From: hporopudas@tnclus.tele.nokia.fi
Subject: Re: Proof of God's Existence
Followup-To: sci.math
Organization: Nokia Telecommunications.
Date: Wed, 2 Sep 1992 13:58:39 GMT


In article <pmanne-010992093107@ma-mac29.uio.no.>, pmanne@math.uio.no
(Per Manne) writes:
> In article <17ui6kINNsft@matt.ksu.ksu.edu>, bubai@matt.ksu.ksu.edu
> (P.Chatterjee) wrote:
>>
>> 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.
>
> The following proof is found in Seven Years of Manifold (1968-1980),
> edited by Ian Stewart and John Jaworski.
>
> THEOREM (due to Anselm, Aquinas, and others.)
> The Axiom of Choice is equivalent to the existence of a unique God.
>
> PROOF:
> =>   (Assuming the equivalence of the Axiom of Choice and Zorn's Lemma.)
> Partially order the set of subsets of the set of all properties of
> objects by inclusion. This set has maximal elements. God is by
> definition (according to Anselm) one of these maximal elements. Now
>
>     God  c  God u {existence}        [c - subset,  u - union]
>
> hence God = God u {existence}. Therefore God exists.
>   To prove uniqueness, let God and God' be two gods. Then
>
>     God u God'  c  God
>
> (according to Aquinas), therefore God' c God. Similarly God c God'.
> Hence God = God'.
>
> <=   Given a set {A_i : i \in I} of sets, let the unique God pick
> x_i \in A_i for each i \in I. (He can do so by omnipotence, proved as for
> existence above.) Then [in TeX notation, or it will look too awkward!]
>
>     (x_i)_{i\in I}  \in  \prod_{i\in I} A_i
>
> as required. QED


   What this really proves. ?

 If we make a substitution God = "existence", we get (modified from above):

  ------------------------------------------------------------------------
>  THEOREM (due to Anselm, Aquinas, and others.)
>  The Axiom of Choice is equivalent to the existence of a unique existence.
>
>  PROOF:
>  =    (Assuming the equivalence of the Axiom of Choice and Zorn's Lemma.)
>  Partially order the set of subsets of the set of all properties of
>  objects by inclusion. This set has maximal elements. Existence is by
>  definition (according to Anselm) one of these maximal elements. Now
>
>      existence  c  existence u {existence}        [c - subset,  u - union]
>
>  hence existence = existence u {existence}. Therefore existence exists.
>    To prove uniqueness, let existence and existence' be two existences. Then
>
>      existence u existence'  c  existence
>
>  (according to Aquinas), therefore existence' c existence. Similarly
>  existence c existence'. Hence existence = existence'.
>
>  <=   Given a set {A_i : i \in I} of sets, let the unique existence pick
>  x_i \in A_i for each i \in I. (He can do so by omnipotence, proved as for
>  existence above.) Then [in TeX notation, or it will look too awkward!]
>
>      (x_i)_{i\in I}  \in  \prod_{i\in I} A_i
>
>  as required. QED
  -------------------------------------------------------------------------

 I think that this does not prove anything.

 Also the following (modified):

  ------------------------------------------------------------------------
>  objects by inclusion. This set has maximal elements. Existence is by
>  definition (according to Anselm) one of these maximal elements. Now
  ------------------------------------------------------------------------

 is questionable, because it is not sure that existence can be uniquely
 characterized as being one "maximal element".

 Although this proof above seems to be unbelievable and I first thought that
 God's existence is an axiom, maybe I was wrong in the latter, maybe it is
 really possible to prove mathematically that God exists.

            Hannu.