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Alternative (1*): A Criterion of Identity for Intensional Entities

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Logic, Meaning and Computation

Part of the book series: Synthese Library ((SYLI,volume 305))

Abstract

The problem of formulating an adequate criterion of identity for propositions and other intensionalia was at one time considered the principle obstacle to the construction of an acceptable general intensional logic. The objection was urged time and again, principally by W. V. Quine, and still has its influence.1 Alonzo Church responded directly to the challenge and attempted to incorporate various criteria of identity into fully formalized intensional logics, different implementations of his logic of sense and denotation. The logistic system which was to be based on the most important of Church’s ideas, synonymous isomorphism, remains unfinished.

In this paper I attempt to clarify the point and nature of demands for criteria of identity and to evaluate various objections against Church’s criterion. My conclusion is that a modification suggested by certain alleged counterexamples appears to fit the data better and so merits further study. Important parts of the overall project require the development of a detailed logistic treatment meeting current standards of rigor. This will not be attempted here, but is reserved for a technical sequel.

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References

  • Almog, J., J. Perry, and H. Wettstein 1989 (editors), Themes from Kaplan, Oxford University Press, Oxford.

    Google Scholar 

  • Anderson, A. R., R. B. Marcus, and R. M. Martin 1975 (editors), The logical enterprise, Yale University Press, New Haven.

    Google Scholar 

  • Anderson, C. A. 1980 Some new axioms for the logic of sense and denotation: Alternative (0), Noûs, vol. 14, pp. 217–234.

    Article  Google Scholar 

  • Anderson, C. A. 1987 Bealer’s Quality and Concept, Journal of Philosophical Logic, vol. 16, pp. 115–164.

    Article  Google Scholar 

  • Anderson, C. A. 1989 Russellian intensional logic, in Almog, Perry and Wettstein 1989, pp. 67–103.

    Google Scholar 

  • Anderson, C. A. 1991 Review of Cresswell 1985, Philosophical Review, vol. 100, pp. 476–479.

    Article  Google Scholar 

  • Anderson, C. A. 1998 Alonzo Church’s contributions to philosophy and intensional logic, Bulletin of Symbolic Logic, vol. 4, no. 2.

    Google Scholar 

  • Angelelli, I. 1984 Frege and abstraction, Philosophy Naturalis, vol. 21, pp. 453–471.

    Google Scholar 

  • Apostel, T. M. 1967 Calculus, vol. 1, second edition, Xerox College Publishing, Lexington.

    Google Scholar 

  • Austin, J. L. 1978 (translator), Gottlob Frege, The foundations of arithmetic, Basil Blackwell, Oxford; English translation of Frege 1884.

    Google Scholar 

  • Bealer, G. 1982 Quality and concept, Oxford University Press, Oxford.

    Book  Google Scholar 

  • Bealer, G. 1994 Property theory: The type-free approach v. the Church approach, Journal of Philosophical Logic, vol. 23, pp. 139–171.

    Article  Google Scholar 

  • Birkhoff, G., and S. MacLane 1944 A survey of modern algebra, Macmillan, New York.

    Google Scholar 

  • Black, M. 1945 The “paradox of analysis” again: a reply, Mind, n.s. 54, pp. 272–273.

    Google Scholar 

  • Black, M. 1946 How can analysis be informative?, Philosophy and Phenomenological Research, vol. 6, pp. 628–631.

    Article  Google Scholar 

  • Carnap, R. 1947 Meaning and necessity, University of Chicago Press, Chicago.

    Google Scholar 

  • Carnap, R. 1963 Replies and systematic expositions, in Schilpp 1963, pp. 859–1013.

    Google Scholar 

  • Church, A. 1941 The calculi of lambda-conversion, Annals of mathematics studies, vol. 6, Princeton University Press, Princeton, New Jersey.

    Google Scholar 

  • Church, A. 1942 Incomplete symbol, in Runes 1942, p. 143.

    Google Scholar 

  • Church, A. 1946a A formulation of the logic of sense and denotation (abstract), The Journal of Symbolic Logic, vol. 11, p. 31.

    Google Scholar 

  • Church, A. 1946b Review of White 1945a, Black 1945, White 1945b, and Black 1946, The Journal of Symbolic Logic, vol. 11, pp. 132–133.

