Re: when laypersons look smarter than math professors Re: a question for the anti-Cantorians

In sci.logic, george
<greeneg@xxxxxxxxxx>
wrote
on 23 May 2005 01:08:27 -0700
<1116835707.783956.148660@xxxxxxxxxxxxxxxxxxxxxxxxxxxx>:
>
> HERC777 wrote:
>>
>> OK, I choose the axioms of the programming language Haskell.
>
> NO, YOU DON'T, DUMBASS.
> Haskell DOESN'T HAVE axioms.
> Haskell IS A PROGRAMMING LANGUAGE.
> IT HAS *SYNTAX*. PERIOD.
> BECAUSE it is a language.

Haskell, if it's like C, C++, Pascal, FORTRAN, COBOL, etc. does
in fact has de facto axioms -- or perhaps limitations. To wit:

[1] All numbers are finitely represented, and therefore there is
a finite cardinality of numbers. (Even if there's an
indefinitely large integer capability in the language,
e.g. LISP, there's only so much RAM anyway.) In this
context, infinity is a token (well, it is also in mathemathics;
we can talk about it but never reach it) and there's only
one infinity.

[2] All algorithms must terminate.

[3] All sets are finite, for reasons similar to [1].

This is of course one of HERC's differences; he looks at everything
through a complexity filter. (Many mathematics professionals
are perfectly comfortable with a proof that a number exists,
and don't bother to compute it. :-) )

>
> Jeezus.
>
>> If you can't inspect the set in Haskell its a load of crap,
>
> SEZ WHO? You certainly can NOT find ANY "axiom of Haskell"
> that says THAT! Haskell DOES NOT even HAVE sets ANYway!
>

That shouldn't be too hard to rectify; Haskell has polymorphism.
Unfortunately a quick cursory search didn't pull up an equivalent
to Java's class library API, so I can't say for sure whether
they bothered to define one.

It's an interesting language, in some respects, though I don't
expect to have to learn it in my place of employment at this time.
But then, who knows? :-)

--
#191, ewill3@xxxxxxxxxxxxx
It's still legal to go .sigless.
.

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