From: zeleny@husc9.harvard.edu (Michael Zeleny)
Newsgroups: sci.math
Subject: Re: Topos theory for mere mortals (?)
Date: 29 Sep 92 06:02:50 GMT
Article-I.D.: husc3.1992Sep29.020251.15930
Organization: The Phallogocentric Cabal

In article <1a793rINNsgu@usenet.INS.CWRU.Edu> 
cxm7@po.CWRU.Edu (Colin Mclarty) writes:

>In a previous article, zeleny@husc9.harvard.edu (Michael Zeleny) says:

>>In article <19qoafINNiqf@usenet.INS.CWRU.Edu> 
>>cxm7@po.CWRU.Edu (Colin Mclarty) writes:

CML:
>>>	There is a difference though for Platonists.  Set theoretic
>>>realists generally think there is some one universe of all sets, AC 
>>>is true in it or is not, and that universe is really the only place 
>>>to work.  So the question of what to "postulate" may be hard but
>>>it has some right answer--they are not "postulates" at all in the
>>>sense of "postulate theorists" like Huntingdon (of the many 
>>>axiomatizations of Boolean algebra).  Zeleny has made this point 
>>>well in another context.  Category theorists, even if realists, tend 
>>>to think it is worth working in all kinds of various ambient 
>>>categories for various purposes.  So that you always do need to say 
>>>what you postulate about your present ambient.

MZ:
>>I have hesitated for a long time before following up on this claim,
>>especially since I don't recollect too well just what point it is that I
>>made in another context.  However, I wish to go on record as stating that,
>>though it probably is a sociological fact that most realists who bother
>>thinking about it, think that there is exactly one universe of all sets,
>>and that, conversely, some people have gone on record announcing their
>>conversion to formalism on the grounds of their loss of belief in the
>>unique existence of such a universe, I do not myself believe that a realist
>>philosophy of mathematics cannot accomodate a multiplicity of set-theoretic
>>(or type-theoretic) universes possessed of different size and structural
>>properties.  There is, after all, no good reason to suppose that everything
>>in the mathematical universe is a set, or equivalently, that the
>>development of a particular set theory is bound to yield privileged
>>insights into the nature of all mathematical objects.  So your contrast
>>between set theory and category theory may be right, but only for
>>accidental reasons.
>>
>>cordially,
>>mikhail zeleny@husc.harvard.edu
>>"Un de mes plus grands plaisirs est de jurer Dieu quand je bande."

CML:
>	Yes, I think it is just a sociological remark.  To me, the
>point is that a set theorist could be quite realist but also believe
>the term "set" is more or less ambiguous, so that various alternative
>"universes of all sets" really exist depending on which sense you mean.

Soit.

CML:
>	The remark I refer to was the very nice point that axiomatization
>and proof theoretic strength are mere technicalities to a realist, and
>what matters is to know the truths about a subject.

I am glad somebody appreciated it.

>Colin McLarty
>"Un de mes voeux les plus sincere est de voir disparaitre ce sig qui
>ne fait signe que de trop de catolicisme en guise de sacrilege"

Bah, mon vieux, veuille te plaindre du divin marquis, car c'est lui qui
montre son catholicisme en guise de sacrilege; quant `a moi, je ne suis
qu'un transmetteur de ses sentiments pieux et galants.  Cependant je ne
saurai desobeir `a cet ordre imperatif qu'est pour moi ton voeu sincere.

cordially,
mikhail zeleny@husc.harvard.edu
"Nous donnons la mort, nous saurons la subir."