The Math Forum

Search All of the Math Forum:

Views expressed in these public forums are not endorsed by NCTM or The Math Forum.

Math Forum » Discussions » sci.math.* » sci.math

Notice: We are no longer accepting new posts, but the forums will continue to be readable.

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

Advanced Search

Back to Topic List Back to Topic List Jump to Tree View Jump to Tree View   Messages: [ Previous | Next ]
Graham Cooper

Posts: 4,495
Registered: 5/20/10
Re: Peer-reviewed arguments against Cantor Diagonalization
Posted: Nov 1, 2012 12:15 AM
  Click to see the message monospaced in plain text Plain Text   Click to reply to this topic Reply

On Nov 1, 8:38 am, "Jesse F. Hughes" <> wrote:
> "LudovicoVan" <> writes:
> > "Jesse F. Hughes" <> wrote in message
> >

> >> "LudovicoVan" <> writes:
> >>> "Jesse F. Hughes" <> wrote in message
> >>>

> > <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.


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.

if( if(t(S),f(R)) , if(t(R),f(S)) ).
if the sun's out then it's not raining
if it's raining then the sun's not out

Point your RSS reader here for a feed of the latest messages in this topic.

[Privacy Policy] [Terms of Use]

© The Math Forum at NCTM 1994-2018. All Rights Reserved.