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 23:27:44 -0700
<1116916064.263351.168910@xxxxxxxxxxxxxxxxxxxxxxxxxxxx>:
>
> The Ghost In The Machine wrote:
>
>> Haskell, if it's like C, C++, Pascal, FORTRAN, COBOL, etc.
>
> NO, it ISN'T like ANY of the above.
> It's a functional language.
> Those are imperative.
>
>> does in fact has de facto axioms
>
> Shut the *** up,moron.
> There are NO SUCH THINGS as
> "de facto axioms". Axioms are
> SENTENCES in a language.
> Haskell doesn't even HAVE sentences.
> It has expressions (because it's functional).
> There are NO axioms ANYwhere around this discussion,
> if we are discussing Haskell and computing paradigms.

There are implied axioms. Admittedly, the ground gets
very murky here.

>
>> -- or perhaps limitations.
>
> Well, OF COURSE, the whole PARADIGM has limitations.
>
>> To wit:
>>
>> [1] All numbers are finitely represented,
>
> Wrong. Haskell doesn't have any opinions
> about "all numbers", OR about any "representation"
> of ANYthing.
>
>> and therefore there is
>> a finite cardinality of numbers.
>
> Not according to Haskell.
> For all finite numbers, you can write a Haskell
> program that counts higher than them. Therefore
> Haskell does not support any finite cardinality of
> numbers.

All machines have a finite number of numbers; there's only so
much RAM.

>
>> (Even if there's an
>> indefinitely large integer capability in the language,
>> e.g. LISP, there's only so much RAM anyway.)
>
> Of course, but Herc didn't say a DAMN thing about
> RAM axioms. He said he was taking his axioms
> FROM HASKELL. WHICH IS IMPOSSIBLE.

It is possible but, given Herc's history, unlikely. At
best, one gets a set of rather general axioms (computers
are finite).

>
>> In this context, infinity is a
>> token (well, it is also in mathemathics;
>> we can talk about it but never reach it)
>
> Oh, bull***. In this context, all tokens are
> WHATEVER THE LANGUAGE SAYS THEY ARE, and it just
> so happens that Haskell DOES NOT HAVE a "token"
> for infinity.

Not even a Inf? (0xFFFsomething)

>
>> and there's only one infinity.
>
> What utter bull***. Actually, there are only
> NONE,but once you START faking them, you can KEEP
> faking them as high AS YOU LIKE.

I am referring to IEE754. Of course one can create
arbitrary tokens.

>
>>
>> [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.
>


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

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