×

How Bertrand Russell discovered his paradox. (English) Zbl 0379.01010


MSC:

01A60 History of mathematics in the 20th century
03A05 Philosophical and critical aspects of logic and foundations
03E50 Continuum hypothesis and Martin’s axiom
01A55 History of mathematics in the 19th century
PDFBibTeX XMLCite
Full Text: DOI

References:

[1] Borel, E., Lecons sur la theorie des fonctions (1898), Paris · JFM 29.0336.01
[2] Bunn, R., Developments in the foundations of mathematics, 1870-1910, (Grattan-Guinness, I., From the Calculus to Set Theory, 1630-1910: an introductory history (1978)), 220-255, London
[3] Cantor, G., Über eine Eigenschaft des Inbegriffes aller reellen algebraischen Zahlen, J. rei. ang. Math., 77, 258-262 (1874), =[1932, 115-118] · JFM 06.0057.01
[4] Cantor, G., Über eine elementare Frage der Mannigfaltigkeitslehre, Jber. Dtsch. Math.-Ver., 1, 75-78 (1892), =[1932, 278-281] · JFM 24.0066.02
[5] Cantor, G., Beiträge zur Begründung der transfiniten Mengenlehre [part 1], Math. Ann., 46, 481-512 (1896), =[1932, 282-311] · JFM 26.0081.01
[6] Cantor, G., (Zermelo, E., Gesammelte Abhandlungen… (1932)), Berlin: repr. 1962, Hildesheim
[7] Crossley, JN, A note on Cantor’s theorem and Russell’s paradox, Austral. j. phil., 51, 70-71 (1973)
[8] Couturat, L., De l’infini mathématique (1896), Paris: repr. 1969, New York; 1973, Paris · JFM 27.0049.10
[9] Dedekind, R., Ähnliche (deutliche Abbildung und ähnliche Systeme. 1887.7.11, (Gesammelte mathematische Werke, vol. 3 (1887)), 447-449, (1932, Berlin)
[10] Du, Bois; Reymond, P., Über die Paradoxien des Infinitärkalkus, Math. Ann., 11, 149-167 (1876)
[11] Frege, G., (Hermes, H., Wissenschaftlicher Briefwechsel (1976)), and others, Hamburg
[12] Grattan-Guinness, I., The correspondence between Georg Cantor and Philip Jourdain, Jber. Dtsch. Math.-Ver., 73, 111-130 (1971), pt. 1 · Zbl 0225.01008
[13] Grattan-Guinness, I., Bertrand Russell on his paradox…, J. phil. logic, 1, 103-110 (1972) · Zbl 0239.01022
[14] Grattan-Guinness, I., Dear Russell – Dear Jourdain… (1977), London
[15] Hannequin, A., Essai critique sur l’hypothèse des atomes… (1895), Paris · JFM 30.0079.06
[16] Hardy, GH, A theorem concerning the infinite cardinal numbers, Quart. j. math., 35, 87-94 (1903) · JFM 34.0077.02
[17] Hardy, GH, The continuum and the second number class, (Proc. London Math. Soc., 4 (1906)), 10-17, 2 · JFM 37.0073.04
[18] Jourdain, PEB, De infinito in mathematica, Riv. di mat., 8, 121-136 (1906)
[19] Jourdain, PEB, A correction and some remarks, Monist, 23, 145-148 (1913)
[20] Korselt, A., Über einen Beweis des Aquivalenzsatzes, Math. Ann., 70, 294-296 (1911) · JFM 42.0090.01
[21] Russell, B., Review of Hannequin 1895, Mind, 5, 410-417 (1896), (n.s.)
[22] Russell, B., (The Principles of Mathematics (1903)), Cambridge 2nd ed. 1937, London
[23] Russell, B., Introduction to Mathematical Philosophy (1919), London · JFM 47.0036.12
[24] Russell, B., My mental development, (Schilpp, PA, The Philosophy of Bertrand Russell (1944)), New York
[25] Russell, B., Portraits from Memory (1956), London
[26] Russell, B., My Philosophical Development (1959), London
[27] Russell, B., Autobiography, vol. 1 (1967), London
[28] Schönflies, A., Die Entwicklung der Lehre von den Punktmannigfaltigkeiten part 1, Jber. Dtsch. Math.-Ver., 8 (1900), pt. 2
[29] Schröder, E., Über… G. Cantorsche Sätze, Abh. Kaiserl. Leop.-Car. Akad. Naturf., 71, 301-362 (1898)
[30] Whitehead, AN, On cardinal numbers, Amer. j. math., 24, 367-394 (1902) · JFM 33.0074.02
[31] Zermelo, E., Beweis, dass jede Menge wohlgeordnet werden kann, Math. Ann., 59, 514-516 (1904) · JFM 35.0088.03
[32] Zermelo, E., Untersuchungen über die Grundlagen der Mengenlehre, I [and only], Math. Ann., 65, 261-281 (1908) · JFM 39.0097.03
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.