Date: Jan 23, 2013 11:51 AM
Author: David Bernier
Subject: Re: ZFC and God

On 01/23/2013 08:36 AM, Jesse F. Hughes wrote:
> WM<mueckenh@rz.fh-augsburg.de> writes:
>

>> On 23 Jan., 12:47, "Jesse F. Hughes"<je...@phiwumbda.org> wrote:
>>> WM<mueck...@rz.fh-augsburg.de> writes:
>>>> On 22 Jan., 21:18, "Jesse F. Hughes"<je...@phiwumbda.org> wrote:
>>>>> WM<mueck...@rz.fh-augsburg.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/how-to-distinguish-bet...
>>>
>>> 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 web-published 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
ex-communicating WM, right? Better face the "heretics" head-on
with logic!

David Bernier

--
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File descriptor 9 (/.console_lock) leaked on lvm invocation. Parent PID
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Please specify a *single* volume group to restore.