On-line papers
Here is the directory containing my papers listed
below together with their plain TeX source files.
Review of 18 Unconventional Essays on the Nature of Mathematics
A review of the book edited by Reuben Hersh,
which appeared in the November 2007 issue of the
American Mathematical Monthly.
Hilbert's Mistake
Here are the slides for a talk given at
the Second New York Graduate Student Logic Conference,
March 18, 2007.
L'infinito nell'aritmetica
A portion of a talk,
in pdf format with links, given in Italian at the
Rimini Meeting 2006.
The mystery of stochastic mechanics
These are notes, in a large font for
transparencies, of a talk pointing out two defects in stochastic
mechanics.
The mystery is how a theory with such a natural and appealing derivation
can be so right and yet so wrong. I do not understand this.
For more on stochastic mechanics, see Quantum Fluctuations
and the references therein; also Dynamical Theories of Brownian Motion.
Infinity
A talk, Completed versus Incomplete Infinity
in Arithmetic, addressed to non-mathematicians, for the conference
on
Infinity in Science, Philosophy, and Theology, Pontifical Lateran
University, Vatican City, November 9-11, 2005 -- also in
Italian.
Book Review
A review of Dennis Hesseling's
"Gnomes in the Fog: The Reception of Brouwer's Intuitionism
in the 1920s", to appear in the Bulletin of the American
Mathematical Society.
Syntax and Semantics
This is a paper that I will give at the
International Symposium "Foundations and the Ontological
Quest" to be held at the Pontifical Lateran University in Rome,
January 7--10. An almost identical talk was given at the
international conference
Il problema
dei fondamenti oggi held in Mendrisio, Switzerland, on
November 16, 2001.
Mathematics and Faith
I was asked to give a
paper
(or pdf format)
on this topic at the
Jubilee for Men and Women from the World of Learning,
held at the Vatican, 23-24 May 2000.
Mathematics and the Mind
Text of a talk
(or pdf format)
at the Tokyo conference
Toward a Science of Consciousness -- Fundamental Approaches,
Tokyo, May 25-28, 1999.
Understanding Intuitionism
This is a paper
(or pdf format)
presented at the
Rencontre du
Reseau Georges Reeb, March 24-28, 1997.
Debate
In November 1995, Ennio De Giorgi and I gave lectures at
the University of Rome "La Sapienza" and then debated the foundations
of mathematics in Forlì. Here are the revised texts
of my lecture Confessions of an apostate mathematician,
in English
(or pdf format)
and Italian
(or pdf format)
(with many thanks to
Professor Gianfranco Basti for correcting the Italian).
IST
A paper published in 1977: Internal set theory.
Ezekiel's Wheel
This is a poem I wrote many years ago for Nancy Wong Nelson (1930-1988).
ps or html.
Ramified recursion and intuitionism
Presented to the Colloque Trajectorien,
Strasbourg/Obernai, June 12-16, 1995.
It is an
introduction to recent work of Bellantoni, Cook, and Leivant on
ramified recursion with some remarks on a possible logic of the
feasible. This paper
(or pdf format)
is
thinking out loud, not a finished work.
Space-Time-Chance
A non-technical talk on Space-Time-Chance.
To my home page.