From: hporopudas@tnclus.tele.nokia.fi
Subject: Re: Proof of God's Existence
Organization: Nokia Telecommunications.
Date: Mon, 7 Sep 1992 10:21:10 GMT


In article <1992Sep7.061526.21429@guinness.idbsu.edu>,
holmes@opal.idbsu.edu (Randall Holmes) writes:
> In article <1992Sep4.192528.21285@guinness.idbsu.edu>
holmes@opal.idbsu.edu (Randall Holmes) writes:
>>In article <1992Sep1.090011.1@tnclus.tele.nokia.fi>
hporopudas@tnclus.tele.nokia.fi writes:
>>>
>>>In article <17ui6kINNsft@matt.ksu.ksu.edu>, bubai@matt.ksu.ksu.edu
>>>(P.Chatterjee) writes:
>>>> I was told by somebody that there is a mathematical proof of God's existence;
>>>> was wondering if somebody could shed some light on the same.
>>>>
>>>> Thanks. Looking forward to the response.
>>>
>>>   I think that God's existence is an axiom. He says in the Holy Bible (Second
>>> book of Moses 3:14-15 in Old Testament and also in Johannes 8:28-29 in New
>>> Testament) that He is "Existence Himself".
>>>   If someone is arguing that "Existence Himself" does not exist, I think that
>>> at the same time he/she is arguing that he/she himself/herself does not exist.
>>>
>>>              Hannu.
>>
>>This reminds me of the student who responded to my (true) assertion
>>that we can prove in ZF that the universe does not exist (i.e., there
>>is no set containing everything) by asking why we were bothering with
>>the course (or anything) if there were a mathematical proof that
>>nothing exists.  It is not a prerequisite for the existence of
>>individual objects that the abstract object "existence" exist.
>>--
>>The opinions expressed		|     --Sincerely,
>>above are not the "official"	|     M. Randall Holmes
>>opinions of any person		|     Math. Dept., Boise State Univ.
>>or institution.			|     holmes@opal.idbsu.edu
>


  I think that correct form of first proposition is: "God is Existence".

  If we make the substitution God = "Existence", we get (modified):


> I can expand on this.
>
> Proposition:  Existence is the attribute of existence.
>
> Proposition: An attribute can be identified with the class which is
> its extension.
>
> Lemma:  Existence is the universal class (or set).
>
> Proof of Lemma:  Apply the two propositions.
>
> Theorem 1:  The non-existence of Existence is consistent with accepted
> principles of mathematical reasoning.
>
> Proof of Theorem 1:  The non-existence of the universal set (i.e.,
> Existence) is a theorem of ZFC (Thomas Jech, _Set Theory_, p. 2).
>
> Theorem 2:  The existence of Existence is consistent with accepted
> principles of mathematical reasoning.
>
> Proof of Theorem 2: The existence of Existence (the universal set) is an
> axiom of NFU ("New Foundations" with ur-elements) (it is the case
> "{x|x=x} exists" of the stratified comprehension scheme).  NFU is
> consistent if ZFC is consistent; this is a result of Jensen (in
> Synthese, vol.  19).
>
> Not only is the existence of Existence independent of accepted principles of
> mathematical reasoning, but the believer can model the universe of the
> atheist inside his own (bounded Zermelo set theory can be modelled in
> NFU + Infinity; stronger versions of NFU can model ZFC) and the
> atheist can model the universe of the believer (ZFC models NFU and
> strong extensions thereof).  Both ZFC and extensions of NFU are
> adequate set theories for all mathematical purposes.  It seems that
> the status of Existence resembles that of the Parallel Postulate or the
> Continuum Hypothesis.
>
> Since the working set theory of most mathematicians is ZFC or none at
> all, we must conclude that most mathematicians are atheists or
> agnostics in their official capacity.
>
> I hope that this is enlightening.
>

>
> --
> The opinions expressed		|     --Sincerely,
> above are not the "official"	|     M. Randall Holmes
> opinions of any person		|     Math. Dept., Boise State Univ.
> or institution.			|     holmes@opal.idbsu.edu


  What this stuff really was. ???  I think that some where inside of it was
  a statement which asserted that stuff's writer does not belong in the
  real world. ?

           Hannu.

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