FOM: list of papers/books
friedman at math.ohio-state.edu
Thu Oct 1 21:53:31 EDT 1998
I would like to make a start at compiling the list I called for in my
5:24PM 10/1/98 posting:
***I would like to make a list of books and papers (and perhaps other forms of
publication) that are of this type - with the help of the fom. I have a
short list I will share with you later, but I would like to see postings on
the fom mentioning such books and papers. I.e.,
***where there at least appears to be a claim of or the strong suggestion of
the insignificance of at least some substantial work done in mainline f.o.m.***
Here are some general categories to look for:
1. Writings by mathematicians who got interested in f.o.m. and/or p.o.m.
Possibly Hersh, etc.
2. Writings by mathematicians who remain disinterested in f.o.m. and/or
p.o.m. Possibly Bourbaki, etc.
3. Writings by mathematical logicians who remain disinterested in f.o.m.
and/or p.o.m. Possibly MacIntyre, Sacks, etc.
4. Writings by mathematical logicians who got interested in f.o.m. and/or
5. Writings by specialists in f.o.m. Possibly Feferman, etc.
6. Writings by philosophers who got interested in f.o.m. and/or p.o.m.
Possibly Wittgenstein, etc.
NOTE: Some of this crticism may be productive, or even fully justified!!
Productive criticism is a contribution of the highest order. But I want to
see these things examined, discussed, and dissected on the fom list.
Here is a start of such a list:
Angus Macintyre, The strength of weak systems, in: Schriftenreihe der
Wittgenstein-Gesellschaft, 13 logic, Philosophy of Science and
Epistemology, Wien 1987, 43-59.
Angus Macintyre (with Georg Kreisel), Constructive logic versus
algebraization I, L.E.J. Brouwer Cent. Symp., Troelstra, eta al, eds.,
North-Holland, 1982, 217-260.
[Also, perhaps a contribution by Macintyre in the upcoming Sicily meeting
volume. Is it out yet?]
Keith Devlin, Goodbye, Descartes: The End of Logic and the Search for a New
Cosmology of the Mind, 1998.
Keith Devlin, Life by the Numbers (Preface) 1998.
Keith Devlin, Logic and Information Vol 1, 1991.
Keith Devlin, Mathematics: The New Golden Age, 1991.
Keith Devlin, Mathematics: The Science of Patterns : The Search
for Order in Life, Mind and the Universe (Scientific American Paperback
Keith Devlin, All the Math That's Fit to Print: Articles from the
Manchester Guardian (Spectrum Series) 1994.
Keith Devlin, The Joy of Sets: Fundamentals of Contemporary
Set Theory (Undergraduate Texts in Mathematics) 1993.
Keith Devlin (with Duska Rosenberg), Language at Work : Analyzing Communication
Breakdown in the Workplace to Inform Systems Design (Csli Lecture Notes No.
Keith Devlin, Language of Mathematics: Making the Invisible Visible, 1998.
Keith Devlin (with Eric Stockdale), Sentencing (Criminal Law Library, No
Keith Devlin et al, Calculus: An Electronic Companion, 1998.
Keith Devlin, Sentencing offenders in magistrates' courts.
[I have no idea which of these books by Devlin other than the first one
fits the criteria in question. What do the fom subscribers think?]
Solomon Feferman, Godel's program for new axioms: Why, where, how and
what?, in Godel 96, Lecture Notes in Logic 6 (1996), 3-22.
Solomon Feferman, Does mathematics need new axioms?, to appear in The
American Mathematical Monthly.
Gerald Sacks, Remarks against foundations, Historia Mathematica, 1975, 523-528.
Mathias (on the fom) should help us with a comprehensive list of
publications by Bourbaki that meet the criteria.
Juliet Floyd, ?? Has written a number of papers about Wittgenstein vs.
Godel. Should be able to provide list of relevant writings.
Burton Dreben, ?? Has very strong known views on Wittgenstien vs. Godel,
and has influenced others.
Rohit Parikh, ?? Has expressed strong views about Wittgenstein vs. Godel.
Juliet Floyd (on the fom) should help us with a comprehensive list of
publications by these scholars that meet the criteria.
Jon Barwise, ??
I'll ask Barwise what he has written that meets this criteria.
Reuben Hersh, What is mathematics, really?
