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Volumn 2, Issue 4, 2009, Pages 612-646

Measuring the Size of Infinite Collections of Natural Numbers: Was Cantor'S Theory of Infinite Number Inevitable?

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EID: 84989179918     PISSN: 17550203     EISSN: 17550211     Source Type: Journal    
DOI: 10.1017/S1755020309990128     Document Type: Review
Times cited : (66)

References (82)
  • 3
    • 61149102215 scopus 로고    scopus 로고
    • Infinite number and the world soul; In defense of Carlin and Leibniz
    • Arthur, R. (1999). Infinite number and the world soul; in defense of Carlin and Leibniz. The Leibniz Review, 9, 105-116.
    • (1999) The Leibniz Review , vol.9 , pp. 105-116
    • Arthur, R.1
  • 4
    • 61249277379 scopus 로고    scopus 로고
    • Leibniz on infinite number, infinite wholes, and the whole world: A reply to Gregory Brown
    • Arthur, R. (2001). Leibniz on infinite number, infinite wholes, and the whole world: A reply to Gregory Brown. The Leibniz Review, 11, 103-116.
    • (2001) The Leibniz Review , vol.11 , pp. 103-116
    • Arthur, R.1
  • 6
    • 0037440322 scopus 로고    scopus 로고
    • Numerosities of labeled sets: A new way of counting
    • Benci, V., Di Nasso, M. (2003). Numerosities of labeled sets: A new way of counting. Advances in Mathematics, 173, 50-67.
    • (2003) Advances in Mathematics , vol.173 , pp. 50-67
    • Benci, V.1    Di Nasso, M.2
  • 8
    • 60950683463 scopus 로고    scopus 로고
    • An Euclidean measure of size for mathematical universes
    • Benci, V., Di Nasso, M., Forti, M. (2007). An Euclidean measure of size for mathematical universes. Logique et Analyse, 50, 43-62.
    • (2007) Logique et Analyse , vol.50 , pp. 43-62
    • Benci, V.1    Di Nasso, M.2    Forti, M.3
  • 12
    • 4244143302 scopus 로고
    • Dordrecht, The Netherlands: Reidel
    • Bolzano, B. (1973). Theory of Science. Dordrecht, The Netherlands: Reidel.
    • (1973) Theory of Science
    • Bolzano, B.1
  • 13
    • 84989164432 scopus 로고
    • Einleitung zur Grössenlehre. Erste Begriffe der allgemeinen Grössenlehre
    • In Jan Berg, editor Stuttgart-Bad Cannstatt, Germany: Friedrich Fromann Verlag
    • Bolzano, B. (1975a). Einleitung zur Grössenlehre. Erste Begriffe der allgemeinen Grössenlehre. In Jan Berg, editor. Gesamtausgabe, II A 7. Stuttgart-Bad Cannstatt, Germany: Friedrich Fromann Verlag.
    • (1975) Gesamtausgabe II A , vol.7
    • Bolzano, B.1
  • 14
    • 84929706661 scopus 로고
    • Paradoxien des Unendlichen. Hamburg
    • Germany: Felix Meiner Verlag Steele, London: Routledge and Kegan Paul, and New Haven: Yale University Press
    • Bolzano, B. (1975b). Paradoxien des Unendlichen. Hamburg, Germany: Felix Meiner Verlag. Translated as Paradoxes of the Infinite, edited by Donald A. Steele, London: Routledge and Kegan Paul, and New Haven: Yale University Press, 1950.
    • (1975) Translated As Paradoxes of the Infinite, Edited by Donald A , vol.1950
    • Bolzano, B.1
  • 15
    • 0005289866 scopus 로고
    • Differentials, higher-order differentials and the derivative in the Leibnizian calculus
    • Bos, H. (1974). Differentials, higher-order differentials and the derivative in the Leibnizian calculus. Archive for History of Exact Sciences, 14, 1-90.
    • (1974) Archive for History of Exact Sciences , vol.14 , pp. 1-90
    • Bos, H.1
  • 17
    • 79551585963 scopus 로고    scopus 로고
    • Natural numbers and infinite cardinal number
    • In Hecht, H., Mikosch, R., Schwarz I., Siebert, H., Werthers, R., editors Stuttgart, Germany: Steiner
    • Breger, H. (2008). Natural numbers and infinite cardinal number. In Hecht, H., Mikosch, R., Schwarz, I., Siebert, H., Werthers, R., editors. Kosmos und Zahl. Stuttgart, Germany: Steiner, pp. 309-318.
    • (2008) Kosmos und Zahl , pp. 309-318
    • Breger, H.1
  • 18
    • 61249662188 scopus 로고    scopus 로고
    • Leibniz on wholes, unities, and infinite number
    • Brown, G. (2000). Leibniz on wholes, unities, and infinite number. The Leibniz Review, 10, 21-51.
