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In article <Bzsrvt.167@umassd.edu> pmsc13sg@UMASSD.EDU writes:
>    Is there a relationship between sets and Plato's Forms?

Some people think so; that is why the popular term for mathematical
realists is "platonists".  Plato's Forms were ideal exemplars of
mundane objects; sets do not have this character (the set of all
natural numbers is not a perfect natural number).  There is a
relationship between sets and form with a small f (to avoid calling
the objects of mathematics "abstract", which I think is
epistemologically misleading, I call them formal objects), but they
are not Forms in Plato's sense.  Moreover, the use of mathematical
objects is quite different from that of Plato's Forms.


>================================================================================
>	"In that world, you'll be able to rise in the morning with the spirit
>you had known in your childhood: that spirit of eagerness, adventure and cer-
>tainty which comes from dealing with a rational universe."
>                                                              AYN RAND
>================================================================================
>Stephen Grossman <PMSC13SG@UMASS.EDU>
>================================================================================


-- 
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

In article <BzzHDI.2Bv@umassd.edu>
pmsc13sg@UMASSD.EDU (Stephen Grossman) writes:

>In article <1992Dec28.155555.21505@guinness.idbsu.edu>,
>holmes@opal.idbsu.edu (Randall Holmes) writes:

>>In article <Bzsrvt.167@umassd.edu> 
>>(Stephen Grossman) pmsc13sg@UMASSD.EDU writes:
SG:
>>>Is there a relationship between sets and Plato's Forms?

RH:
>>Plato's Forms were ideal exemplars of
>>mundane objects; sets do not have this character (the set of all
>>natural numbers is not a perfect natural number).  

SG:
>Perhaps I should have asked about Kantian, subjective forms. I am starting 
>"Plato, Kant and Aristotle in Math" by Glenn Marcus (2nd Renaissance Books,
>1991, audio) and should have some wisdom on math soon.

Indeed, you should.  Alas, you will not.

You will not have any "wisdom on math" for the same reason you will
not have any on "Kantian, subjective forms".  The reason is that your
hallowed sourses of holy Objectivism lie.  There are no such things as
subjective forms; moreover, Kantian philosophy is not concerned with
the question of forms, period.  End of this discourse.

SG:
>Marcus says scientists (excepting computer scientists w/info theory) use
>only pre-20th century math and quotes a leading mathematician on the 
>impracticality of math. Comments?

Sure thing, I will give you comments.  Modern mathematics is widely
used in physics, chemistry, and biology.  Consequently, Marcus is a
fraud or an ignoramus; most likely, he is both.  You, on the other
hand, are a tiresome, gullible fool.  It takes all kinds.

>================================================================================
>	"In that world, you'll be able to rise in the morning with the spirit
>you had known in your childhood: that spirit of eagerness, adventure and cer-
>tainty which comes from dealing with a rational universe."
>                                                              AYN RAND
>================================================================================
>Stephen Grossman <PMSC13SG@UMASS.EDU>
>================================================================================

cordially,
mikhail zeleny@husc.harvard.edu
"Le cul des femmes est monotone comme l'esprit des hommes."

In article <1992Dec28.194652.18875@husc3.harvard.edu>, zeleny@husc10.harvard.edu (Michael Zeleny) writes:
>In article <BzzHDI.2Bv@umassd.edu>
>pmsc13sg@UMASSD.EDU (Stephen Grossman) writes:
>
>>In article <1992Dec28.155555.21505@guinness.idbsu.edu>,
>>holmes@opal.idbsu.edu (Randall Holmes) writes:
>
>>>In article <Bzsrvt.167@umassd.edu> 
>>>(Stephen Grossman) pmsc13sg@UMASSD.EDU writes:
>SG:
>>>>Is there a relationship between sets and Plato's Forms?
>
>RH:
>>>Plato's Forms were ideal exemplars of
>>>mundane objects; sets do not have this character (the set of all
>>>natural numbers is not a perfect natural number).  
>
>SG:
>>Perhaps I should have asked about Kantian, subjective forms. I am starting 
>>"Plato, Kant and Aristotle in Math" by Glenn Marcus (2nd Renaissance Books,
>>1991, audio) and should have some wisdom on math soon.
>
>Indeed, you should.  Alas, you will not.
>
>You will not have any "wisdom on math" for the same reason you will
>not have any on "Kantian, subjective forms".  The reason is that your
>hallowed sourses of holy Objectivism lie.  There are no such things as
>subjective forms; moreover, Kantian philosophy is not concerned with
>the question of forms, period.  End of this discourse.

