1899-1930: FROM HILBERT TO BROUWER 
(PHIL 296)

SYLLABUS

Stanford University
Winter Quarter, 1997

 

 
INSTRUCTOR:              Aldo Antonelli, aldo@csli.stanford.edu;

MEETING TIMES: Tue, 2:15-4:05 in 60-62J (subject to rescheduling);

INSTRUCTOR'S OFFICE: Building 100, room 101L;

OFFICE HOURS: Mon and Wed 11-12, and by appointment.

In this seminar we will read a number of original papers in the foundational debate in the first three decades of the century. Most material will be drawn from the collection that Prof Paolo Mancosu (UC Berkeley) edited for Oxford UP. A tentative schedule and reading list follows.

Tentative Program:

 
Week 1:                  Hilbert's Foundations of Geometry. I

Week 2: Hilbert's Foundations of Geometry. II

Week 3: Hilbert's Program. Part I

Week 4: Brouwer.Part I

Week 5: Brouwer. Part II.

Week 6: Weyl, The Continuum and the conversion to intuitionism.

Week 7: Hilbert. Part II

Week 8: Hilbert. Part III

Week 9: Brouwer. Part III

Week 10: Emergence of intuitionistic logic.

Required textbooks:

1. D. Hilbert, Foundations of Geometry, Open Court
2.  P. Mancosu, ed., From Brouwer to Hilbert. Philosophy of Mathematics in the 1920s, Oxford University Press (Forthcoming). (Packet of readings) [PM].
3.  H. Weyl, The Continuum, Dover, 1994.
4.  Second Packet of Readings, available at the Stanford Bookstore.

 

 

Optional Textbooks:

5. P. Benacerraf, H. Putnam, eds., Philosophy of Mathematics. Selected Readings. Cambridge University Press, 1987.
6.  S.G. Shanker, Gödel's theorem in Focus, Routledge, 1990

Readings:

• Week 1: D. Hilbert, Foundations of Geometry, Open Court, Ch.1
•  Week 2:
1. D. Hilbert, Foundations of Geometry, Open Court, Ch.2
2.  P. Bernays, ``Hilbert's significance for the philosophy of mathematics,'' 1922, English translation in [PM]
• Week 3:
1. D. Hilbert, ``On the Concept of Number,'' 1900 (Translated in the appendix to the first edition of the translation of the Foundations of Geometry, 1902)
2.  D. Hilbert, ``On the foundations of logic and arithmetic,'' 1904. Translated in J. Van Heijenoort, ed., From Frege to Gödel, Harvard University Press, 1967, pp. 129-138.
3.  D. Hilbert, ``Axiomatic thinking,'' 1917, appendix to J. Fang, Hilbert. Towards a Philosophy of Modern Mathematics II, Paideia Press, 1970.
• Week 4:
1. L. Brouwer, ``On the Foundations of Mathematics,'' 1908, in CWI, pp.105-106
2.  L. Brouwer, ``The unreliability of the logical principles,'' 1908, in CWI, pp.107-111.
3.  L. Brouwer, ``Intuitionism and Formalism,'' 1912. English translation in P. Benacerraf, H. Putnam, eds., Philosophy of Mathematics. Selected Readings Cambridge University Press, 1987.
• Week 5: L. Brouwer, ``Intuitionistic set theory,'' 1918. English translation in [PM].
•  Week 6:
1. H. Weyl, The continuum, 1918. English translation published by Dover, 1994.
2.  H. Weyl, ``On the new foundational crisis of mathematics,'' 1921. English translation in [PM]
• Week 7:
1. D. Hilbert, ``On the new grounding of mathematics,'' 1922. English translation in [PM]
2.  P. Bernays, ``On Hilbert's thought concerning the grounding of arithmetic,'' 1922, English translation in [PM]
3.  P. Bernays, ``Reply to the note by Mr Aloys Mueller `On numbers as signs','' 1923, English translation in [PM]
4.  D. Hilbert, ``On the Infinite,'' 1925. English translation in P. Benacerraf, H. Putnam, eds., Philosophy of Mathematics. Selected Readings, Cambridge University Press, 1987.
• Week 8:
1. D. Hilbert, ``Problems of the grounding of mathematics,'' 1928, English translation in [PM].
2.  P. Bernays, ``The Philosophy of Mathematics and Hilbert's proof theory,'' 1930, English translation in [PM].
3.  D. Hilbert, ``The foundation of elementary number theory,'' 1931, English translation in [PM].
• Week 9:
1. L. Brouwer, ``Intuitionistic reflections on Formalism,'' 1927, English translation in [PM].
2.  L. Brouwer, ``Mathematics, Science and Language,'' 1929, English translation in [PM].
3.  L. Brouwer, ``The Structure of the Continuum,'' 1929 English translation in [PM].
• Week 10:
1. L. Brouwer, ``Intuitionistic splitting of the fundamental notions of mathematics,'' 1923, English translation in [PM]
2.  M. V. Glivenko, ``On some points of the logic of Mr Brouwer,'' 1929, English translation in [PM].
3.  A. Heyting, ``On intuitionistic logic,'' 1930, English translation in [PM].