    • (2000) The Leibniz Review , vol.10 , pp. 21-51
    • Brown, G.1
  • 19
    • 84888374186 scopus 로고
    • Quantitative relations between infinite sets
    • Bunn, R. (1977). Quantitative relations between infinite sets. Annals of Science, 34, 177-191.
    • (1977) Annals of Science , vol.34 , pp. 177-191
    • Bunn, R.1
  • 23
    • 63149133879 scopus 로고    scopus 로고
    • Infinity, continuity, and composition: The contribution of Gregory of Rimini
    • Cross, R. (1998). Infinity, continuity, and composition: The contribution of Gregory of Rimini. Medieval Philosophy and Theology, 7, 89-110.
    • (1998) Medieval Philosophy and Theology , vol.7 , pp. 89-110
    • Cross, R.1
  • 24
    • 80052209855 scopus 로고
    • Henry of Harclay on the infinite
    • Dales, R. C. (1984). Henry of Harclay on the infinite. Journal of the History of Ideas, 45, 295-301.
    • (1984) Journal of the History of Ideas , vol.45 , pp. 295-301
    • Dales, R.C.1
  • 27
    • 84989175764 scopus 로고    scopus 로고
    • Numerosities of point sets over the real line
    • Forthcoming Available from
    • Di Nasso, M., Forti, M. (2009). Numerosities of point sets over the real line.Transactions of the American Mathematical Society. Forthcoming. Available from: http://www.dm.unipi.it/dinasso/papers.html.
    • (2009) Transactions of the American Mathematical Society
    • Di Nasso, M.1    Forti, M.2
  • 28
    • 0001950073 scopus 로고    scopus 로고
    • A general extension theorem for binary relations
    • Duggan, J. (1999). A general extension theorem for binary relations. Journal of Economic Theory, 86, 1-16.
    • (1999) Journal of Economic Theory , vol.86 , pp. 1-16
    • Duggan, J.1
  • 29
    • 84989178656 scopus 로고
    • Leónard de Vinci et les deux infinis
    • Seconde Serie. Paris, France: De Nobele
    • Duhem, P. (1955). Leónard de Vinci et les deux infinis. In Études sur Leónard de Vinci, Seconde Serie. Paris, France: De Nobele, pp. 3-53, 368-407.
    • (1955) Études sur Leónard de Vinci , vol.3 , Issue.53 , pp. 368-407
    • Duhem, P.1
  • 33
    • 0003954555 scopus 로고
    • Galileo Evanston IL: Northwestern University. Reprinted by Dover
    • Galileo (1939). Dialogues Concerning Two New Sciences. Evanston, IL: Northwestern University. Reprinted by Dover 1954.
    • (1939) Dialogues Concerning Two New Sciences , vol.1954
  • 37
    • 0013196933 scopus 로고    scopus 로고
    • Y-at-il vraiment autant de nombres pairs que des naturels
    • Pétry, A., editor Cahiers du Centre de Logique Louvain-la-Neuve, Belgium: Bruylant-Academia
    • Gilbert, T., Rouche, N. (1996). Y-at-il vraiment autant de nombres pairs que des naturels In Pétry, A., editor. Méthodes et Analyse Non Standard, Cahiers du Centre de Logique, Vol. 9. Louvain-la-Neuve, Belgium: Bruylant-Academia, pp. 99-139.
    • (1996) Méthodes et Analyse Non Standard , vol.9 , pp. 99-139
    • Gilbert, T.1    Rouche, N.2
  • 38
    • 0003913615 scopus 로고
    • In Feferman, S., Dawson, J. W., Kleene, S., C., Moore, G. H., Solovay, R., van Heijenoort, J., editors. New York: Oxford University Press
    • Gödel, K. (1990). Collected Works. In Feferman, S., Dawson, J. W., Kleene, S. C., Moore, G. H., Solovay, R., van Heijenoort, J., editors. Vol. II. New York: Oxford University Press.
    • (1990) Collected Works , vol.2
    • Gödel, K.1
  • 39
    • 84989213284 scopus 로고
    • Oxford, UK: Clarendon Press. Foreword by Michael Dummett. Reprinted in paperback, with revisions
    • Hallett, M. (1984). Cantorian Set Theory and Limitation of Size. Oxford, UK: Clarendon Press. Foreword by Michael Dummett. Reprinted in paperback, with revisions, 1986, 1988.
    • (1984) Cantorian Set Theory and Limitation of Size , vol.1986 , pp. 1988
    • Hallett, M.1
  • 40
    • 84882138193 scopus 로고    scopus 로고
    • In Henninger M., editor. Two volumes. New York: Oxford University Press
    • Harclay, H. (2008). Ordinary Questions. In Henninger, M., editor. Two volumes. New York: Oxford University Press.
