[FOM] Is anyone on this list an expert on Conjoint Measure a la Luce?

[Michael Lamport Commons]

Is anyone on this list an expert on Conjoint Measure a la Luce?

My Best,

Michael Lamport Commons, Ph.D.
Assistant Clinical Professor of Psychiatry

Program in Psychiatry and the Law
Department of Psychiatry
Harvard Medical School
Massachusetts Mental Health Center
74 Fenwood Road
Boston, MA 02115-6113

Telephone (617) 497-5270
Facsimile    (617) 491-5270

Commons at tiac.net
http://www.tiac.net/~commons/
----- Original Message -----
From: <Everdell at aol.com>
To: <fom at cs.nyu.edu>
Sent: Saturday, April 12, 2003 9:44 PM
Subject: [FOM] Re: Papers of Poincare (Bill Everdell)


>
> In a message dated 4/11/03, Colin McLarty writes on Poincaré:
>
> << Many logicians since have claimed he implicitly posed limitations - or
> that he should have posed limitations. But the limitations are not to be
> found in his math or his philosophy. He even wrote one philosophic paper,
a
> month before he died, saying that some mathematicians reject the
> well-ordering theorem as non-constructive. But he explicitly claimed to
> understand the issue better than those mathematicians do. He says the
> constructivists (or, in his words, pragmatists) and the Cantorians both
only
> understand one side of the argument, while he understands both sides.
(This
> is the 1912 "logique d l'infini" translated in MATHEMATICS AND SCIENCE
under
> the title "Mathematics and logic".) >>
>
> I'm trying to get these references straighter.  In 1909 (not 1912)
Poincaré
> published "La logique de l’infini" in _Revue de métaphysique et de morale_
> (1909).  This I have read as it was reprinted in Poincaré's posthumous
> _Dernières Pensées_, and always thought had appeared as "The Logic of
> Infinity" in the translated book, _Mathematics and Science, Last Essays_
(NY:
> Dover, 1963).  This is the one to which Russell replied in 1910, and
contains
> the quotation given by Lucas Wiman:
> "Knowledge of the genus does not result in your knowing all its members;
it
> merely provides you with the possibility of constructing them all, or
rather
> constructing as many of them as you may wish.  They will exist only after
> they have been constructed; that is, after they have been defined; X
exists
> only by virtue of its definition." (Mathematics and Science: Last Essays;
> quoted in Chihara, Ontology and the vicious-circle principle, quoted by
Lucas
> Wiman, [FOM], 9Apr03).
>
> In the same year of 1909, Poincaré published "Über Transfinite Zahlen" in
> Acta Mathematica (1909) later reprinted in his Oeuvres, Paris:
> Gauthier-Villars, v11, pp120-124.  In this article he viewed transfinites
as
> an aberration.
>
> None of these, I suppose, is the 1912 "logique de l'infini" cited above by
> McLarty.  Or have I missed something?
>
> Peter Galison has a book on Poincaré in the offing, which should be as
fresh
> as Lucas Wiman might want, but I gather it does not say much about
> mathematical foundations.
>
> -William R. Everdell, St. Ann's School, Brooklyn, NY, USA
>
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