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Bibliographical References Bibliographical References Abbreviations employed for frequently mentioned journals. AHES Archive for History of Exact Sciences AM Acta Mathematica AMM American Mathematical Monthly AS Annals of Science DMV Jahresbericht der Deutschen Mathematiker-Vereinigung FM Fundamenta Mathematica HM Historia Mathematica HPL History and Philosophy of Logic JrM Journal f'tir die reine und angewandte Mathematik (Crelle) JSL Journal of Symbolic Logic LMS Proceedings of the London Mathematical Society MA Mathematische Annalen NAS Proceedings of the National Academy of Sciences, U.S.A. NG Nachrichten der K6nigliche Gesellschaft der Wissenschaften zu G/Sttingen NTM International Journal of History and Ethics of Natural Sciences, Technology and Medicine RHS Revue d'histoire des sciences et de leurs applications ACKERMANN, W. 1937 Die Widerspruchsfreiheit der allgemeinen Mengenlehre, MA 114, 305-15. 1938 Mengentheoretische Begrfindung der Logik, MA 115, 1-22. ALEKSANDROV, P.S. 1916 Sur la puissance des ensembles mesurables B, Comptes Rendus, Acad~mie des Sciences de Paris 162, 323-25. ARISTOTLE Organon, in J. Barnes, ed., The Complete Works of Aristotle, 2 vols., Princeton University Press, 1984. ARNAULD, A. & P. NICOLE 1662 La Logique ou l'Art de Penser, Paris, Flammarion, 1970. A USLEIHREGISTER Handwritten record of books and journals loaned to professors and students of the University of G6ttingen, kept at the Nieders~ichsische Staats- und Universit~itsbib- liothek (Handschriftenabteilung). BEKEMEIER, B. 1987 Martin Ohm (1792-1872): Universitiitsmathematik und Schulmathematik in der neuhumanistischen Bildungsreform, G6ttingen, Vandenhoeck & Ruprecht. 394 Bibliographical References BENACERRAF, P. & H. PUTNAM, eds. 1983 Philosophy of Mathematics: selected readings, Cambridge University Press. BENDIXSON, I. 1883 Quelques th6or6mes de la th6orie des ensembles, AM 2, 415--429. BENSAUDE-VINCENT, B. 1983 A Founder Myth in the History of Science? The Lavoisier Case, in L. Graham, W. Lepenies & P. Weingart, eds. Functions and Uses of Disciplinary Histories, Dor- drecht, Reidel, 53-78. BERNAYS, P. 1930 Die Philosophie der Mathematik und die Hilbertsche Beweistheorie, Bl~itter f~r Deutsche Philosophic 4, 326-67. References to [Bemays 1976], 17-61. 1935 Hilberts Untersuchungen fiber die Grundlagen der Arithmetik, in [Hilbert 1932/35], vol. 3, 196-216. 1935a Sur le platonisme dans les math6matiques, L 'Enseignement Mathdmatique 34, 52- 69. German trans, in [Bernays 1976], English in [Benacerraf & Putnam 1983], 258-71. 1937/42 A System of Axiomatic Set Theory, Parts I-III, JSL 2, 65-77, 6, 1-17, 7, 65- 89, 133-45. 1958 Axiomatic Set Theory, Amsterdam, North-Holland. 1976 Abhandlungen zur Philosophic der Mathematik, Darmstadt, Wissenschaftliche Buchgesellschaft. BERNSTEIN, F. 1905 Untersuchungen aus der Mengenlehre, MA 61, 117-155. BIERMANN, K.R. 1959 Johann Peter Gustav Lejeune Dirichlet. Dokumente )"fir sein Leben und Wirken, Berlin, Akademie-Verlag. 1966 Karl Weierstrass. Ausgew~ihlte Aspekte seiner Biographic, JrM 223, 191-220. 