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Alonzo Church's Contributions to Philosophy and Intensional Logic

Published online by Cambridge University Press:  15 January 2014

C. Anthony Anderson
C. Anthony Anderson*
Affiliation:
Department of Philosophy, University of California, Santa Barbara, Santa Barbara, CA 93106, USA.E-mail: caanders@humanitas.ucsb.edu
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Extract

§0. Alonzo Church's contributions to philosophy and to that most philosophical part of logic, intensional logic, are impressive indeed. He wrote relatively few papers actually devoted to specifically philosophical issues, as distinguished from related technical work in logic. Many of his contributions appear in reviews for The Journal of Symbolic Logic, and it can hardly be maintained that one finds there a “philosophical system”. But there occur a clearly articulated and powerful methodology, terse arguments, often of “crushing cogency”, and philosophical observations of the first importance.

Many of the less formal philosophical contributions center around questions concerning meaning, but there are important clarifications and insights into matters of the epistemology and ontology of the sciences, especially the formal sciences.

1.1. The logistic method. Church's writings on philosophical matters exhibit an unwavering commitment to what he called the “logistic method”. The term did not catch on and now one would just speak of “formalization”. The use of these ideas is now so common and familiar among logicians and logically-oriented philosophers that they are simply taken for granted. But they deserve to be celebrated and re-emphasized, for there are (still) philosophers who seriously underestimate and even consciously reject these techniques.

Type
Research Article
Information
Bulletin of Symbolic Logic , Volume 4 , Issue 2 , June 1998 , pp. 129 - 171
Copyright
Copyright © Association for Symbolic Logic 1998