    SG         Zeleny has perfected the argumentum ad loudmouth. I sympathize 
with the burden of studying under Nozick but you should really make some sort 
effort at evidence. Perhaps, tho, in these postmodern times one should not
expect much beyond another drink. I feel unaccountably sad. "Its unnerved me
dreadfully." Barbara Stanwyck said that. I wonder what I should do. The lack of
subjective forms unnerves me dreadfully. Is there a hole in being as Sartre 
imagined? Would everything be drawn into the hole? Would creatures from the 
other side contact us? I, for one, take no small comfort in Parmenides' plenum.
There are surely subjective forms, most especially in Kant. Of course, study 
Kant thru the shattered glass of symbolic logic, elucidation, or whatever
postmodern style is regnant in the remnants (John Milton, move over) of the 
university, and all sort of odd corners come to hand. If you haven't yet dis-
covered subjective forms in Kant or anywhere else, who am i to throw cold water
on your lack of objectivity? The multicultural ethos will find no enemy here, 
bub. No, I think that your metaphysical confusion exists as much as Ayn
Rand's wisdom. To be rather academic let us note the rather large description
of non-noumnal items in _The Critique of Pure Wisdom_. If Zeleny would 
demonstrate the use of whatever he does when he "does" philosophy, why, I'm 
sure social solidarity would increase. Then again, you may be in obscene 
contact with noumenal reality. Why not? Look at Madonna. They discuss her in 
alt.postmodern. "My flock was lovely: lovelier I." Should you claim that your
philosophy(?) provides a new reading of the noumena, I, for one, won't be sur-
prised. I knew you had it in you, Mikey. And, God love ya, you didn't dis-
appoint. I feel I'm in bad taste. I've unleashed my wisdom (or my wit, anyway)
in an inappropriate context. Like sledgehammers and flies. Yccchh! A gentleman
would never indulge himself. I'm not really educated. I just know philosophy.
>SG:
>>Marcus says scientists (excepting computer scientists w/info theory) use
>>only pre-20th century math and quotes a leading mathematician on the 
>>impracticality of math. Comments?
>
>Sure thing, I will give you comments.  Modern mathematics is widely
>used in physics, chemistry, and biology.  Consequently, Marcus is a
>fraud or an ignoramus; most likely, he is both.  You, on the other
>hand, are a tiresome, gullible fool.  It takes all kinds.

    This perfect example of the argumentum ad snobbum is an object lesson         
for the wary. Always provide evidence before your interlocutor does. It saves
one from embarrassing gaffes. In this regard we might consider leading
mathematician Hardy's claim that math is useless. After my ongoing study of
the Objectivist philosophy of math is complete I shall inform the hoi polloi.

    I really don't talk this way. The guys in the bar would look at me funny
and some big jerk would probably stick his face in mine and scream some 
childishly humorous remark. I'd spot the pointed ashtray, and in the spirit
of philosophy, wonder about its effect on his throat. Well, he sat down and I 
went back to my _New York Times and St. Pauli Girl (and torritos and salsa
sauce. Hey look, guys, it's Mikey! Mikey, how th' hell are ya. Ya want a beer?
================================================================================
	"In that world, you'll be able to rise in the morning with the spirit
you had known in your childhood: that spirit of eagerness, adventure and cer-
tainty which comes from dealing with a rational universe."
                                                              AYN RAND
================================================================================
Stephen Grossman <PMSC13SG@UMASS.EDU>
================================================================================

>From: pmsc13sg@UMASSD.EDU (Stephen Grossman)

>    SG         Zeleny has perfected the argumentum ad loudmouth.

