Hostname: page-component-78c5997874-v9fdk Total loading time: 0 Render date: 2024-11-09T22:38:15.455Z Has data issue: false hasContentIssue false
  • English
  • Français

The Senses of Functions in the Logic of Sense and Denotation

Published online by Cambridge University Press:  15 January 2014

Kevin C. Klement
Kevin C. Klement*
Affiliation:
Philosophy Department, University of Massachusetts, 352 Bartlett Hall, 130 Hicks Way Amherst, Massachusetts 01003, USAE-mail:[email protected], URL: http://people.umass.edu/klement/
Get access Rights & Permissions [Opens in a new window]

Abstract

This paper discusses certain problems arising within the treatment of the senses of functions in Alonzo Church's Logic of Sense and Denotation. Church understands such senses themselves to be “sense-functions,” functions from sense to sense. However, the conditions he lays out under which a sense-function is to be regarded as a sense presenting another function as denotation allow for certain undesirable results given certain unusual or “deviant” sense-functions. Certain absurdities result, e.g., an argument can be found for equating any two senses of the same type. An alternative treatment of the senses of functions is discussed, and is thought to do better justice to Frege's original theory.

Type
Research Article
Information
Bulletin of Symbolic Logic , Volume 16 , Issue 2 , June 2010 , pp. 153 - 188
Copyright
Copyright © Association for Symbolic Logic 2010

