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Volumn , Issue , 2005, Pages

Higher-order Logic

Author keywords

Boolos; Deductive system; Higher order logic; Language; Logic; Model theory; Plural; Second order logic; Semantics

Indexed keywords


EID: 33750540865     PISSN: None     EISSN: None     Source Type: Book    
DOI: 10.1093/0195148770.003.0025     Document Type: Chapter
Times cited : (12)

References (51)
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    • Nominalist Platonism
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    • Hilbert, D., and W. Ackermann [1928], Grundzüge der theoretischen Logik, Berlin, Springer; translated as Principles of mathematical logic by L. Hammond, G. Leckie, and F. Steinhardt, New York, Chelsea, 1950. (Historical source. Still quite readable.).
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    • New York, Oxford University Press. (Extensive development of and justification for higher-order logic. Philosophical, mathematical, and historical treatment. Most of the book requires some background in logic. Extensive bibliography.)
    • Shapiro, S. [1991], Foundations without foundationalism: A case for second-order logic, New York, Oxford University Press. (Extensive development of and justification for higher-order logic. Philosophical, mathematical, and historical treatment. Most of the book requires some background in logic. Extensive bibliography.)
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    • Shapiro, S. [1999], "Do not claim too much: Second-order logic and first-order logic," Philosophia Mathematica, 3rd ser., 7, 42-64. (Reply to some of the critics of.)
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    • Shapiro, S. [2001], "Systems between first-order logic and second-order logics," in Handbook of philosophical logic, vol. 1, 2nd ed., edited by D.M. Gabbay and F. Geunthner, Dordrecht, Kluwer Academic Publishers, 131-187.
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    • Shapiro, S.1
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    • Einige Bemerkungen zur axiomatischen Begründung der Mengenlehre
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    • Skolem, T. [1922], "Einige Bemerkungen zur axiomatischen Begründung der Mengenlehre," in Matematikerkongressen i Helsingfors den 4-7 Juli 1922, Helsinki, Akademiska Bokhandeln, 217-232; translated as "Some remarks on axiomatized set theory" in van, 291-301.
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    • A philosophical letter of Alfred Tarski
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    • Tharp, L. [1975], "Which logic is the right logic?," Synthèse 31, 1-31; reprinted in, 47-67.
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    • Van Heijenoort, J. (editor) [1967], From Frege to Gödel, Cambridge, MA, Harvard University Press. (Collection of many original papers in logic, translated into English. Includes works by Frege, Peano, Dedekind, Cantor, Hilbert, Russell, Zermelo, Löwenheim, Skolem, Weyl, Ackermann, von Neumann, Bernays, and Gödel.)
    • (1967) From Frege to Gödel
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    • Kreisel, the continuum hypothesis and second-order set theory
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    • Weston, T. [1976], "Kreisel, the continuum hypothesis and second-order set theory," Journal of Philosophical Logic 5, 281-298; reprinted in, 385-402.
    • (1976) Journal of Philosophical Logic , vol.5 , pp. 281-298
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