Lieber herr bernays!, lieber herr godel! godel on finitism, constructivity and hilbert's program

Dialectica

Volumn 62, Issue 2, 2008, Pages 179-203

  Feferman, Solomon ^a  

^a NONE

Author keywords

[No Author keywords available]

Indexed keywords

EID: 61449522271     PISSN: 00122017     EISSN: None     Source Type: Journal    
DOI: 10.1111/j.1746-8361.2008.01136.x     Document Type: Article

References (55)

1. Awodey, Steven and André W. Carus (2001), Carnap, completeness and categoricity: the Gobelbarkeitssatz of 1928, Erkenntnis 54, 145-171
2. Bernays, Paul (1930), Die Philosophie de Mathematik und die Hilbertsche Beweistheorie, Blätter für deutsche Philosophie 4, 326-367
3. -(1935), Hilberts Untersuchungen über die Grundlagen der Mathematik, in Hilbert (1935), 196-216
4. -(1967), Hilbert, David, in (P. Edwards, Eds.) Encyclopedia of Philosophy vol. 3, Macmillan, New York, 496-504
5. -(1976), Kurze Biographie, in (G. Miiller, eds.) Sets and Classes: On the work of Paul Bernays (North-Holland, Amsterdam), xiv-xvi
6. -(1976a), Abhandlungen zur Philosophie der Mathematik (Wissenschaftliche Buchgesellschaft, Darmstadt)
7. Davis, Martin (2005), What did Gödel believe and when did he believe it? Bull. Symbolic Logic 11, 194-206
8. Feferman, Solomon (1962), Transfinite recursive progressions of axiomatic theories, J. Symbolic Logic 27, 259-316
9. Gentzen, Gerhard (1936), Die Widerspruchsfreiheit der reinen Zahlentheorie, Mathematische Annalen 112, 493-465
10. (1969), The Collected Papers of Gerhard Gentzen (M. E. Szabo, ed.), (North-Holland, Amsterdam)
11. Gödel, Kurt (1931), Über formal unentscheidbare Sätze der Principia Mathematica und verwandter Systeme I, Monatshefte für Mathematik und Physik 38, 173-198
12. -(1931c), Diskussion zur Grundlegung der Mathematik, Erkenntnis 2, 147-151
13. -(1933o), The present situation in the foundations of mathematics, in Gödel (1995), 45-53
14. -(1938a), Vortrag bei Zilsel, in Gödel (1995) with facing English translation, 86-113
15. -(1941), In what sense is intuitionistic logic constructive? in Gödel (1995), 189-200
16. -(1958), Über eine bisher noch nicht benützte Erweiterung des finiten Standpunktes, Dialectica 12, 280-287
17. -(1972), On an extension of finitary mathematics which has not yet been used, in Gödel (1990), 271-280
18. -(1986), Collected Works, Vol. I: Publications 1929-1936 (S. Feferman, etal., eds.), (Oxford University Press, New York)
19. -(1990), Collected Works, Vol. II: Publications 1938-1974 (S. Feferman, etal., eds.), (Oxford University Press, New York)
20. -(1995), Collected Works, Vol. Ill: Unpublished Essays and Lectures (S. Feferman, et al., eds.), (Oxford University Press, New York)
21. -(2003), Collected Works, Vol. IV: Correspondence A-G (S. Feferman, et al., eds.), (Clarendon Press, Oxford)
22. -(2003a), Collected Works, Vol. V: Correspondence H-Z (S. Feferman, et al., eds.), (Clarendon Press, Oxford)
23. Herbrand, Jacques (1931), Sur la non-contradiction de l'arithmétique, J. fiür die reine und angewandte Mathematik 166, 1-8
24. Hilbert, David (1926), Über das Unendliche, Mathematische Annalen 95, 161-190
25. -(1931), Die Grundlegung der elementaren Zahlenlehre, Mathematische Annalen 104, 485-94
26. -(1931a), Beweis des tertium non datur, Nachrichten von der Gesellschaft der Wissenschaften zu Göttingen, Math.-Physik. Klasse, 120-125
27. -(1935), Gesammelte Abhandlungen, vol. 3 (Springer, Berlin)
28. Hilbert, David and Paul Bernays (1934), Grundlagen der Mathematik, Vol. I (Springer, Berlin); 2nd edition, 1968 (Springer, Berlin)
29. nd edition, 1970 (Springer, Berlin)
