메뉴 건너뛰기




Volumn 39, Issue 117, 2007, Pages 61-86

The completeness of the real line

Author keywords

Continuity; Geometry; Infinitesimals; Intuition; Space

Indexed keywords


EID: 70749110086     PISSN: 00111503     EISSN: 18704905     Source Type: Journal    
DOI: 10.22201/iifs.18704905e.2007.583     Document Type: Review
Times cited : (4)

References (51)
  • 5
    • 0011343336 scopus 로고
    • Stetigkeit und irrationale Zahlen
    • Page references are to Beman's English translation Dedekind 1963.)
    • Dedekind, Richard, 1872, Stetigkeit und irrationale Zahlen, Vieweg, Braunschweig. (Page references are to Beman's English translation, pp. 1-27 in Dedekind 1963.)
    • (1872) Vieweg, Braunschweig. , pp. 1-27
    • Dedekind, R.1
  • 6
    • 70749147275 scopus 로고    scopus 로고
    • i Hume's Atomism about Events: A Response to Ulrich Meyer
    • Dummett, Michael, 2005, "Hume's Atomism about Events: a Response to Ulrich Meyer", Philosophy, vol. 80, pp. 141-144
    • (2005) Philosophy , vol.80 , pp. 141-144
    • Dummett, M.1
  • 7
    • 42649107828 scopus 로고    scopus 로고
    • i Is Time a Continuum of Instants?
    • -, 2000, "Is Time a Continuum of Instants?", Philosophy, vol. 75, pp. 497-515
    • (2000) Philosophy , vol.75 , pp. 497-515
    • Dummett, M.1
  • 8
    • 28244451575 scopus 로고    scopus 로고
    • i The Rise of Non-Archimedean Mathematics and the Roots of a Misconception I: The Emergence of Non-Archimedean Systems of Magnitudes
    • Ehrlich, Philip, 2006, "The Rise of Non-Archimedean Mathematics and the Roots of a Misconception I: The Emergence of Non-Archimedean Systems of Magnitudes", Archive for History of Exact Sciences, vol. 60, no. 1, pp. 1-121
    • (2006) Archive for History of Exact Sciences , vol.60 , pp. 1-121
    • Ehrlich, P.1
  • 10
    • 0003717547 scopus 로고
    • trans., introd., and commentary Thomas L. Heath, Dover, New York, 3 vols
    • Euclid, 1956, The Thirteen Books of Euclid's Elements, trans., introd., and commentary Thomas L. Heath, Dover, New York, 3 vols
    • (1956) The Thirteen Books of Euclid's Elements
    • Euclid1
  • 11
    • 0039108467 scopus 로고    scopus 로고
    • i Why a Little Bit Goes a Long Way: Logical Foundations of Scientifically Applicable Mathematics
    • Oxford University Press, New York, pp
    • Feferman, Solomon, 1998, "Why a Little Bit Goes a Long Way: Logical Foundations of Scientifically Applicable Mathematics", In the Light of Logic, Oxford University Press, New York, pp. 284-298
    • (1998) In the Light of Logic , pp. 284-298
    • Feferman, S.1
  • 14
    • 4243539729 scopus 로고
    • i What is Cantor's Continuum Problem?
    • Gödel, Kurt, 1947 (1960), "What is Cantor's Continuum Problem?", originally published in The American Mathematical Monthly, vol. 54, pp. 515-525,1947. (Page references are to the reprinting of the expanded 1960 version in Benacerraf and Putnam 1983, pp. 420-485.)
    • (1947) The American Mathematical Monthly , vol.54 , pp. 515-525
    • Gödel, K.1
  • 19
    • 60950595048 scopus 로고    scopus 로고
    • Logique et mathématique du Continu chez Charles Sanders Peirce
    • Doctoral Thesis, École des Hautes Études en Sciences Sociales, Paris
    • Havenel, Jérôme, 2006, "Logique et mathématique du Continu chez Charles Sanders Peirce", Doctoral Thesis, École des Hautes Études en Sciences Sociales, Paris
