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Re: Peer-reviewed arguments against Cantor Diagonalization
Posted:
Nov 1, 2012 12:15 AM
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On Nov 1, 8:38 am, "Jesse F. Hughes" <je...@phiwumbda.org> wrote:
> "LudovicoVan" <ju...@diegidio.name> writes:
> > "Jesse F. Hughes" <je...@phiwumbda.org> wrote in message
> >news:87mwz2qu53.fsf@phiwumbda.org...
> >> "LudovicoVan" <ju...@diegidio.name> writes:
> >>> "Jesse F. Hughes" <je...@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.)
>
Can you state explicitly what it proves?
I don't see how MODUS PONENS might make this deduction.
LHS->RHS & LHS -> RHS
where RHS = "X > size({1,2,3...})"
nor how the enumeration of a set and it's index inclusion or not has
anything to do what's in the superset.
Herc
--
if( if(t(S),f(R)) , if(t(R),f(S)) ).
if the sun's out then it's not raining
ergo
if it's raining then the sun's not out
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