[FOM] Questions on Cantor

[Director CPFS]

The last remark puzzles me. The EPR paradox is, to borrow W.V.O. Quine's
term 'veridical', or as Roger Penrose puts it, merely a puzzle. More
mantled, I'd say than 'dismantled'.

_____________________________________ 

Professor Ranjit
Nair 
Director 
Centre for Philosophy & Foundations of
Science 
P.B. No. 4017,  Malaviya Nagar P.O. 
New Delhi 110017 
India


Tel. +91 11 65951738 / 46170795
Cell 9810332846 (Delhi)


e-mail: director at cpfs.res.in 
director.cpfs at gmail.com
president at wias.in

URL
http://www.cpfs.res.in/ 
http://goidirectory.nic.in/ministries_categories.php?ct=39#groupE060

________________________________________________ 
From:Frode
Bjørdal <frode.bjordal at ifikk.uio.no> 
To:pratt at cs.stanford.edu (more)

Date:Mon, January 28, 2013 6:52 am 
Subject:Re: [FOM] Questions
on Cantor 



Thank you for usefully hinting to the fact that Cantor held
well ordering to be a fundamental principle, Vaughan. 


But it is a result of Bernays that Foundation, or the Axiom of
Regularity, is independent of the other axioms of ZFC. So it is unclear to
me what you mean by "passage", or what connection it is that
that you think is easy to see in hindsight. (Is there something in
Mirimanoff's text that resolves this? Not that I noticed from reading
it.)


Also, it seems to me that Russell's and Poincare's full vicious
circle principles which founded the predicativist program should be
mentioned as more full fledged forerunners to foundation.


By the way, it took many years for the EPR paradox to be dismantled
in physics.


Frode



2013/1/27 Vaughan Pratt pratt at cs.stanford.edu>
As far as I'm aware the passage
from well-ordered sets to well-founded sets was first made by Dmitry
Mirimanoff in 1917, see
http://retro.seals.ch/digbib/view?rid=ensmat-001:1917:19::170&id=hitlist&id2=&id3=

In hindsight this is an easy connection to see, but before
Mirimanoff it seems highly unlikely that anyone saw it.  In 1904
Koenig presented an argument that some sets could not be well-ordered,
which within a day or so was shown to be unsound (the same fate that
befell the Einstein-Podolsky-Rosen paradox a third of a century later).
 Koenig continued to write about well-ordered sets in his 1914 book,
which Mirimanoff acknowledges and then says "Je donnerai dans un
autre travail les raisons qui m'ont determine a ne pas rattacher cette
etude a la theorie de J. Konig."

By this sentence I
understand that Mirimanoff is claiming priority for the adaptation of
well-ordering in general to well-founded sets in particular.

Since this is decades after Cantor had contributed anything further of
significance to set theory, it seems safe to infer from Mirimanoff's
priority claim that Cantor had never given any thought whatsoever to the
concept of a well-founded set, since otherwise people would have noticed
long before Mirimanoff.

The closest thing before well-founded
sets would seem to be Russell's idea of a set that does not belong to
itself, "un ensemble de premiere sorte" in Mirimanoff's
preamble.

Vaughan Pratt

On 1/26/2013 3:32 AM, Frode
Bjørdal wrote:
I have
not studied Cantor's texts, but from what I recall I have heard
and
seen conflicting accounts as to how and whether he implicitly
presupposed a well-founded notion of sets. Could some please

(1) give textual evidence for him assuming i) well-foundedness, ii)
non-wellfoundedness and (perhaps) iii) full naivety,

and

(2) confirm textually that he presupposed extensionality?


Best regards from

Frode

*********************************************************


Frode Bjørdal
Professor i filosofi
IFIKK,
Universitetet i Oslo
www.hf.uio.no/ifikk/personer/vit/fbjordal/index.html
 http://www.hf.uio.no/ifikk/personer/vit/fbjordal/index.html>

Questions on C


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  Frode Bjørdal Professor i filosofi IFIKK, Universitetet i
Oslo www.hf.uio.no/ifikk/personer/vit/fbjordal/index.html







_____________________________________ 

Professor Ranjit Nair

Director 
Centre for Philosophy & Foundations of
Science 
P.B. No. 4017, Malaviya Nagar P.O. 
New
Delhi 110017 
India 

    Tel. +91 11
65951738 / 46170795
Cell 9810332846 (Delhi) 

e-mail: director at cpfs.res.in  
director.cpfs at gmail.com
president at wias.in

URL
http://www.cpfs.res.in/ 
http://goidirectory.nic.in/ministries_categories.php?ct=39#groupE060 

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