    • (2006)
    • Havenel, J.1
  • 20
    • 0011894114 scopus 로고
    • Hilbert, David, 1971, Foundations of Geometry, 2nd ed. Open Court, La Salle. (Translated from the 10th German edition by Leo Unger; revised and enlarged by Paul Bernays.)
    • (1971) Foundations of Geometry
    • Hilbert, D.1
  • 22
    • 0005655845 scopus 로고
    • i Quantum Gravity
    • P. Davies ed, Cambridge University Press, Cambridge, pp
    • Isham, Chris, 1989, "Quantum Gravity", in P. Davies (ed.), The New Physics, Cambridge University Press, Cambridge, pp. 70-93
    • (1989) The New Physics , pp. 70-93
    • Isham, C.1
  • 26
    • 70749092114 scopus 로고    scopus 로고
    • i Dummett on the Time-Continuum
    • Meyer, Ulrich, 2005, "Dummett on the Time-Continuum", Philosophy, vol. 80, pp. 135-140
    • (2005) Philosophy , vol.80 , pp. 135-140
    • Meyer, U.1
  • 27
    • 60950668366 scopus 로고    scopus 로고
    • i The Genesis of the Peircean Continuum
    • Moore, Matthew E., 2007, "The Genesis of the Peircean Continuum", Transactions of the Charles S. Peirce Society, vol. 43, no. 3, pp. 425-469
    • (2007) Transactions of the Charles S. Peirce Society , vol.43 , Issue.3 , pp. 425-469
    • Moore, M.E.1
  • 28
    • 70749087801 scopus 로고    scopus 로고
    • i Archimedean Intuitions
    • -, 2002, "Archimedean Intuitions", Theoria, vol. 68, pp. 185-204
    • (2002) Theoria , vol.68 , pp. 185-204
    • Moore, M.E.1
  • 31
    • 34249828052 scopus 로고
    • i Platonism and Mathematical Intuition in Kurt Gödel's Thought
    • Parsons, Charles, 1995, "Platonism and Mathematical Intuition in Kurt Gödel's Thought", Bulletin of Symbolic Logic, vol. 1, no. 1, pp. 44-74
    • (1995) Bulletin of Symbolic Logic , vol.1 , pp. 44-74
    • Parsons, C.1
  • 32
    • 0040019682 scopus 로고
    • i Mathematical Intuition
    • 95-113 Page references are to the reprinting in Hart, 1996
    • -, 1979-1980, "Mathematical Intuition", Proceedings of the Aristotelian Society, vol. 80, pp. 145-68. (Page references are to the reprinting in Hart 1996, pp. 95-113.)
    • (1979) Proceedings of the Aristotelian Society , vol.80 , pp. 145-168
  • 33
    • 70749122575 scopus 로고
    • ed. Christian J.W. Kloesel and Nathan Houser, Indiana University Press, Bloomington. 1992a
    • Peirce, Charles Sanders, 1992a, The Essential Peirce 1 (1867-1893), ed. Christian J.W. Kloesel and Nathan Houser, Indiana University Press, Bloomington
    • (1867) The Essential Peirce , vol.1
    • Peirce, C.S.1
  • 34
    • 0003975659 scopus 로고
    • ed. K. Ketner, introd. K. Ketner and H. Putnam, Harvard University Press, Cambridge
    • -, 1992b, Reasoning and the Logic of Things, ed. K. Ketner, introd. K. Ketner and H. Putnam, Harvard University Press, Cambridge
    • (1992) Reasoning and the Logic of Things
    • Peirce, C.S.1
  • 35
    • 0009195796 scopus 로고
    • ed. Carolyn Eisele, Mouton, The Hague, 3 vols
    • Peirce, Charles Sanders, 1976, New Elements of Mathematics, ed. Carolyn Eisele, Mouton, The Hague, 3 vols
    • (1976) New Elements of Mathematics
    • Peirce, C.S.1
  • 36
    • 0003426044 scopus 로고
    • i The Collected Papers of Charles Sanders Peirce, ed
    • Harvard University Press, Cambridge, 8 vols