Why, yes, he has, actually! I was going to commend him for that myself,
but he has been too modest to accept my commendations in the past.

I wonder if Grossman actually knows what "ad" means, or if he
only *mistakenly* called himself a loudmouth?

>I sympathize
>with the burden of studying under Nozick but you should really make some sort
>effort at evidence.

I suspect Zeleny will prefer not to answer, but I would personally
be quite amazed if he has in fact studied under Nozick. It would
rock my worldview.

> No, I think that your metaphysical confusion exists as much as Ayn
>Rand's wisdom.

Again, I must concur with Grossman's assessment.

>To be rather academic let us note the rather large description
>of non-noumnal items in _The Critique of Pure Wisdom_.

Oh, let's not. I had enough trouble with the other three Critiques.

>mathematician Hardy's claim that math is useless. After my ongoing study of
>the Objectivist philosophy of math is complete I shall inform the hoi polloi.

We polloi are holding our breath.
("The hoi polloi" is redundant.)

Jamie

In article <BzzHDI.2Bv@umassd.edu> pmsc13sg@UMASSD.EDU writes:
>In article <1992Dec28.155555.21505@guinness.idbsu.edu>, holmes@opal.idbsu.edu 
>(Randall Holmes) writes:
>>In article <Bzsrvt.167@umassd.edu> pmsc13sg@UMASSD.EDU writes:
>>>    Is there a relationship between sets and Plato's Forms?
>
>Plato's Forms were ideal exemplars of
>>mundane objects; sets do not have this character (the set of all
>>natural numbers is not a perfect natural number).  
>
>    Perhaps I should have asked about Kantian, subjective forms.

Do you actually read other people's postings, or do you just look for
key words and consult Rand to find out what we are supposed to be
saying?  You should know very well that I do not consider formal
objects to be subjective in any way, shape or form.

 I am starting 
>"Plato, Kant and Aristotle in Math" by Glenn Marcus (2nd Renaissance Books,
>1991, audio) and should have some wisdom on math soon.

You won't get wisdom on math by reading any of those gentlemen.  Try
Bertrand Russell (OK, Mikhail, I won't ennoble him anachronistically).
I'd agree with you about his politics, but he's good on math _and_ a
good writer.  There are other people to read, of course.

>    Marcus says scientists (excepting computer scientists w/info theory) use
>only pre-20th century math and quotes a leading mathematician on the 
>impracticality of math. Comments?

This is not true for scientists in general, and the computer
scientists in particular are using a lot more 20th century math than
information theory; the theory of types, for example, is applied in
CS.


>================================================================================
>	"In that world, you'll be able to rise in the morning with the spirit
>you had known in your childhood: that spirit of eagerness, adventure and cer-
>tainty which comes from dealing with a rational universe."

Since the universe (as opposed to its loal inhabitants) is already
rational, you should already be able to do this, no?  (At least, if
you have a strong stomach).

>                                                              AYN RAND
>================================================================================
>Stephen Grossman <PMSC13SG@UMASS.EDU>
>================================================================================


-- 
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

In article <1hsep4INN266@cat.cis.Brown.EDU>, PL436000@brownvm.brown.edu (Jamie) writes:
>>From: pmsc13sg@UMASSD.EDU (Stephen Grossman)
> 
>>    SG         Zeleny has perfected the argumentum ad loudmouth.
> 
> Why, yes, he has, actually! I was going to commend him for that myself,
> but he has been too modest to accept my commendations in the past.
> 
> I wonder if Grossman actually knows what "ad" means, or if he
> only *mistakenly* called himself a loudmouth?

Apparently you don't know what it means either, unless you're
kidding...<:-)

-Ken
-- 
miner@kuhub.cc.ukans.edu | Graecis ac barbaris, sapientibus et
opinions are my own      | insipientibus debitor sum