Emil Leon Post

From MANY-VALUED LOGIC, 1969 by Nicholas Rescher

The actual inauguration of many-valued logic must be dated from the pioneering papers of the Pole Jan Łukasiewicz and the American Emil L. Post, published in the early 1920s, in which the first developed systematizations of many-valued logic are presented.¹   (etc).

¹See Łukasiewicz (1920) and Post (1921). The former of these is translated in S. McCall (ed.), Polish Logic : 1920-1939 (Oxford, 1967), pp. 16-18 ; and the latter is reprinted in J. van Jeijenoort (ed.), From Frege to Gödel : A Source Book in Mathematical Logic, 1879-1931 (Cambridge, Mass., 1967), pp. 265-283.

(pages 7-8).

 

Post discovered his family of many-valued systems independently of the work of Łukasiewicz. His findings were presented in some six pages of his 1921 paper, and he never again returned to the subject in any publication. Whereas Łukasiewicz began with a 3-valued system that he afterwards generalized to n-valued (and even to infinitely many values), Post presented his n-valued systems in full generality.⁹ However, he did not contemplate the idea of infinite-valued systems although his ideas for system construction can in fact be extended to the infinite-valued case (etc). Still, viewed as systems of many-valued propositional logic, Post's systems have a serious shortcoming. For Post's own semantical interpretation of his systems, the only one that has been devised to date, proceeds in terms of sets of propositions, and is not a propositional interpretation at all.   (page 9).

⁹ Moreover, whereas the systems of Łukasiewicz allow for only one designated (truth-like) truth-valued, Post introduced an arbitrary number of designated truth-values. [?]

New York, etc. : McGraw-Hill 1969.

From THE STRUCTURE OF THE SYSTEM OF STRICT IMPLICATION by C. I. Lewis

The System of Strict Implication, as presented in Chapter V of A Survey of Symbolic Logic (University of California Press, 1918), contained an error with respect to one postulate. This was pointed out by Dr. E. L. Post, and was corrected by me in the Journal of Philosophy, Psychology, and Scientific Method (XVII [1920], 300). [etc] Appendix II, Symbolic Logic (1932) by C. I. Lewis and C. H. Langford. p. 492. -------------------------------------------------------------------------------- The Two-Valued Iterative Systems Of Mathematical Logic BY EMIL L. POST PRINCETON PRINCETON UNIVERSITY PRESS LONDON : HUMPHREY MILFORD OXFORD UNIVERSITY PRESS 1941 -------------------------------------------------------------------------------- Copyright 1941 PRINCETON UNIVERSITY PRESS PRINTED IN U.S.A. Lithoprinted by Edwards Brothers, Inc., Lithoprinters Ann Arbor, Michigan, 1941 -------------------------------------------------------------------------------- Dedicated to CASSIUS J. KEYSER in one of whose pedagogical devi- ces the author belatedly recognized the true source of his truth-table me- thod. -------------------------------------------------------------------------------- BIBLIOGRAPHY [ selections. ] 12. W. S. Jevons. Pure Logic London, 1864. 14. Stanislaw Lesniewski. Grudz�ge eines Neuen Systems der Grudlage der Mathematik. Fund. Math., Vol. 14, (1929), pp. 1 - 81. 15. C. I. Lewis and C. H. Langford. Symbolic Logic. New York, 1932. 22. E. L. Post. Determination of all Closed Systems of Truth Tables. Abstract, Bull. Amer. Math. Soc., Vol. 26, (1920), p. 437. 23. E. L. Post Introduction to A General Theory of Elementary Propositions. Amer. Jour. Math., Vol. 43, 1921), pp, 163 - 185. 25. Josiah Royce. An Extension of the Algebra of Logic. Jour. Philos. etc., Vol. 10, (1913), pp. 617 - 633. 27. H. M. Sheffer. A Set of Five Independent Postulates for Boolean Algebras, with Application to Logical Constants. Trans. Amer. Math. Soc., Vol. 14, (1913), pp. 481 - 488. 32. Oswald Veblen. The Cambridge Colloquium Lectures. 1916, Part II. (Analysis Situs). 42. Eustachy Zylinski. Some Remarks Concerning the Theory of Deduction. Fund. Math., Vol. 7, (1925), pp. 203 - 209. ( pages 119 - 122.) -------------------------------------------------------------------------------- Bibliographic : 1. Post, Emil Leon, 1897-1954. The two-valued iterative systems of mathematical logic,, by Emil L. Post. Princeton, Princeton University Press, 1941. 122 p. 23 cm. Series title: Annals of mathematics studies ; no. 5. 2. Post, Emil Leon, 1897-1954. Works. 1994. Solvability, provability, definability : the collected works of Emil L. Post /, Martin Davis, editor. Boston : Birkh�user, 1994. xxviii, 554 p. ; 27 cm. Series title: Contemporary mathematicians 3. Post, Emil Leon, 1897-1954. The two-valued iterative systems of mathematical logic,, by Emil L. Post. Princeton, Princeton University Press, 1941. New York : Kraus Reprint, 1965. 122 p. ; 23 cm. 4. Uspenskii, V. A.. Mashina Posta /, V.A. Uspenskii. Moskva : "Nauka," Glav. red. fiziko-matematicheskoi lit-ry, 1979. 94 p. : ill. ; 21 cm. Series title: Populiarnye lektsii po matematike ; vyp. 54 Language: Russian 5. Uspenskii, V. A.. Mashina Posta /, V.A. Uspenskii. Moskva : "Nauka," Glav. red. fiziko-matematicheskoi lit-ry, 1988. 95 p. : ill. ; 21 cm. Series title: Populiarnye lektsii po matematike ; vyp. 54, Populiarnye lektsii po matematike ; vyp. 54 Language: Russian 6. Uspenskii, V. A.. Mashina Posta /, V.A. Uspenskii. Izd. 2., perer. Moskva : "Nauka," Glav. red. fiziko-matematicheskoi lit-ry, 1988. 95 p. : ill. ; 21 cm. Series title: Populiarnye lektsii po matematike ; vyp. 54 Language: Russian 7. Post, Emil Leon, 1897-1954. The two-valued iterative systems of mathematical logic,, by Emil L. Post Princeton, Princeton University Press, 1941; New York, Kraus Reprint Corp., 1965 122 p. illus. 23 cm Series title: Annals of mathematics studies ; no. 5. ( University of California Catalogue )