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Functions of Propositions

Published online by Cambridge University Press:  12 March 2014

M. J. Cresswell
M. J. Cresswell*
Affiliation:
Victoria University of Wellington
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Extract

In [1] (p. 131 et seq) Professor A. N. Prior suggests a calculus of functions of propositions in which the range of the function variables is not restricted to truth functions.1 If f, g, … etc. represent such variables and we have quantification over all variables we can introduce propositional identity by definition as (ƒ)(ƒp ⊃ ƒq) Alternatively identity may be primitive with the usual axioms and schemata (v.e.g. [4] p. 190 et seq). We shall refer to such systems as ‘functorial calculi’2 (abbreviated as FC).

Type
Research Article
Information
The Journal of Symbolic Logic , Volume 31 , Issue 4 , December 1966 , pp. 545 - 560
Copyright
Copyright © Association for Symbolic Logic 1997

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References

[1]Prior, A. N., Time and Modality, Oxford 1957.Google Scholar
[2]Tarski, A., Logic, Semantics and Metamathematics, Oxford 1956.Google Scholar
[3]Goodstein, R. L., On the formalization of indirect discourse, this Journal, Vol. 23 (1958), p. 417.Google Scholar
[4]Prior, A. N., Is the concept of referential opacity really necessary? Acta Philosophica Fennica, Fasc. 16 (1963), Modal and Many-Valued Logics, pp. 189–199.Google Scholar
[5]Prior, A. N., Formal Logic, Oxford 1955 (2nd. ed. 1961).Google Scholar
[6]Jonathan Cohen, L., The Diversity of Meaning, Methuen 1962.Google Scholar
[7] Articles by Prior, A. N. and Cohen, L. J. in Philosophical Studies, vol. XII (1961), pp. 72–78, Vol. XIV (1963), pp. 12–28, Vol. XV (1954), pp. 33–40.Google Scholar
[8]Smiley, T. J., Prepositional functions, Proceedings of the Aristotelian Society, Supplementary Volume XXXIV (1960), pp. 33–46.Google Scholar
[9]Hilbert, D. and Ackermann, W., Principles of Mathematical Logic (English translation of Grundzuge der Theoretischen Logik, Berlin 1928, 2nd ed. 1938), Chelsea 1951.Google Scholar
[10]Church, Alonzo, Introduction to Mathematical Logic, vol. I, Princeton 1956.Google Scholar
[11]Church, Alonzo, A formulation of the simple theory of Types, this Journal, Vol. 5 (1940), p. 56.Google Scholar
[12]Henkin, Leon, Completeness in the theory of types, this Journal, Vol. 15 (1950), pp. 81–91.Google Scholar
[13]Rosser, J. B. and Turquette, A. R., Many-Valued Logics, North Holland, 1952.Google Scholar
[14]Prior, A. N., The interpretation of two systems of modality, Journal of Computing Systems, vol. 1, no 4 (1954), pp. 217–218.Google Scholar
[15]Prior, A. N., Quantification and modality, Notre Dame Journal of Formal Logic, vol. III (1963), p. 142.Google Scholar
[16]Henkin, Leon, The completeness of the first-order functional calculus, this Journal, Vol. 14 (1949), p. 159.Google Scholar
[17]Kleene, S. C., Introduction to Metamathematics, North Holland, 1952.Google Scholar
[18]Richard Montague, Syntactical treatments of modality, Acta Philosophica Fennica, (1963), Modal and Many-valued Logics, pp. 153–166.Google Scholar
[19]Wang, Hao, Logic of many-sorted theories, this Journal, Vol. 17 (1952), pp. 105–116.Google Scholar
[20]Hao, Wang, A Survey of Mathematical Logic, Amsterdam and Peking, 1963.Google Scholar