
Re: ZFC and God
Posted:
Jan 23, 2013 11:51 AM


On 01/23/2013 08:36 AM, Jesse F. Hughes wrote: > WM<mueckenh@rz.fhaugsburg.de> writes: > >> On 23 Jan., 12:47, "Jesse F. Hughes"<je...@phiwumbda.org> wrote: >>> WM<mueck...@rz.fhaugsburg.de> writes: >>>> On 22 Jan., 21:18, "Jesse F. Hughes"<je...@phiwumbda.org> wrote: >>>>> WM<mueck...@rz.fhaugsburg.de> writes: >>> >>>>>> That is potential infinity. That proof is not necessary, because the >>>>>> set is obviously potentially infinite. No, you shoudl give a proof, >>>>>> that there is a larger k than all finite k. >>> >>>>> Er, no. When I say that the union is infinite, I do not mean that it >>>>> contains an infinite number. >>> >>>> But you mean that the tree contains infinite paths. And just that is >>>> impossible without ... >>> >>>> In order to shorten this discussion please have a look at >>> >>> http://math.stackexchange.com/questions/284328/howtodistinguishbet... >>> >>> No. It's irrelevant. >> >> You are in error. >>> >>> We're talking about whether you can prove that >>> >>> U_n=1^oo {1,...,n} >>> >>> is finite. I'm not switching topics to paths in trees (despite the >>> fact that the ignorance of your question is obvious). >> >> The union of FISs is finite. Yes that is my claim. But I cannot give >> an upper limit, because the finite numbers have no upper limit. This >> is called potentially infinite. >>> >>>> There it has meanwhile turned out ... But see it with your own eyes >>>> what you would not believe if I told you. >>> >>>> The index omega is in reach, it seems. >>> >>> You're playing your usual little game of trying to change the topic. >>> I won't have it. >>> >>> I take it that this new tack is so that you don't have to concede the >>> point: there is no mathematical publication which claims that the >>> above union contains elements larger than any natural, nor any >>> publication which claims that this is what it means to be infinite. >> >> I know. But if you hace read the discussion, you have seen that two >> matheologians claim just this. Why do they? Because they cannot answer >> the question: What paths are (as subsets of the set of nodes) in a >> Binary Tree that is the union of all its levels? Are there only the >> finite paths? Or are there also the infinite paths? >> Try to answer it, and you will see that you need the omegath level or >> must confess that it is impossible to distinguish both cases. Hence, >> Cantor's argument applies simultaneously to both or to none. > > I'm not interested in the webpublished claims of two individuals on a > different topic than we're discussing. > > Once again, let me remind you what you claimed. You claimed ZF was > inconsistent, and in particular that ZF proves that the union > > U_n {1,...,n} > > is both finite and infinite. > > Now, we've had two competing definitions of infinite in this > particular discussion. > > (1) A set S is infinite if there is no natural n such that S = n. > > (2) A set S is infinite if it contains a number greater than every > natural n. > > The first definition is what mathematicians almost always mean, and > they *never* mean the second, but this is mere semantics. Let's talk > results. > > We both agree that, using definition (1), the above union is infinite > and (I think) we agree that we cannot show it is finite (=not > infinite). If I'm mistaken on this point, then please show me. > > On the other hand we both agree that, per definition (2), the union is > "finite", but I have seen no contradiction result, since you have not > shown that the union is "infinite" in this sense. Nor can you find a > single publication in which a mathematician has claimed the union > above (i.e., the set N of natural numbers) contains an element larger > than every natural. > > So, let's not get distracted by paths and whatsits. Just do what you > said you could do: show that ZF proves a contradiction. Either show > me that there is a natural k such that > >  U_n {1,...,n}  = k > > or show me that there is an element k in U_n {1,...,n} such that k is > larger than every natural number. > > But don't distract us from the topic at hand. >
I love logical "theological" debate from you. Anyway, it's no use excommunicating WM, right? Better face the "heretics" headon with logic!
David Bernier
 dracut:/# lvm vgcfgrestore File descriptor 9 (/.console_lock) leaked on lvm invocation. Parent PID 993: sh Please specify a *single* volume group to restore.

