From: holmes@opal.idbsu.edu (Randall Holmes)
Subject: Re: Proof of God's Existence
Organization: Boise State University Math Dept.
Date: Mon, 7 Sep 1992 06:15:26 GMT

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 can expand on this.

Proposition:  God is the attribute of existence.

Proposition: An attribute can be identified with the class which is
its extension.

Lemma:  God is the universal class (or set).

Proof of Lemma:  Apply the two propositions.

Theorem 1:  The non-existence of God is consistent with accepted
principles of mathematical reasoning.

Proof of Theorem 1:  The non-existence of the universal set (i.e.,
God) is a theorem of ZFC (Thomas Jech, _Set Theory_, p. 2).

Theorem 2:  The existence of God is consistent with accepted
principles of mathematical reasoning.

Proof of Theorem 2: The existence of God (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 God 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 God 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
Newsgroups: sci.math