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References

REFERENCES

[1] Anderson, C. Anthony, Some new axioms for the logic of sense and denotation: Alternative (0), Noûs, vol. 14 (1980), pp. 217–234.CrossRefGoogle Scholar
[2] Anderson, C. Anthony, Some difficulties concerning Russellian intensional logic, Noûs, vol. 20 (1986), pp. 35–46.CrossRefGoogle Scholar
[3] Anderson, C. Anthony and Zeleny, Mikhail (editors), Logic, meaning and computation: Essays in memory of Alonzo Church, Kluwer Academic Publishers, forthcoming.CrossRefGoogle Scholar
[4] Ayer, A. J., Language, truth and logic, Dover Publications, Inc., New York, 1946.Google Scholar
[5] Carnap, Rudolf, The logical syntax of language, Kegan Paul Trench, Trubner & Co., London, 1937.Google Scholar
[6] Carnap, Rudolf, Meaning and necessity, The University of Chicago Press, Chicago, Illinois, 1947.Google Scholar
[7] Carnap, Rudolf, The methodological character of theoretical concepts, The foundations of science and the concepts of psychology and psychoanalysis (Feigl, Herbert and Scriven, Michael, editors), Minnesota Studies in the Philosophy of Science, vol. 1, University of Minnesota Press, Minneapolis, 1956.Google Scholar
[8] Church, Alonzo, Review of Alfred North Whitehead and Bertrand Russell, Principia Mathematica, second edition, volumes II and III, Bulletin of the American Mathematical Society, vol. 34 (1928), pp. 237–240.CrossRefGoogle Scholar
[9] Church, Alonzo, A set of postulates for the foundation of logic, Annals of Mathematics, vol. 33 (1932), pp. 346–366.CrossRefGoogle Scholar
[10] Church, Alonzo, A set of postulates for the foundation of logic (second paper), Annals of Mathematics, vol. 34 (1933), pp. 839–864.CrossRefGoogle Scholar
[11] Church, Alonzo, A formulation of the simple theory of types, Journal of Symbolic Logic, vol. 5 (1940), pp. 56–68.CrossRefGoogle Scholar
[12] Church, Alonzo, The calculi of lambda-conversion, Annals of Mathematics Studies, no. 6, Princeton University Press, Princeton, 1941.Google Scholar
[13] Church, Alonzo, Truth, semantical, Dictionary of philosophy (Runes, D. D., editor), Philosophical Library, New York, 1942.Google Scholar
[14] Church, Alonzo, Frege, (Friedrich Ludwig) Gottlob, Dictionary of philosophy (Runes, D. D., editor), Philosophical Library, New York, 1942.Google Scholar
[15] Church, Alonzo, Carnap's Introduction to Semantics, The Philosophical Review, vol. 52 (1943), pp. 298–304.CrossRefGoogle Scholar
[16] Church, Alonzo, Introduction to mathematical logic, Part I, Princeton University Press, Princeton, 1944.Google Scholar
[17] Church, Alonzo, A formulation of the logic of sense and denotation (abstract), Journal of Symbolic Logic, vol. 11 (1946), p. 31.Google Scholar
[18] Church, Alonzo, On Carnap's analysis of statements of assertion and belief, Analysis, vol. 10 (1950), pp. 97–99.CrossRefGoogle Scholar
[19] Church, Alonzo, A formulation of the logic of sense and denotation, Structure, method and meaning (Henle, Paul et al., editors), The Liberal Arts Press, New York, 1951.Google Scholar
[20] Church, Alonzo, The needfor abstract entities in semantic analysis, American Academy of Arts and Sciences Proceedings, vol. 80 (1951), pp. 110–133, reprinted as Intensional Semantics in Martinich [50].Google Scholar
[21] Church, Alonzo, Intensional isomorphism and identity of belief, Philosophical Studies, vol. 5 (1954), pp. 65–73.CrossRefGoogle Scholar
[22] Church, Alonzo, Introduction to mathematical logic, vol. 1, Princeton University Press, Princeton, New Jersey, 1956.Google Scholar
[23] Church, Alonzo, Propositions and sentences, The problem of universals: A symposium (Bochenski, J., editor), University of Notre Dame Press, Notre Dame, 1956.Google Scholar
[24] Church, Alonzo, Logic and analysis, Atti del XII Congresso Internazionale de Filosofia, vol. 4 (1958), pp. 71–81.Google Scholar
[25] Church, Alonzo, Mathematics and logic, Logic, methodology and philosophy of science, Proceedings of the 1960 international congress (Nagel, Ernest, Suppes, Patrick, and Tarski, Alfred, editors), Stanford University Press, Stanford, 1962.Google Scholar
[26] Church, Alonzo, Denotation, in Encyclopedia Brittanica, 1964.Google Scholar
[27] Church, Alonzo, Paul J. Cohen and the continuum problem, Proceedings of international congress of mathematicians (Pterovsky, I. G., editor), Mir Publishers, Moscow, 1968, pp. 15–20.Google Scholar
[28] Church, Alonzo, On Scheffier's approach to indirect quotation, Semantica filosofica: Problemas y discussiones (Simpson, Thomas Moro, editor), Siglo XXI Argentina Editores S. A., Buenos Aires, 1973.Google Scholar
[29] Church, Alonzo, Postscript 1968, Semanticafilosofica: Problemasy discusiones (Simpson, Thomas Moro, editor), Siglo XXI Argentina Editores S. A., 1973, postscript, in Spanish, to the Spanish translation of [VIII 45, 1943].Google Scholar
[30] Church, Alonzo, Outline of a revised formulation of the logic of sense and denotation (Part I), Noûs, vol. 7 (1973), pp. 24–33.CrossRefGoogle Scholar
[31] Church, Alonzo, Outline of a revised formulation of the logic of sense and denotation (Part II), Noûs, vol. 8 (1974), pp. 135–156.CrossRefGoogle Scholar
