Abstract
This chapter considers the highpoint of ‘classical’ logic, syllogistic, which is a simple system, but one that is very important in practice. It is a system of what is called the logic of ‘terms’, i.e. for the variables which appear in it we can substitute terms only, and not sentences. It can be axiomatized on the basis of the sentential calculus with the help of some special axioms and ‘syllogistic functors’.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
Bibliography
Russell, B. A. W. (3) Introduction to, Mathematical Philosophy, London, 1919.
Russell, B. A. W. (4) Mathematical Logic as based on the Theory of Types,Am. Journ. of Math. 3, 1908, p. 222 ff. Cf. P.M.
Chwistek, L. (1) Antynomie Logiki formalnej. Przegl. Filozoficzna 24, 1921.
Tarski, A. (2) Der Wahrheitsbegriff in den formalisierten Sprachen, Studia Philos. (Lwów) I, 1935.
Quine, W. V. O. (2) On the Theory of Types, JSL 3, 1938.
Quine, W. V. O. (3) Mathematical Logic, New York, 1940; 2nd edit. Cambridge, 1951.
Church, A. (2) A Formulation of the Simple Theory of Types, JSL 5, 1940.
Fraenkel, B. et Y. Bar-Hillel, Le problème des antinomies et ses développements récentes, Rev. d. metaphys et d. morale, 46, 1939.
Fitch, F. B. (1) A System of Formal Logic without an analogue to the Curry W-Operator, JSL 1, 1936.
Ackermann, W. (1) Ein System der typenfreien Logik I, Leipzig, 1941.
Bernays, 1. A System of axiomatic Set Theory, JSL 2, 1937; 6, 1941; 7, 1942; 8, 1943.
Behmann, H. (1) Zu den Widerspruchen der Logik und Mengenlehre, Jahresber. d. Math. Ver. 40 (1931).
Ushenko, A. M. The Problems of Logic, London, 1941.
Thomas, No (2) CS(n): An extension of CS, Dominican Studies I I (1949).
Thomas, No (3) A New Decision Procedure for Aristotle’s Syllogistic, Mind, 61, 1952.
Thomas, No (4) The Faris System and Syllogistic, JSL 20, 1955.
Black, H. (2) A New Method of Presentation of the Theory of the Syllogism, Journal of Philosophy, 1945.
Curry, H. B. (3) A Mathematical Treatment of the Rules of the Syllogism,Mind, 45 (1936) p. 209 ff.
Moisil, G. C. (2) Recherches sur le syllogisme, ibid. 25, 1939.
Hilbert, D. und P. Bernays, Grundlagen der Mathematik, Berlin, I, 1934; II, 1939, repr. Ann Arbor, Mich. 1944.
Chwistek, L. (3) New Foundations of formal Metamathematics, JSL 3, 1938.
Ackermann, W. (1) Ein System der typenfreien Logik I, Leipzig, 1941.
Bernays, P. A System of axiomatic Set Theory, JSL 2, 1937; 6, 1941; 7, 1942; 8, 1943.
Quine, W. V. O. (5) On the Logic of Quantification, JSL 10, 1945.
Russell, B. A. W. (2) On Denoting, Mind 14, 1905; repr. in Logic and Knowledge; Essays 1901–1950, New York, 1956.
Moore, G. E. Russell’s ‘Theory of Descriptions’ in The Philosophy of Bertrand Russell, edit. P. A. Schilpp, Evanston, Chicago, 1944.
Quine, W. V. O. (3) Mathematical Logic, New York, 1940; 2nd edit. Cambridge, 1951.
Rights and permissions
Copyright information
© 1959 Springer Science+Business Media Dordrecht
About this chapter
Cite this chapter
Bocheński, J.M. (1959). The Logic of Predicates and Classes. In: A Precis of Mathematical Logic. Synthese Library, vol 1. Springer, Dordrecht. https://doi.org/10.1007/978-94-017-0592-9_3
Download citation
DOI: https://doi.org/10.1007/978-94-017-0592-9_3
Publisher Name: Springer, Dordrecht
Print ISBN: 978-90-481-8329-6
Online ISBN: 978-94-017-0592-9
eBook Packages: Springer Book Archive