    • (2008) Ordinary Questions
    • Harclay, H.1
  • 42
    • 84989173632 scopus 로고
    • Ph.D Dissertation, MIT Now newly typeset Available froms
    • Katz, F. M. (1981). Sets and Their Sizes. Ph.D. Dissertation, MIT. Now newly typeset (2001). Available from: http://citeseerx.ist.psu.edu/viewdoc/summarydoi= 10.1.1.28.7026.
    • (1981) Sets, Their Sizes
    • Katz, F.M.1
  • 45
    • 0346533474 scopus 로고
    • Gerhardt C. I., editor Berlin: Weidmann. Reprint by G. Olms
    • Leibniz, G.W. (1875-1890). Gerhardt, C. I., editor. Die philosophischen Schriften. Berlin: Weidmann. Reprint by G. Olms.
    • (1875) Die Philosophischen Schriften
    • Leibniz, G.W.1
  • 48
    • 85027258737 scopus 로고    scopus 로고
    • Robert grosseteste
    • Available from
    • Lewis, N. (2007). Robert Grosseteste. Stanford Encyclopedia of Philosophy. Available from: http://plato.stanford.edu/entries/grosseteste/.
    • (2007) Stanford Encyclopedia of Philosophy
    • Lewis, N.1
  • 52
    • 54449095671 scopus 로고    scopus 로고
    • Mathematical explanation: Why it matters
    • In Paolo Mancosu, editor Oxford, UK: Oxford University Press
    • Mancosu, P. (2008a). Mathematical Explanation: Why it matters. In Paolo Mancosu, editor. The Philosophy of Mathematical Practice. Oxford, UK: Oxford University Press, pp. 134-149.
    • (2008) The Philosophy of Mathematical Practice , pp. 134-149
    • Mancosu, P.1
  • 54
    • 67349254082 scopus 로고
    • Torricelli's infinitely long solid and its philosophical reception in the XVIIth century
    • Mancosu, P., Vailati, E. (1991). Torricelli's infinitely long solid and its philosophical reception in the XVIIth century. Isis, 82, 50-70.
    • (1991) Isis , vol.82 , pp. 50-70
    • Mancosu, P.1    Vailati, E.2
  • 56
    • 79957117286 scopus 로고
    • Henry of harclay and the infinite
    • In Maierù, A., Paravicini Bagliani, A., editors Roma, Italy: Edizioni di storia e letteratura
    • Murdoch, J. (1981a). Henry of Harclay and the infinite. In Maierù, A., Paravicini Bagliani, A., editors. Studi sul XIV secolo in memoria di Anneliese Maier. Roma, Italy: Edizioni di storia e letteratura, pp. 219-261.
    • (1981) Studi sul XIV Secolo in Memoria di Anneliese Maier , pp. 219-261
    • Murdoch, J.1
  • 57
    • 84989175742 scopus 로고
    • Mathematics and infinity in the later middle ages
    • In Dahlstrom, D. O., Ozar, D. T. and Sweeney, L., editors Washington DC
    • Murdoch, J. (1981b). Mathematics and infinity in the later middle ages. In Dahlstrom, D. O., Ozar, D. T. and Sweeney, L., editors. Infinity, Proceedings of the American Catholic Philosophical Association, Vol. 55. Washington, DC, pp. 40-58.
    • (1981) Infinity, Proceedings of the American Catholic Philosophical Association , vol.55 , pp. 40-58
    • Murdoch, J.1
  • 58
    • 33746551344 scopus 로고
    • Infinity and continuity
    • In Kretzmann, N., Kenny, A., Pinborg, J., editors Cambridge, UK: Cambridge University Press
    • Murdoch, J. (1982). Infinity and continuity. In Kretzmann, N., Kenny, A., Pinborg, J., editors. The Cambridge History of Later Medieval Philosophy. Cambridge, UK: Cambridge University Press, pp. 564-592.
    • (1982) The Cambridge History of Later Medieval Philosophy , pp. 564-592
    • Murdoch, J.1
  • 59
    • 84969642512 scopus 로고    scopus 로고
    • Philosophical method and Galileo's paradox of infinity
    • In B. van Kerchove, editor Hackensack, NJ: World Scientific
    • Parker, M. (2009). Philosophical method and Galileo's paradox of infinity. In B. van Kerchove, editor. New Perspectives on Mathematical Practices. Hackensack, NJ: World Scientific, pp. 76-113.
    • (2009) New Perspectives on Mathematical Practices , pp. 76-113
    • Parker, M.1
  • 61
    • 84989204126 scopus 로고
    • L'infinito nel pensiero di S. Tommaso e di G. Duns Scoto
    • Scotistici; Studia Scotistica 2 Rome, Italy
    • Petruzzellis, N. (1968). L'infinito nel pensiero di S. Tommaso e di G. Duns Scoto. In De Doctrina Ioannis Duns Scoti, Acta Congr. Scotistici; Studia Scotistica 2, Vol. 2. Rome, Italy, 435-445.