[32] Church, Alonzo, A remark concerning Quine's paradox about modality, Analisis Filosófico, vol. 2 (1982), in Spanish; English translation in Salmon and Soames [62].Google Scholar
[33] Church, Alonzo, Russell's theory of identity of propositions, Philosophia Naturalis, vol. 21 (1984), pp. 513–522.Google Scholar
[34] Church, Alonzo, A revised formulation of the logic of sense and denotation, Alternative (1), Noûs, vol. 27 (1993), pp. 141–157.CrossRefGoogle Scholar
[35] Church, Alonzo, Intensionality and the paradox of the name relation, Themes from Kaplan (Almog, Joseph, Perry, John, and Wettstein, Howard, editors), Oxford University Press, New York and Oxford, 1989.Google Scholar
[36] Davidson, Donald, The method of extension and intension, The philosophy of Rudolf Carnap (Schilpp, P. A., editor), Open Court, La Salle, Illinois, 1963, pp. 311–349.Google Scholar
[37] Davidson, Donald, The structure and content of truth, The Journal of Philosophy, vol. 87 (1990), pp. 279–328.CrossRefGoogle Scholar
[38] Dummett, Michael, Truth, Proceedings of the Aristotelian society, new series, vol. 59, 1959, reprinted with a postscript in his Truth and other enigmas , Cambridge, Massachusetts, Harvard University Press, 1978, pp. 141–162.CrossRefGoogle Scholar
[39] Gödel, Kurt, Russell's mathematical logic, The philosophy of Bertrand Russell (Schilpp, P. A., editor), Tudor Publishing Co., New York, 1944, pp. 125–153.Google Scholar
[40] Goodman, Nelson, On likeness of meaning, Analysis, vol. 10 (1949), pp. 1–7.CrossRefGoogle Scholar
[41] Goodman, Nelson, On some differences about meaning, Analysis, vol. 13 (1953), pp. 90–96.CrossRefGoogle Scholar
[42] Goodman, Nelson, Problems and projects, Bobbs-Merrill Company, Inc., Indianapolis and New York, 1972.Google Scholar
[43] Grice, Paul, Method in philosophical psychology (from the banal to the bizarre), Proceedings and Addresses of the American Philosophical Association, vol. 48 (1974–1975), pp. 23–53.CrossRefGoogle Scholar
[44] Kaplan, David, The language of L-Church-O, unpublished notes, 1974.Google Scholar
[45] Kaplan, David, How to Russell a Frege-Church, Journal of Philosophy, vol. 72 (1975), pp. 716–729.CrossRefGoogle Scholar
[46] Kaplan, David, Significance and analyticity: A comment on some recent proposals of Carnap, RudolfCarnap, logical empiricist (Hintikka, Jaakko, editor), D. Reidel Publishing Company, Dordrecht and Boston, 1975.Google Scholar
[47] Kaplan, David, On the logic of demonstratives, Contemporary perspectives in the philosophy of language (French, Peter A., Uehling, Theodore E. Jr., and Wettstein, Howard K., editors), University of Minnesota Press, Minneapolis, 1979.Google Scholar
[48] Kemeny, John, A new approach to semantics: Part II, Journal of Symbolic Logic, vol. 21 (1956), pp. 149–161.CrossRefGoogle Scholar
[49] Kripke, Saul, A puzzle about belief, Meaning and use (Margalit, A., editor), Reidel Publishing Company, Dordrecht, 1979, pp. 239–283.CrossRefGoogle Scholar
[50] Martinich, A. P. (editor), The philosophy of language, Oxford University Press, New York and London, 1985.Google Scholar
[51] Mates, Benson, Synonymity, University of California Publications in Philosophy, vol. 25 (1950), pp. 201–226.Google Scholar
[52] Myhill, John, Problems arising in the formalization of intensional logic, Logique et Analyse, vol. 1 (1958), pp. 74–83.Google Scholar
[53] Parsons, Charles, Intensional logic in extensional language, Journal of Symbolic Logic, vol. 47 (1982), pp. 289–328.CrossRefGoogle Scholar
[54] Parsons, Terence, The logic of sense and denotation: Extensions and applications, in [3].Google Scholar
[55] Putnam, Hilary, Synonymity, and the analysis of belief sentences, Analysis, vol. 14 (1954), pp. 114–122.CrossRefGoogle Scholar
[56] Quine, W.V.O., Two dogmas of empiricism, From a logical point of view, Harvard University Press, Cambridge, Massachusetts, 1953.Google Scholar
[57] Russell, Bertrand, Principles of mathematics, Cambridge University Press, Cambridge, 1903.Google Scholar
[58] Russell, Bertrand, On denoting, Mind, new series, vol. 14 (1905), pp. 479–493.CrossRefGoogle Scholar
[59] Salmon, Nathan, On the very possibility of language: A sermon on the consequences of missing Church, in [3].Google Scholar
[60] Salmon, Nathan, A problem in the Frege-Church theory of sense and denotation, Noûs, vol. 27 (1993), pp. 158–166.CrossRefGoogle Scholar
[61] Salmon, Nathan, Being of two minds: Belief with doubt, Noûs, vol. 29 (1995), pp. 1–20.CrossRefGoogle Scholar
[62] Salmon, Nathan and Soames, Scott (editors), Propositions and attitudes, Oxford University Press, Oxford and New York, 1988.Google Scholar
[63] Tarski, Alfred, The concept of truth in formalized languages, Logic, semantics, metamathematics (Woodger, J. H., translator), Oxford at the Clarendon Press, Oxford, 1956.Google Scholar
[64] Tarski, Alfred, Some methodological investigations on the definability of concepts, Logic, semantics, metamathematics (Woodger, J. H., editor), Oxford at the Clarendon Press, Oxford, 1956.Google Scholar