1966a Richard Dedekind im Urteil der Berliner Akademie, Forschungen und Fortschritte 40, 301-302. BOCHE/qSKI, I.M. 1956 Formale Logik, Mfinchen, Alber. DU BOIS-REYMOND, P. 1875 Versuch einer Classification der willkfirlichen Functionen reeller Argumente nach ihren Aenderungen in den kleinsten lntervallen, JrM 79, 21-37. 1880 Der Beweis des Fundamentalsatzes der Integralrechnung, MA 16, 115-128. BOLLING, R. 1997 Georg Cantor - Ausgew~ihlte Aspekte seiner Biographic, DMV 99, 49-82. BOLLINGER, M. 1972 Geschichtliche Entwicklung des Homologiebegriffs, AHES 9, 94-170. BOLZANO, B. 1817 Rein analytischer Beweis des Lehrsatzes dass zwischen je zwei Werten die ein entgegengesetztes Resultat gewiihren, wenigstens eine reelle Wurzel der Gleichung liege, Prag, Haase. Reprint in Ostwald's Klassiker no. 153. English trans, in [Ewald 1996, vol. 1]. 1837 Wissenschaftslehre, 4 vols., Seidel, Sulzbach. Reprinted in 1937. Selections trans- lated as Theory of Science, Oxford, Blackwell, 1972. Bibliographical References 395 1851 Paradoxien des Unedlichen, Leipzig, Reclam. Reprint in Leipzig, Meiner, 1920, and Hamburg, 1975. English trans. London, Routledge, 1950. BOOLE, G. 1847 The mathematical analysis of Logic, Cambridge, Macmillan. References to the reprint Oxford, Basil Blackwell, 1951. Reprinted in [Ewald 1996, vol.1]. BOOLOS, G. 1971 The Iterative Concept of Set, Journal of Philosophy 68, 215-31. Reprint in [Bena- cerraf & Putnam 1983]. BOREL, E. 1898 Lemons sur la theorie des fonctions, Paris, Gauthier-Villars. BORGA, M., P. FREGUGLIA & D. PALLADINO 1985 I contributi fondazionali della scuola di Peano, Milano, Angeli. BOS, H., H. MEHRTENS & I. SCHNEIDER, eds. 1981 Social history of nineteenth century mathematics, Boston, Birkh~iuser. BO'ITAZZINI, U. 1977 Riemanns Einfluss auf Betti und Casorati, AHES 18, 27-37. 1985 Dall'Analisi Matematica al Calcolo Geometrico: Origini Delle Prime Ricerche di Logica di Peano, HPL 6, 25-52. 1986 The Higher Calculus: A History of Real and Complex Analysis from Euler to Weierstrass, New York, Springer. BOURBAKI, N. 1949 Foundations of Mathematics for the Working Mathematician, JSL 14, 1-8. 1950 The Architecture of Mathematics, AMM 67, 221-32. Reprinted in [Ewald 1996], vol.2. 1954 Thdorie des ensembles, Pads, Hermann. 1994 Elements of the history of mathematics, Berlin, Springer (original edition 1969). BROUWER, L.E.J. 1910 Zur Analysis Situs, MA 68, 422-34. English trans, in [Brouwer 1975/76]. 1911 Beweis der Invarianz der Dimensionszahl, MA 70, 161-65. English trans, in [Brouwer 1975/76]. 1918 Begrtindung der Mengenlehre unabh~'agig vom logischen Satz vom ausgeschlosse- nen Dritten, I, Verhandelingen der Koninklijke Nederlandse Akademie van Weten- schappen te Amsterdam 12. English trans, in [Brouwer 1975/76]. 1925 Zur Begrtindung der intuitionistischen Mathematik, I, MA 93, 244-57. English trans, in [Brouwer 1975/76]. 1975/76 Collected Works, A. Heyting and H. Fredenthal, eds., 2 vols., Amsterdam, North-Holland. BUNN, R. 1980 Developments in the Foundations of Mathematics from 1870 to 1910, in [Grattan- Guinness 1980]. BURALI-FORTI, C. 1896 Le classi finite, Atti della Academia delle Scienze di Torino 32, 34-52. 1897 Una questione sui numeri transfiniti, Rendiconti del Circolo Matematico di Pal- ermo 11, 154-64. References to the English trans, in [van Heijenoort 1967], 104- 11. 