    Article  Google Scholar 

  • Church, A. 1951 A formulation of the logic of sense and denotation, in Henle, Kallen and Langer 1951, pp. 3–24.

    Google Scholar 

  • Church, A. 1954 Intensional isomorphism and identity of belief, Philosophical Studies, vol. 5, pp. 65–73.

    Article  Google Scholar 

  • Church, A. 1956 Introduction to mathematical logic, vol. I, Princeton University Press, Princeton, New Jersey.

    Google Scholar 

  • Church, A. 1993 A revised formulation of the logic of sense and denotation, Alternative (1), Noûs, vol. 27, pp. 141–157.

    Article  Google Scholar 

  • Cresswell, M. J. 1985 Structured meanings: The semantics of propositional attitudes, MIT Press, Cambridge, Massachusett.

    Google Scholar 

  • Davidson, D. 1963 The method of extension and intension, in Schilpp 1963, pp. 311–349.

    Google Scholar 

  • De Morgan, A. 1860 Syllabus of a proposed system of logic, in Heath 1966, pp. 147–207.

    Google Scholar 

  • Frege, G. 1884 Die Grundlagen der Arithmetik, Wilhelm Koebner, Breslau.

    Google Scholar 

  • Frege, G. 1919 Negation, Beiträge zur Philosophie des deutschen Idealismus 1, pp. 143–157; English translation in Geach and Black 1966, pp. 117-135.

    Google Scholar 

  • Fine, H. B. 1906 College algebra, Ginn and Company; reprinted by Dover, New York, 1961.

    Google Scholar 

  • Geach, P. 1957 Mental acts, their content and their objects, Routledge & Kegan Paul, London; Humanities Press, New York.

    Google Scholar 

  • Geach, P., and M. Black 1966 (editors), Translations from the philosophical writings of Gottlob Frege, Basil Blackwell, Oxford.

    Google Scholar 

  • Gellert, W., H. Küstner, M. Hellwich, and H. Kästner 1977 The VNR concise encyclopedia of mathematics, Van Nostrand Reinhold, New York.

    Book  Google Scholar 

  • Grandy, R. 1976 Anadic logic, Synthese, vol. 32, pp. 395–402.

    Article  Google Scholar 

  • Grim, P. 1991 The incomplete universe. Totality, knowledge, and truth, MIT Press, Cambridge, Massachusetts.

    Google Scholar 

  • Hahn, L. E. 1986 (editor), The philosophy of W. V. Quine, Library of Living Philosophers, vol. 25, Open Court, La Salle.

    Google Scholar 

  • Heath, P. 1966 (editor), On the syllogism and other logical writings by Augustus De Morgan, Yale University Press, New Haven.

    Google Scholar 

  • Henle, P., H. M. Kallen, and S. K. Langer 1951 (editors), Structure, method and meaning, Essays in honor of Henry M. Sheffer, The Liberal Arts Press, New York.

    Google Scholar 

  • Hilbert, D., and W. Ackermann 1938 Principles of mathematical logic, English translation of the second German edition, Chelsea, New York, 1950.

    Google Scholar 

  • Hochberg, H. 1977 Properties, abstracts, and the axiom of infinity, Journal of Philosophical Logic, vol. 6, pp. 193–207.

    Article  Google Scholar 

  • Kamke, E. 1950 Theory of sets, English translation of the second German edition by F. Bagemihl, Dover, New York.

    Google Scholar 

  • Kaplan, D. 1975 How to Russell a Frege-Church, The Journal of Philosophy, vol. 72, pp. 715–729.

    Article  Google Scholar 

  • Kaplan, D. 1986 Opacity, in Hahn 1986, pp. 229–289.

    Google Scholar 

  • King, J. 1996 Structured propositions, Journal of Philosophical Logic, vol. 25, pp. 495–521.

    Article  Google Scholar 

  • Linsky, L. 1949 Some notes on Carnap’ s concept of intensional isomorphism and the paradox of analysis, Philosophy of Science, vol. 16, pp. 343–347.

    Article  Google Scholar 

  • Linsky, L. 1967 Referring, Humanities Press, New York.

