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Topic: Peer-reviewed arguments against Cantor Diagonalization
Replies: 23   Last Post: Nov 2, 2012 1:46 AM

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Jesse F. Hughes

Posts: 9,776
Registered: 12/6/04
Re: Peer-reviewed arguments against Cantor Diagonalization
Posted: Oct 31, 2012 6:36 PM
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"LudovicoVan" <julio@diegidio.name> writes:

> "Jesse F. Hughes" <jesse@phiwumbda.org> wrote in message
> news:87mwz2qu53.fsf@phiwumbda.org...

>> "LudovicoVan" <julio@diegidio.name> writes:
>>> "Jesse F. Hughes" <jesse@phiwumbda.org> wrote in message
>>> news:87txtaqxih.fsf@phiwumbda.org...

> <snip>
>

>>>> I never said you thought that set theory was a root of evil, but, near
>>>> as I can figger, you said that it was a symptom of a lying culture which
>>>> lies just 'cause it can.

>>>
>>> You could say because it wants, not because it can: anyway, you rephrase
>>> it
>>> as a 13 year old would, but yes, let's say you almost got it, son, though
>>> not quite. OTOH, I am pretty sure you could do better, if only you could
>>> be
>>> any little more honest.

>>
>> Sorry, I've studied too much set theory to be honest, I guess.

>
> Set theory is not responsible for your honesty, big boy.
>

>>>> In an honest culture, we would all admit that
>>>> set theory is a plain falsehood.

>>>
>>> No, I have never said that: there are indeed things that I find are
>>> patently
>>> wrong, the standard theory of cardinality being one of them, but that
>>> does
>>> not mean I'd discard the baby too. Not to mention that we all have
>>> "search"
>>> strategies, and a world of fools and criminals means just do not expect
>>> that
>>> I be a gentlemen. It's a war, mate.

>>
>> See, here's the weird thing. The theorems of ZFC can be confirmed by
>> anyone.

>
> Apart from the fact that proof by consensus is not a valid argument, that's
> not even true.


Who the fuck said anything about proof by consensus?

And, surely, if the argument is invalid, perhaps you can point out the
invalid step.

For that, of course, we should be clear on what argument we are
discussing. There are various arguments that go by the name "Cantor's
theorem". The easiest to analyze, of course, is the proof that, for all
sets X, |X| < |PX|. Are you prepared to show me how that argument is
invalid? If so, we can discuss it.

But I'm not going on some vague, meandering and conspiracy-tinged
rantfest. If you want to claim that the proof is invalid, you have to
show me the step which is invalid.

>> At best, you can complain that either the axioms are false
>> (I'm sure I don't know what that would mean)

>
> At best? Anyway, try and ask Aatu about that: to you he might even
> reply.
>

>> or that the logic we use is
>> mistaken (and that's a mighty hard sell). But it is undeniable that ZFC
>> proves for all X, |X| < |PX|. Anyone can confirm that the proof is a
>> valid argument.

>
> Again, proof by consensus is not a proof, but that is not even true: as you
> should know even too well, not anyone would confirm, and this is not just
> the cranks.


And, again, to say that "anyone can confirm the validity" is not proof
by consensus, you tedious twat.

And, as far as non-cranks "not confirming" the validity, well, that is
the subject of this discussion. Can you name a single, reputable source
that disputes whether ZFC proves Cantor's theorem? (NOTE: I'm talking
about a particular formal theory here, so the various mathematicians who
gave philosophical disputes over Cantor's informal argument are
irrelevant to our purposes here, unless those disputes can explicitly
show an invalid step in this very simple proof.)

>
--
Jesse F. Hughes

"You're ketchup, so I'll put you on meatloaf!"
-- Quincy P. Hughes, age five, tries his hand at insults



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