
Re: Peerreviewed arguments against Cantor Diagonalization
Posted:
Nov 1, 2012 12:15 AM


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 conspiracytinged > 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 noncranks "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