    • (1968) De Doctrina Ioannis Duns Scoti, Acta Congr , vol.2 , pp. 435-445
    • Petruzzellis, N.1
  • 64
    • 0039078826 scopus 로고
    • Basel, Switzerland: Birkhaüser
    • Purkert, W. (1987). Georg Cantor, 1845-1918. Basel, Switzerland: Birkhaüser.
    • (1987) Georg Cantor , pp. 1845-1918
    • Purkert, W.1
  • 65
    • 21244451640 scopus 로고
    • Rabbai Hasdai Crescas (1340-1410) on numerical infinities
    • Rabinovitch, N. (1970). Rabbai Hasdai Crescas (1340-1410) on numerical infinities. Isis, 61, 224-230.
    • (1970) Isis , Issue.61 , pp. 224-230
    • Rabinovitch, N.1
  • 67
    • 0003513971 scopus 로고
    • Cambridge, UK: Cambridge University Press
    • Russell, B. (1903). Principles of Mathematics. Cambridge, UK: Cambridge University Press.
    • (1903) Principles of Mathematics
    • Russell, B.1
  • 68
    • 8444221428 scopus 로고    scopus 로고
    • Thabit ibn Qurra on the infinite and other puzzles; Edition and translation of his discussions with ibn Usayyid
    • Sabra, A. (1997). Thabit ibn Qurra on the infinite and other puzzles; edition and translation of his discussions with ibn Usayyid. Zeitschrift für Geschichte der Arabisch-Islamischen Wissenschaften, 11, 1-33.
    • (1997) Zeitschrift für Geschichte der Arabisch-Islamischen Wissenschaften , vol.11 , pp. 1-33
    • Sabra, A.1
  • 72
    • 84989178595 scopus 로고
    • La paradoxe de la réflexivité des ensembles infinis: Leibniz, Goldbach, Bolzano
    • In Françoise Monnoyeur, editor Paris, France: Belin
    • Sebestik, J. (1992). La paradoxe de la réflexivité des ensembles infinis: Leibniz, Goldbach, Bolzano. In Françoise Monnoyeur, editor. Infini des Mathématiciens, Infini des Philosophes. Paris, France: Belin, pp. 175-191.
    • (1992) Infini des Mathématiciens, Infini des Philosophes , pp. 175-191
    • Sebestik, J.1
  • 74
    • 51449091934 scopus 로고
    • On an algorithm for the approximation of surds from a Provencąl treatise
    • In Hay C., editor Oxford, UK: Clarendon Press
    • Sesiano, J. (1988). On an algorithm for the approximation of surds from a Provencąl treatise. In Hay, C., editor. Mathematics from Manuscript to Print, 1300-1600. Oxford, UK: Clarendon Press, pp. 30-56.
    • (1988) Mathematics from Manuscript to Print 1300-1600 , pp. 30-56
    • Sesiano, J.1
  • 75
    • 84989173639 scopus 로고    scopus 로고
    • Vergleiche zwischen unendlichen Mengen bei Nicolas Oresme
    • In Folkerts M., editor Wiesbaden, Germany: Harrassowitz Verlag
    • Sesiano, J. (1996). Vergleiche zwischen unendlichen Mengen bei Nicolas Oresme. In Folkerts, M., editor. Mathematische Probleme im Mittelater-der lateinische und arabische Sprachbereich. Wiesbaden, Germany: Harrassowitz Verlag, pp. 361-378.
    • (1996) Mathematische Probleme im Mittelater-der Lateinische und Arabische Sprachbereich , pp. 361-378
    • Sesiano, J.1
  • 77
    • 84952497641 scopus 로고
    • Die Unendlichkeit bei Bernard Bolzano
    • In König, G., editor Göttingen, Germany: Vandenhoeck & Ruprecht
    • Spalt, D. (1990). Die Unendlichkeit bei Bernard Bolzano. In König, G., editor. Konzepte des mathematischen Unendlichen im 19. Jahrhundert. Göttingen, Germany: Vandenhoeck & Ruprecht, pp. 189-218.
    • (1990) Konzepte des Mathematischen Unendlichen im 19. Jahrhundert , pp. 189-218
    • Spalt, D.1
  • 78
    • 0000815146 scopus 로고
    • Sur l'extension de l'ordre partiel
    • Szpilrajn, E. (1930). Sur l'extension de l'ordre partiel. Fundamenta Mathematicae, 16, 386-389.
    • (1930) Fundamenta Mathematicae , vol.16 , pp. 386-389
    • Szpilrajn, E.1


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