🚀 go-pugleaf

In article <1992Nov23.150539.14871@news.unige.ch> swann@divsun.unige.ch (SWANN Philip) writes:
>In article <1992Nov20.201258.17652@husc3.harvard.edu>, zeleny@husc10.harvard.edu (Michael Zeleny) writes:
>
>
>> 
>> Great.  Instead of promulgating my doctrinaire image, perhaps I can
>> ask you to elucidate your [censored] comments.  In what sense, and by
>> what kind of argument has the Whitehead and Russell (note the correct
>> order) claim that mathematics is reducible to logic been proved false?
>> What is its relation to the formalist program, and what is the
>> connection between the latter and Montague's proposal?
>
>As far as I know, the paradoxes in set theory and Goedel's work are generally
>accepted as showing that mathematics cannot be derived from logic

This is usually accepted, although it depends on exactly what you mean
by "logic".  If what is called "higher order logic" is logic, then
logicism succeeds, because higher-order logic is equivalent to the
theory of types, which is adequate for all practical mathematical
purposes.

 and
>set theory

This is ridiculous.  Mathematics is generally considered to be
derivable from set theory (ZFC) and most of the derivation is in
place.  The derivation of math from set theory (not logic) has
succeeded.



 - thus killing Hilbert's formalist programme.

_Non sequitur_.  Hilbert was not a logicist; he was a formalist.  The
collapse of Hilbert's program has nothing to do with success or
failure of the logicist claim.  The derivation of mathematics from set
theory (which has succeeded) is also irrelevant to Hilbert's program;
it has succeeded, not failed, but its methods are too strong to be
relevant to Hilbert's program. 

 It would appear
>that *formal* logic and set theory are actually simply just bits of
>mathematics with no special status. (I write this as a complete
amateur).

So I will forgive you.

>Why do you think that what won't work for math will work for natural language
>(which you believe to be just another formal language)?


>
>
>Philip Swann


-- 
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