
Re: ZFC and God
Posted:
Jan 23, 2013 11:02 AM


On 23 Jan., 14:36, "Jesse F. Hughes" <je...@phiwumbda.org> wrote: > WM <mueck...@rz.fhaugsburg.de> writes:
> > I know. But if you have 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.
You are in error. Pause for a while and think it over. > > 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.
You are right, mathematicians prefer (1). But matheologians use (2). An infinite set contains a number of elements, at least aleph_0, which is greater than every finite number. > > 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.
You confuse the things. ZF claimes that the *number of elements* is larger than every finite number. Just this causes the contradiction. A union of finite initial segments cannot have a number of elements that is larger than every finite number.
Regards, WM

