Abstract
For me, mathematical concepts are real. Mathematics is the logical study of mathematical concepts. Logic is rational reasoning, the reasoning that we use in making compelling deductions (even in our discussions of alternative “logics”.)
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References
Bernays, P.: A system of axiomatic set theory. J. Symbolic Logic, 1937–1954 = the first pages of reference [7] below
Cohen, P.J.: The independence of the continuum hypothesis. Proc. Nat. Acad, of Sciences 50 (1963) 1143–1148.
Cohen, P.J.: The independence of the continuum hypothesis. Proc. Nat. Acad, of Sciences 51 (1964) 105–110
Gödel, K.: Über formal unentscheidbare Sätze der Principia Mathematica und verwandter Systeme I. Monatshefte für Math, und Physik 38 (1931) 173–198
Gödel, K.: The consistency of the axiom of choice and of the generalized continuum hypothesis with the axioms of set theory. Princeton, N.J., 1940
Gödel, K.: What is Cantor’s continuum problem? Amer. Math. Monthly 54 (1947) 515–525
Lévy, A.: The role of classes in set theory, 1973 = Pages 173–215 of reference [7] below
Müller, G.H., ed.: Sets and classes; on the work of Paul Bernays. Amsterdam, 1976
Zermelo, E.: Beweis, dass jede Menge wohlgeordnet werden kann. Math. Annalen 59 (1904) 514–516
Zermelo, E.: Neuer Beweis für die Möglichkeit einer Wohlordnung. Math. Annalen 65 (1908) 107–128
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© 1982 Birkhäuser Verlag Basel
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Sard, A. (1982). A View of Mathematics. In: Schempp, W., Zeller, K. (eds) Multivariate Approximation Theory II. International Series of Numerical Mathematics / Internationale Schriftenreihe zur Numerischen Mathematik / Série internationale d’Analyse numérique, vol 61. Birkhäuser Basel. https://doi.org/10.1007/978-3-0348-7189-1_26
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DOI: https://doi.org/10.1007/978-3-0348-7189-1_26
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