396 Bibliographical References BUTZER, P.L. 1987 Dirichlet and His Role in the Founding of Mathematical Physics, Archives interna- tionales d'histoire des sciences 37, 49-82. CANEVA, K.L. 1978 From Galvanism to Electrodynamics: The Transformation of German Physics and Its Social Context, Historical Studies in the Physical Sciences 9, 63-159. CANTOR, G. 1872 Ober die Ausdehnung eines Satzes aus der Theorie der trigonometrischen Reihen, MA 5, 123-32. References to [Cantor 1932], 92-101. 1874 Ober eine Eigenschaft des Inbegriffes aller reellen algebraischen Zahlen, JrM 77, 258-62. References to [Cantor 1932], 115-118. English trans, in [Ewald 1996], vol.2. 1878 Ein Beitrag zur Mannigfaltigkeitslehre, JrM 84, 242-58. References to [Cantor 1932], 119-133. 1879/84 Ober unendliche, lineare Punktmannichfaltigkeiten, MA 15, 1-7, 17, 355-58, 20, 113-21, 21, 51-58, 545-86, 23, 453-88. References to [Cantor 1932], 139- 244. 1883 Grundlagen einer allgemeinen Mannigfaltigkeitslehre, Leipzig, 1883 (separate edition of [Cantor 1879/84], part 5). References to [Cantor 1932], 165-208. Eng- lish trans, in [Ewald 1996], vol.2. 1886 Ober die verschiedenen Standpunkte in bezug auf das aktuelle Unendliche, Zeitschrift fiir Philosophie und philosophische Kritik 88, 224-33. References to [Cantor 1932], 370-76. 1887/88 Mitteilungen zur Lehre vom Transfiniten, Zeitschrift fiir Philosophie und phi- losophische Kritik 91, 81-125, 252-70, 92, 250-65. References to [Cantor 1932], 378-439. 1892 Ober eine elementare Frage der Mannigfaltigkeitslehre, DMV 1, 75-78. References to [Cantor 1932], 278-280. English trans, in [Ewald 1996], vol.2. 1895/97 Beitr/age zur Begrtindung der transfiniten Mengenlehre, MA 46, 481-512, 49, 207-46. References to [Cantor 1932], 282-351. 1915 Contributions to the founding of the Theory of Transfinite Numbers, Chicago, Open Court. Reprint New York, Dover, 1955. 1932 Gesammelte Abhandlungen mathematischen und philosophischen lnhalts, ed. E. Zermelo, Berlin, Springer. Reprint Hildesheim, G. Olms, 1966. 1970 Principien einer Theorie der Ordnungstypen, in [Grattan-Guinness 1970], 83-101. CANTOR, G. & R. DEDEKIND 1932 Aus dem Briefwechsel zwischen Cantor und Dedekind (1899 letters), in [Cantor 1932], 443-450. English trans, in [Ewald 1996], vol.2. 1937 Cantor-Dedekind Briefwechsel, ed. E. Noether and J. Cavaill~s, Paris, Hermann. French translation including the 1899 letters in [Cavaill~s 1962], 187-249. English trans, in [Ewald 1996], vol.2. 1976 Unverrffentlichter Briefwechsel, in [Dugac 1976], 223-262. CARNAP, R. 1929 Abriss der Logistik, mit besonderer Beriicksichtigung der Relationstheorie und ihrer Anwendungen, Wien, Springer, 1929. 1931 Die logizistische Grundlegung der Mathematik, Erkenntnis 2, 91-105. References to the English translation in [Benacerraf & Putnam 1983, 41-52]. 1937 The Logical Syntax of Language, New York, Harcourt, Brace. Bibliographical References 397 1963 Intellectual Autobiography, in P.A. Schilpp, ed., The Philosophy ofR. Carnap, La Salle, II1., Open Court, 1963. CAUCHY, A.L. 1821 Cours d'analyse algObrique, Paris. In Oeuvres completes, ser. 2, Paris, Gauthier- Villars, 1897-99, vol. 3. CAVAILLI~S, J. 1932 Sur
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