Hersh (on the fom) should help us with a comprehensive list of publications
of his (and colleagues) that meet this criteria.
Georg Kreisel, Kurt Godel 1906-1978, Biographical memoirs of the Royal
Society, 26, 1980.
Georg Kreisel, On the kind of data needed for a theory of proofs, in Logic
Colloq., 76, R. Gandy, M. Hyland, eds., North-Holland, 1977, 111-128.
Georg Kreisel, Review of L.E.J. Brouwer, Collected Wrokds, Vol. I, A
Heyting, ed.: Bull. Amer. Math. Soc., 83 (1977), 86-93.
Georg Kreisel, Frege's foundations and intuitionistic logic, Monist, 67
Georg Kreisel, Proof theory: some personal recollections; Appendix, Proof
Theory, by G. Takeuti, 2nd ed,. North-Holland, 1987, 395-405.
Georg Kreisel, Logical aspects of computation: contributions and
distractions, Logic & Computer Science, Odifreddi, ed., Acad. Press, 1990,
Georg Kreisel, Review of Troelstra and van Dalen, Bull. London. Math. Soc.,
22 (1990), 505-511.
Georg Kreisel, On the idea(l) of logical closure, Ann. Pure and Applied
Logic, 56 (1992), 19-41.
Georg Kreisel (with A. Macintyre), Constructive logic versus algebraization
I, L.E.J. Brouwer Cent. Symp., Troelstra, eta al, eds., North-Holland,
Georg Kreisel, Finiteness theorems in arithmetic: an application of
Herbrand's theorem for sigma-2 formulas, in Proceedings of the Herbrand
Symposium, North-Holland, Amsterdam, 1982, 39-55.
Georg Kerisel, Godel's excursions into intuitionistic logic, in P.
Weingartner and L. Schmetterer, eds., Godel Remembered, Bibliopolis,
Naples, 1987, 65-186.
Georg Kreisel, Proof theory and the synthesis of programs: potential and
limitations, Springer Lecture Notes in Computer Science, 203 (1985),
Georg Kreisel, Bertrand Arthur William Russell, Earl Russell 1872-1970,
Bibliographical Memoirs of Fellows of The Royal Society, 19 (1973), 583-620.
Georg Kreisel, From foundations to science: justifying and unwinding
proofs, Recueil des travaux de l'Institut Mathemaique de Belgrade, 2
Georg Kreisel, Wittgenstien's lectures on the foundations of mathematics,
Cambridge 1939, Bulletin of the AMS, 84 (1978), 79-90.
Georg Kerisel, Review of Godel's Collected Works, Volume I, Notre Dame
Journal of Formal Logic, 29 (1988), 160-181.
Georg Kreisel, A notion of mechanistic theory, Synthese 29 (1974), 11-26.
Georg Kreisel, Church's Thesis and the ideal of informal rigour, Notre Dame
J. of Formal Logic, 28 (1987), 499-519.
Georg Kerisel, Review of Godel's Collected Works, Volume II, Notre Dame
Journal of Formal Logic, 31 (1990), 602-641.
Georg Kreisel, Review of Pour El and Richards, jahres. deutsch. Math.
Verein. 94 (1992), 53-55.
Georg Kreisel, Zur Bewertung mathematischer Definitionen, in E. Morscher,
O. Neumaier, and G. Zecha, (eds.), Essays in Scientific Philosophy
(dedicated to Paul Weingartner), Comes, Bad Reichenhall, 1981, 571-589.
Georg Kreisel, Zu Wittgensteins Sensibilitat, in W. Gombocz, H. Rutte, and
W. Sauer, (eds), Traditionen und Perspektiven der Analytischen Philosophie
Festschrift fur Rudolf Haller, Holder-Pichler-Tempsky, Wien, 1989, 203-223.
Georg Kreisel, Suitable descriptions for suitable categories, in G. Schurz,
and G. Dorn, (eds.): Advances in Scientific Philosophy, Essays in Honour of
Paul Weingartner on the Occasion of the 60th Anniversary of his Birthday,
Rodopi, Amsterdam-New York, 1991.
[I don't know which of Kreisel's articles meets the criteria, in addition
to the first.]
Lou van den Dries, various postings on the fom e-mail list.
Comments on any of the above papers/books, and suggestions of other
papers/books possibly meeting the criteria, would be most welcome.
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