NetNews Usenet Archive 1992 #27/NN_1992_27.iso/spool/soc/culture/jewish/20360

Internet Message Format | 1992-11-18 | 3.9 KB

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From: [e-mail] (Randall Holmes)
Subject: Re: Belief and Logic (was re: Belief and science (Einstein))
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Organization: Boise State University
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Date: Wed, 18 Nov 1992 17:40:38 GMT
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In article <[e-mail]> [e-mail] (Michael Zeleny) writes:
>In article <[e-mail]>
>[e-mail] (Randall Holmes) writes:
>
>>In article <[e-mail]>
>>[e-mail] (Herman Rubin) writes:
>
>>>In article <[e-mail]>
>>>[e-mail] (Randall Holmes) writes:
>
>RH:
>>>>It is mathematically provable that the class of all true sentences in
>>>>a reasonable language is impossible to define in that language
>>>>(Tarski's Paradox).  In order to avoid this phenomenon, one has to
>>>>make the expressive capabilities of one's language _weaker_ (making
>>>>the language more expressive does not help!).  In particular, it can
>>>>be applied to ideas in the mind of God, as follows:
>
>HR:
>>>This is the case if the language has only proofs of finite length.  Since
>>>we do not know how to do infinitary operations, although we can handle
>>>some of them, we cannot be sure of what God can or cannot do.
>
>RH:
>>The argument works just as well with infinitary syntax, as long as the
>>lanaguage used is powerful enough to describe its own syntax (which
>>certainly seems likely in the Divine case).
>
>Herman is absolutely right in the literal Cantorian sense.  Genuine
>infinitary syntax, as distinguished from merely transfinite Tarskian
>languages, is _a priori_ ineffable.

I was referring to the latter.  If God uses Absolute Infinite syntax,
then even He cannot understand the overall structure of His own
thought.


  (Would Randall agree that, at
>least in the present theological context, Cantorian set theory is
>inherently superior to the godless NF variants?)

NFU is better for theology; it allows one to distinguish between God
(the Absolute Infinite, still present in NFU, but a little harder to
find) and the created Universe, the oneness of which many theologians
have also maintained.  This distinction is impossible to draw in
Cantorian set theory.


  Note that there
>exists a very respectable diagonal argument to the effect that the
>syntax of natural languages falls in the former category.  (See _The
>Vastness of Natural Languages_ by Langendoen and Postal.)  Perhaps
>that is the reason why the notion of natural language proof has
>managed to resist all analytic efforts for two and a half millenia.

I do not find this argument convincing; natural languages are finitary.

>
>>>--
>>>Herman Rubin, Dept. of Statistics, Purdue Univ., West Lafayette IN47907-1399
>>>Phone: [phone]
>>>[e-mail] (Internet, bitnet)
>>>{purdue,pur-ee}!snap.stat!hrubin(UUCP)
>
>>--
>>The opinions expressed        |     --Sincerely,
>>above are not the "official"    |     M. Randall Holmes
>>opinions of any person        |     Math. Dept., Boise State Univ.
>>or institution.            |     [e-mail]
>
>cordially,
>mikhail [e-mail]
>"Le cul des femmes est monotone comme l'esprit des hommes."


--
The opinions expressed        |     --Sincerely,
above are not the "official"    |     M. Randall Holmes
opinions of any person        |     Math. Dept., Boise State Univ.
or institution.            |     [e-mail]