    Google Scholar 

  • Mellor, D. H. 1990 (editor), F. P. Ramsey, Philosophical papers, Cambridge University Press, Cambridge, England.

    Google Scholar 

  • Myhill, J. 1958 Problems arising in the formalization of intensional logic, Logique et Analyse, vol. 1, pp. 78–83.

    Google Scholar 

  • Myhill, J. 1963 An alternative to the method of extension and intension, in Schilpp 1963, pp. 299–310.

    Google Scholar 

  • Prior, A. N. 1963 Is the concept of referential opacity really necessary?, Acta Philosophicia Fennica, vol. 16, pp. 189–198.

    Google Scholar 

  • Quine, W. V. 1941 Whitehead and the rise of modern logic, in Schilpp 1941, pp. 127–163.

    Google Scholar 

  • Quine, W. V. 1953 From a logical point of view, Harvard University Press, Cambridge, Massachusetts; Harper & Row, New York.

    Google Scholar 

  • Quine, W. V. 1953a Two dogmas of empiricism, in Quine 1953, pp. 20–46.

    Google Scholar 

  • Quine, W. V. 1970 Mathematical logic, revised edition, Harvard University Press, Cambridge, Massachusetts.

    Google Scholar 

  • Quine, W. V. 1975 On the individuation of attributes, in Anderson, Marcus, and Martin 1975, pp. 3–13.

    Google Scholar 

  • Quine, W. V. 1981 Theories and things, Harvard University Press, Cambridge, Massachusetts.

    Google Scholar 

  • Ramsey, F. P. 1927 Universals, in Mellor 1990, pp. 8–30.

    Google Scholar 

  • Ramsey, F. P. 1927 Facts and propositions, in Mellor 1990, pp. 34–51.

    Google Scholar 

  • Richard, M. 1990 Propositional attitudes, An essay on thoughts and how we ascribe them, Cambridge University Press, Cambridge, England.

    Book  Google Scholar 

  • Runes, D. D. 1942 (editor), Dictionary of philosophy, Philosophical Library, New York.

    Google Scholar 

  • Russell, B. 1903 The principles of mathematics, Allen and Unwin, London.

    Google Scholar 

  • Schilpp, P. A. 1941 (editor), The philosophy of Alfred North Whitehead, Library of Living Philosophers, vol. 3, Northwestern University, Evanston: second edition, Tudor, New York.

    Google Scholar 

  • Schilpp, P. A. 1963 (editor), The philosophy of Rudolf Carnap, Library of Living Philosophers, vol. 11, Open Court, La Salle; Cambridge University Press, London.

    Google Scholar 

  • Warner, S. 1965 Modern algebra, Prentice-Hall, Englewood Cliffs; reprinted by Dover, New York, 1990.

    Google Scholar 

  • Wells, R. 1952 Review of Church 1951, The Journal of Symbolic Logic, vol. 17, p. 133.

    Article  Google Scholar 

  • White, M. G. 1945a A note on the “paradox of analysis”, Mind, n.s. 54, pp. 71–72.

    Google Scholar 

  • White, M. G. 1945b Analysis and identity: A rejoinder, Mind, n.s. 54, pp. 357–361.

    Google Scholar 

  • Williamson, T. 1986 Criteria of identity and the axiom of choice, The Journal of Philosophy, vol. 83, pp. 380–394.

    Article  Google Scholar 

  • Williamson, T. 1990 Identity and discrimination, Basil Blackwell, Oxford & Cambridge.

    Google Scholar 

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Authors
  1. C. Anthony Anderson
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Editors and Affiliations

  1. University of California, Santa Barbara, USA

    C. Anthony Anderson

  2. PTYX, Los Angeles, California, USA

    Michael Zelëny

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Anderson, C.A. (2001). Alternative (1*): A Criterion of Identity for Intensional Entities. In: Anderson, C.A., Zelëny, M. (eds) Logic, Meaning and Computation. Synthese Library, vol 305. Springer, Dordrecht. https://doi.org/10.1007/978-94-010-0526-5_19

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  • DOI: https://doi.org/10.1007/978-94-010-0526-5_19

  • Publisher Name: Springer, Dordrecht

  • Print ISBN: 978-94-010-3891-1

  • Online ISBN: 978-94-010-0526-5

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