    • -, 1931-1958, The Collected Papers of Charles Sanders Peirce, ed. Charles Hartshorne, Paul Weiss and Arthur Burks, Harvard University Press, Cambridge, 8 vols
    • (1931) Charles Hartshorne. Paul Weiss and Arthur Burks
    • Peirce, C.S.1
  • 37
    • 84857366616 scopus 로고
    • i Letter to the Editor
    • Reprinted in Peirce 1931-1958, pp. 360-365
    • -, 1900, "Letter to the Editor", Science, vol. 2, pp. 430-433. (Reprinted in Peirce 1931-1958, pp. 360-365.)
    • (1900) Science , vol.2 , pp. 430-433
    • Peirce, C.S.1
  • 42
    • 8444242073 scopus 로고
    • i The Law of Mind
    • 1992 312-333 Page references are to the reprinting in Peirce
    • -, 1892, "The Law of Mind", Monist, vol. 2, pp. 533-559. (Page references are to the reprinting in Peirce 1992a, pp. 312-333.)
    • (1892) Monist , vol.2 , pp. 533-559
  • 43
    • 79959047227 scopus 로고
    • i Peirce's Continuum
    • ed. K.L. Ketner, Harvard University Press, Cambridge, pp
    • Putnam, Hilary, 1992, "Peirce's Continuum", Reasoning and the Logic of Things, ed. K.L. Ketner, Harvard University Press, Cambridge, pp. 37-54
    • (1992) Reasoning and the Logic of Things , pp. 37-54
    • Putnam1    Hilary2
  • 45
    • 0004232766 scopus 로고    scopus 로고
    • rev. ed, Princeton University Press, Princeton
    • Robinson, Abraham, 1996, Non-Standard Analysis, rev. ed., Princeton University Press, Princeton
    • (1996) Non-Standard Analysis
    • Robinson, A.1
  • 47
    • 0007383359 scopus 로고
    • 3rd ed, Publish or Perish, Houston
    • Spivak, Michael, 1994, Calculus, 3rd ed., Publish or Perish, Houston
    • (1994) Calculus
    • Spivak, M.1
  • 48
    • 3142670237 scopus 로고    scopus 로고
    • i Bromver and Weyl: The Phenomenology and Mathematics of the Intuitive Continuum
    • Van Atten, Mark, Dirk van Dalen and Richard Tieszen, 2002, "Bromver and Weyl: The Phenomenology and Mathematics of the Intuitive Continuum", Philosophia Mathematica, vol. 10, no. 2, pp. 203-226
    • (2002) Philosophia Mathematica , vol.10 , Issue.2 , pp. 203-226
    • Van Atten, M.1    D.van Dalen2    Tieszen, R.3
  • 49
    • 34250387166 scopus 로고
    • i Kreisel, the Continuum Hypothesis and Second Order Set Theory
    • Weston, Thomas, 1976, "Kreisel, the Continuum Hypothesis and Second Order Set Theory", Journal of Philosophical Logic, vol. 5, pp. 281-298
    • (1976) Journal of Philosophical Logic , vol.5 , pp. 281-298
    • Weston, T.1
  • 50
    • 0009286582 scopus 로고
    • Die heutige Erkenntnislage in der Mathematik
    • (Page references are to Mancosu's English translation in Mancosu 1998, pp. 123-142.)
    • Weyl, Hermann, 1925, "Die heutige Erkenntnislage in der Mathematik", Symposion, vol. 1, pp. 1-32. (Page references are to Mancosu's English translation in Mancosu 1998, pp. 123-142.)
    • (1925) Symposion , vol.1 , pp. 1-32
    • Weyl, H.1
  • 51
    • 0001638843 scopus 로고
    • Über die neue Grundlagenkrise der Mathematik
    • (Page references are to Mancosu's English translation in Mancosu 1998, pp. 86-118.)
    • -, 1921, "Über die neue Grundlagenkrise der Mathematik", Mathematische Zeitschrift, vol. 10, pp. 39-79. (Page references are to Mancosu's English translation in Mancosu 1998, pp. 86-118.)
    • (1921) Mathematische Zeitschrift , vol.10 , pp. 39-79
    • Weyl, H.1


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.