30. Kreisel, Georg (1960), Ordinal logics and the characterization of informal concepts of proof, Proc. International Congress of Mathematicians, 14-21 August 1958 (Cambridge University Press, Cambridge), 289-299
31. -(1965), Mathematical logic, in (T. L. Saaty, ed.) Lectures on Modern Mathematics, vol. 3 (Wiley, New York), 95-195
32. -(1970), Principles of proof and ordinals implicit in given concepts, in (J. Myhill, et al., eds.) Intuitionism and Proof Theory (North-Holland, Amsterdam), 489-516
33. -(1980), Kurt Gödel, 28 April 1906-14 January 1978, Biographical Memoirs of Fellows of the Royal Society 26, 148-224; corrections, ibid. 27, 697 and 28, 718
34. -(1987), Gödel's excursions into intuitionistic logic, in (P. Weingartner and L. Schmetterer, eds.) Gödel Remembered (Bibliopolis, Naples), 65-186
35. Mancosu, Paolo (1998), (ed.) From Brouwer to Hilbert. The debate on the Foundations of Mathematics in the 1920s (Oxford, New York)
36. Parsons, Charles (1995), Platonism and mathematical intuition in Kurt Gödel's thought, Bull. Symbolic Logic 1, 44-74
37. -(2008) Paul Bernays' later philosophy of mathematics, in (C. Dimitracopoulos et al., eds.) Logic Colloquium 2005, Lecture Notes in Logic 28, 129-150
38. Reid, Constance (1970), Hilbert (Springer, New York)
39. Spector, Clifford (1962), Provably recursive functional of analysis. A consistency proof of analysis by an extension of principles formulated in current intuitionistic mathematics, in (J. C. E. Dekker, ed.) Recursive Function Theory(American Mathematical Society, Providence), 1-27
40. Tait, William (1961), Nested recursion, Mathematische Annalen 143, 236-250
41. -(1968), Constructive reasoning, in (B. van Rootselaar and J. F. Staal, eds.), Logic, Methodology and Philosophy of Science III (North-Holland, Amsterdam), 185-199
42. -(1981), Finitism, The Journal of Philosophy 78, 524-546
43. -(2005), The Provenance of Pure Reason (Oxford University Press, New York)
44. -(2005a), Gödel's reformulation of Gentzen's first consistency proof for arithmetic: The no-counterexample interpretation, Bull. Symbolic Logic 11, 225-238
45. -(2006), Kurt Gödel, Collected Works. Vol. IV, Selected Correspondence A-G, Vol. V, Selected Correspondence, H-Z, Philosophia Mathematica (series III) 14, 76-114
46. Takeuti, Gaisi (2003), Memoirs of a Proof Theorist. Gödel and other logicians (World Scientific, Singapore)
47. Taussky-Todd, Olga (1987), Remembrances of Kurt Gödel, in (P. Weingartner and L. Schmetterer,eds.) Gödel Remembered (Bibliopolis, Naples), 29-48
48. Turing, Alan (1939), Systems of logic based on ordinals, Proc. London Mathematical Society (ser. 2) 45, 161-228
49. (M. Davis, ed.) The Undecidable. Basic papers on undecidable propositions, unsolvable problems and computable functions (Raven Press, Hewlett, NY, 1965)
50. van Atten, Mark (2006), Brouwer meets Husserl. On the phenomenology of choice sequences, Synthese Library vol. 335 (Springer, Berlin)
51. van Heijenoort, Jean (1967), From Frege to Gödel: A source book in mathematical logic, 1879-1931(Harvard University Press, Cambridge)
52. Wang, Hao (1981), Some facts about Kurt Gödel, J. Symbolic Logic 46, 653-659
53. Zach, Richard (1998), Numbers and functions in Hilbert's finitism, Taiwanese J. for Philosophy and History of Science 10, 33-60
54. -(2001), Hilbert's Program. Historical, philosophical and metamathematical perspectives, PhD Dissertation, University of California, Berkeley
55. -(2003), Hilbert's Program, Stanford Encyclopedia of Philosophy, http://plato.stanford.edu/entries/hilbert-program/