Further references:

• J. Van Heijenoort, ed., From Frege to Gödel, Harvard University Press, 1967 is a general reference and a most useful source.
•  S.G. Shanker, Goedel's theorem in Focus, Routledge, 1990 (also a general reference on Gödel's theorems).
•  Week 1 and 2:
1. G. Birkhoff, M.K. Bennett, ``Hilbert's Grundlagen der Geometrie,'' Rendiconti del Circolo Matematico di Palermo, 36, 1987, pp. 343-389.
2.  M.M. Toepell, ``Über die Entstehung von Hilberts `Grundlagen der Geometrie',''Vandenhoeck & Ruprecht, 1986.
• Week 3:
1. W. Peckhaus, Hilbertprogramm und Kritische Philosophie, Vandenhoeck & Ruprecht, 1990
2.  H. Poincarè, Science and Method, Dover 1952.
• Week 4 and 5:
1. J. Largeault, Intuition et Intuitionisme, Vrin, Paris, 1993.
2.  W. Van Stigt, Brouwer's Intuitionism, North Holland, 1990.
• Week 6:
1. S. Feferman, ``Weyl vindicated: `Das Kontinuum' 70 years later.'' In Atti del Congresso Temi e Prospettive della logica e della filosofia della scienza contemporanea. Cesena 7-10 gennaio 1987. Vol. I. CLUEB, Bologna, 1988, pp. 59-93.
2.  D. Van Dalen, ``Hermann Weyl's Intuitionistic Mathematics,'' The Bulletin of Symbolic Logic, Vol. I, 1995, pp. 145-169.
• Week 7 and 8:
1. J. von Neumann, ``The formalist foundations of mathematics,'' in P. Benacerraf, H. Putnam, eds., Philosophy of Mathematics. Selected Readings, Cambridge University Press, 1987.
2.  G. Kreisel, ``Hilbert's Programme,'' in P. Benacerraf, H. Putnam, eds., Philosophy of Mathematics. Selected Readings, Cambridge University Press, 1987.
3.  M. Detlefsen, Hilbert's Program, Reidel, 1986.
4.  ``Hilbert,'' Revue Internationale de Philosophie,' 47, 1993 (Articles by Gochet, Sinaceur, Detlefsen, Gauthier, Majer, van Bendegem).
5.  ``A symposium on Hilbert's program,'' Journal of Symbolic Logic, 53, 1988. (Articles by Sieg, Feferman, Simpson.)

 

 
 
 

• Week 9:
1. W. Van Stigt, Brouwer's Intuitionism, North Holland, 1991.
2.  Detlefsen., M., ``Brouwerian Intuitionism,'' Mind, 99, 1990, pp. 501-534.
3.  Dummett, M., Elements of Intuitionism, Oxford University Pres, 1977.
4.  Troelstra, A.S., Principles of Intuitionism, Springer Verlag, 1969.

 

 
 
 

• Week 10: C. Thiel, ``Die Kontroverse um die intuitionistische Logik vor ihrer Axiomatisierung durch Heyting im Jahre 1930'', History and Philosophy of Logic, 9, 1988, 67-75.

 

 
 
 

 
Tue Jan 7 09:33:50 PST 1997