, unless you're much worse
at expressing yourself than you appear to be. Clever of you to omit
all the context above. I didn't say anything about what use infinite
sets were, and neither did you until just now - my comments, which
you said you disagreed with, were about the question of whether
computers can "do" infinite sets as well as people can. Not the
same question at all.

>The OPs argument is that infinite set theory is useless. This appears true
>to me, because any describably physical system can only have a countable
>number of states.
>
>However, I am also aware that through the 18th and 19th centuries number
>theory was regarded as the "Queen of Mathematics" because it did not have
>(and people believed it could not have) any practical use. This was a
>failure of their imaginations - shame on Fermat for not considering internet
>cryptography when he was investigating primes. Perhaps infinite set theory
>does have some purpose, and there is some phyiscally realisable model that
>the theory relates to, and this is just the failure of our imaginations when
>we consider it somehow different from the rest of mathematics?
>
>
>
>
>


************************

David C. Ullrich
.

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