Divergent conceptions of the continuum in 19th and early 20th century mathematics and philosophy

Axiomathes

Volumn 15, Issue 1, 2005, Pages 63-84

  Bell, John L ^a  

^a NONE

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EID: 33846030614     PISSN: 11221151     EISSN: 15728390     Source Type: Journal    
DOI: 10.1007/s10516-004-7108-4     Document Type: Article

References (28)

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2. Brentano, F.: 1988, Philosophical Investigations on Space, Time and the Continuum. Translated by Barry Smith. Croom Helm.
3. Brentano, F.: 1974, Psychology from an Empirical Standpoint. Humanities Press.
4. Brouwer, L. E. J.: 1975, in A. Heyting (ed.), Collected Works, 1. North-Holland.
5. Hilbert, D.: 1926, 'On the Infinite.' Translated from German original in Mathematicsche Annalen 95 (1926). In Jean van Heijenoort, ed., From Frege to Gödel: A Source Book in Mathematical Logic, Harvard University Press, 1981. pp. 1879-1931.
6. Kant, I.: 1964, Critique of Pure Reason. Macmillan.
7. Mancosu, P.: 1998, From Brouwer to Hilbert: The Debate on the Foundations of Mathematics in the1920s. Oxford: Clarendon Press.
8. Peirce, C. S.: 1976, The New Elements of Mathematics, Vol. III. Mouton Publishers and Humanities Press.
9. Peirce, C. S.: 1992, in Kenneth Laine Ketner (ed.), Reasoning and the Logic of Things. Harvard University Press.
10. Rescher, N.: 1967, The Philosophy of Leibniz. Prentice-Hall.
11. Weyl, H.: 1929, 'Consistency in Mathematics". Rice Institute Pamphlet 16, 245-265. Reprinted in Weyl [1968] II, pp. 150-170.
12. Weyl, H.: 1932, The Open World: Three Lectures on the Metaphysical Implications of Science. Yale University Press.
13. Weyl, H.: 1940, Philosophical Essays in Memory of Edmund Husserl, Harvard University Press. Reprinted in Weyl [1968] III, pp. 684-709.
14. Weyl, H.: 1946, 'Mathematics and Logic: A brief survey serving as a preface to a review of "The Philosophy of Bertrand Russell".' American mathematical Monthly 53, 2-13.
15. Weyl, H.: 1950, Space-Time-Matter, tr. Henry L. Brose. New York: Dover, 1950.
16. (English translation of Raum, Zeit, Materie, Berlin: Springer Verlag, 1918.)
17. Weyl, H.: 1954, Address on the Unity of Knowledge. Columbia University Bicentennial Celebration, 1954. Reprinted in Weyl [1968] IV, pp. 623-630.
18. Weyl, H.: 1963, Philosophy of Mathematics and Natural Science. New York: Atheneum.
19. (An expanded Engish version of Philosophie der Mathematik und Naturwissenschaft, München: Leibniz Verlag, 1927.)
20. Weyl, H.: 1968, in K. Chandrasehharan, (ed.), Gesammelte Abhandlungen, I-IV, Berlin: Springer-Verlag.
21. Weyl, H.: 1969, "Insight and Reflection". (Lecture delivered at the University of Lausanne, Switzerland, May 1954.
22. Translated from German original in Studia Philosophica, 15, 1955.) In T.L. Saaty and F.J. Weyl, (eds), The Spirit and Uses of the Mathematical Sciences, New York: McGraw-Hill. pp. 281-301.
23. Weyl, H.: 1985, 'Axiomatic versus Constructive Procedures in Mathematics.', Mathematical Intelligencer 7(4), 10-17, 38.
24. Weyl, H.: 1987, The Continuum: A Critical Examination of the Foundation of Analysis, tr. S. Pollard and T. Bole. Kirksville, Mo.: Thomas Jefferson University Press.
25. (English translation of Das Kontinuum, Leipzig: Veit, 1918.)
26. Weyl, H.: 1998, 'On the New Foundational Crisis in Mathematics'. (English Translation of 'Über der neue Grundslagenkrise der Mathematik,' Mathematische Zeitschrift 10(1921), 37-79. In Mancosu (1998), 86-122.
27. Weyl, H.: 1998a 'On the Current Epistemological Situation in Mathematics.' English translation of 'Die Heutige Erkenntnislage in der Mathematik, Symposion 1, (1925-1927), 1-32. In Mancosu 1998, 123-142.
28. Van dalen, D.: 1995, "Hermann Weyl's Intuitionistic Mathematics', Bulletin of Symbolic Logic 1(2), 145-169.