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

REFERENCES

[1] Anderson, C. Anthony, Some models for the Logic of Sense and Denotation with an application to Alternative (0) , Ph.D. thesis, UCLA, 1977.Google Scholar
[2] Anderson, C. Anthony, Some new axioms for the Logic of Sense and Denotation: Alternative (0), Noûs, vol. 14 (1980), pp. 217–34.Google Scholar
[3] Anderson, C. Anthony, General intensional logic, Handbook of philosophical logic. Vol. 2, Extensions of classical logic (Gabbay, D. and Guenthner, F., editors), Kluwer, Dordrecht, 1984, pp. 355–85.Google Scholar
[4] Anderson, C. Anthony, Semantic antinomies in the Logic of Sense and Denotation, Notre Dame Journal of Formal Logic, vol. 28 (1987), pp. 99–114.Google Scholar
[5] Anderson, C. Anthony, Alonzo Church's contributions to philosophy and intensional logic, this Bulletin, vol. 4 (1998), pp. 129–71.Google Scholar
[6] Carnap, Rudolf, Meaning and necessity, 2nd ed., University of Chicago Press, Chicago, 1956, (first edition 1947).Google Scholar
[7] Church, Alonzo, The calculi of lambda-conversion, Princeton University Press, Princeton, 1941.Google Scholar
[8] Church, Alonzo, A formulation of the Logic of Sense and Denotation (abstract), The Journal of Symbolic Logic, vol. 11 (1946), p. 31.Google Scholar
[9] Church, Alonzo, A formulation of the Logic of Sense and Denotation, Structure, method and meaning: Essays in honor of Henry M. Sheffer (Henle, P., Kallen, H., and Langer, S., editors), Liberal Arts Press, New York, 1951, pp. 3–24.Google Scholar
[10] Church, Alonzo, Outline of a revised formulation of the Logic of Sense and Denotation, part 1, Noûs, vol. 7 (1973), pp. 24–33.Google Scholar
[11] Church, Alonzo, Outline of a revised formulation of the Logic of Sense and Denotation, part 2, Noûs, vol. 8 (1974), pp. 135–56.CrossRefGoogle Scholar
[12] Church, Alonzo, Intensional isomorphism and identity of belief, Propositions and attitudes (Salmon, N. and Soames, S., editors), Oxford University Press, 1988, (first published 1954), pp. 159–68.Google Scholar
[13] Church, Alonzo, A revised formulation of the Logic of Sense and Denotation. Alternative (1), Noûs, vol. 27 (1993), pp. 141–57.Google Scholar
[14] Cocchiarella, Nino, Russell's paradox of the totality of propositions, Nordic Journal of Philosophical Logic, vol. 5 (2000), pp. 25–38.Google Scholar
[15] Denyer, Nicholas, Rieger's problem with Frege's ontology, Analysis, vol. 63 (2003), pp. 166–70.Google Scholar
[16] Dummett, Michael, Frege: Philosophy of language, Harvard University Press, Cambridge, Mass., 1974.Google Scholar
[17] Dummett, Michael, The interpretation of Frege's philosophy, Harvard University Press, Cambridge, Mass., 1981.Google Scholar
[18] Frege, Gottlob, Comments on sense and meaning, In Frege [23], pp. 118–25.Google Scholar
[19] Frege, Gottlob, Function and concept, In Frege [25], pp. 137–56.Google Scholar
[20] Frege, Gottlob, On sense and meaning, In Frege [25], pp. 157–77.Google Scholar
[21] Frege, Gottlob, Notes for Ludwig Darmstädter, In Frege [23], pp. 253–57.Google Scholar
[22] Frege, Gottlob, Basic laws of arithmetic, University of California Press, Berkeley, 1964, (Furth, M., editor; originally published as Grundgesetze der Arithmetik, 2 vols. H. Pohle, Jena, 1893–1902).Google Scholar
[23] Frege, Gottlob, Posthumous writings, University of Chicago Press, Chicago, 1979, (Long, P. and White, R., editors).Google Scholar
[24] Frege, Gottlob, Philosophical andmathematical correspondence, University of Chicago Press, Chicago, 1980, (Kaal, H., editor).Google Scholar
[25] Frege, Gottlob, Collected papers on mathematics, logic and philosophy, Basil Blackwell, New York, 1984, (McGuinness, B., editor).Google Scholar
[26] Henkin, Leon, Notes on Church's lectures on “Sense and Denotation”, Unpublished; taken at Princeton, Spring, 1946.Google Scholar
[27] Hindley, J. Roger and Seldin, Jonathan P., Introduction to combinators and λ-calculus, Cambridge University Press, Cambridge, 1986.Google Scholar
[28] Kaplan, David, Foundations of intensional logic , Ph.D. thesis, UCLA, 1964.Google Scholar
[29] Kaplan, David, How to Russell a Frege-Church, The Journal of Philosophy, vol. 72 (1975), pp. 716–29.CrossRefGoogle Scholar
[30] Klement, Kevin, Frege and the logic of sense and reference, Routledge, New York, 2002.Google Scholar
[31] Klement, Kevin, The number of senses, Erkenntnis, vol. 58 (2003), pp. 302–323.Google Scholar
[32] Klement, Kevin, Does Frege have too many thoughts? A Cantorian problem revisited, Analysis, vol. 65 (2005), pp. 44–49.Google Scholar
[33] Klement, Kevin, A Cantorian argument against Frege's and early Russell's theories of descriptions, Russell vs. Meinong: The legacy of “On Denoting” (Griffin, N. and Jacquette, D., editors), Routledge, New York, 2008, pp. 65–77.Google Scholar
[34] Montague, Richard, Formal philosophy, Yale University Press, 1974.Google Scholar
[35] Myhill, John, Problems arising in the formalization of intensional logic, Logique et Analyse, vol. 1 (1958), pp. 78–82.Google Scholar
[36] Parsons, Charles, Intensional logic in extensional language, The Journal of Symbolic Logic, vol. 47 (1982), pp. 289–328.Google Scholar
[37] Parsons, Terence, The Logic of Sense and Denotation: Extensions and applications, Logic, meaning and computation: Essays in memory of Alonzo Church (Anderson, C. A. and Zelëny, M., editors), Kluwer, Dordrecht, 2001, pp. 507–44.Google Scholar
[38] Ramsey, Frank P., The foundations of mathematics, Philosophical papers, Cambridge University Press, Cambridge, 1990, (first published 1925), pp. 164–224.Google Scholar
[39] Rieger, Adam, Paradox without Basic Law V: A problem with Frege's ontology, Analysis, vol. 62 (2002), pp. 327–30.Google Scholar
[40] Russell, Bertrand, Mathematical logic as based on the theory of types, American Journal of Mathematics, vol. 30 (1908), pp. 222–262.Google Scholar
[41] Russell, Bertrand, The principles of mathematics, 2nd ed., Cambridge University Press, Cambridge, 1931, (first edition 1903).Google Scholar
[42] Schönfinkel, Moses, On the building blocks of mathematical logic, From Frege to Gödel: A source book in mathematical logic (van Heijenoort, J., editor), Harvard University Press, Cambridge, Mass., 1967, (first published 1924), pp. 355–66.Google Scholar