Abstract
Many philosophers still countenance senses or meanings in the broadly Fregean vein.However, it is difficult to posit the existence of senses without positing quite a lot ofthem, including at least one presenting every entity in existence. I discuss a number ofCantorian paradoxes that seem to result from an overly large metaphysics of senses, and various possible solutions. Certain more deflationary and non-traditional understandings of senses, and to what extent they fare better in solving the problems, are also discussed. In the end, it is concluded that one must divide senses into various ramified-orders in order to avoid antinomy, but that the philosophical justification of such orders is, as yet, still somewhat problematic.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
REFERENCES
Anderson, C. Anthony: 1980, ‘Some New Axioms for the Logic of Sense and Denotation: Alternative (0)’, Noû s 14, 217-234.
Anderson, C. Anthony: 1987, ‘Semantical Antinomies in the Logic of Sense and Denotation’, Notre Dame Journal of Formal Logic 1, 99-114.
Berkeley, George: 1713, Three Dialogues Between Hylas and Philonous, Hackett, Indianapolis (1979 edition).
Carnap, Rudolf: 1947, Meaning and Necessity, University of Chicago Press, Chicago (2nd ed. 1956).
Church, Alonzo: 1951, ‘A Formulation of the Logic of Sense and Denotation’, in P. Henle, H. Kallen and S. Langer (eds.), Structure, Method and Meaning: Essays in Honor of Henry M. Sheffer, Liberal Arts Press, New York, pp. 3-24.
Church, Alonzo: 1993, ‘A Revised Formulation of the Logic of Sense and Denotation. Alternative (1)’, Noû s 27, 141-157.
Cocchiarella, Nino: 2000, ‘Russell's Paradox of the Totality of Propositions’, Nordic Journal of Philosophical Logic 5, 25-37.
Dummett, Michael: 1973, Frege: Philosophy of Language, Harvard University Press, Cambridge, MA (2nd ed., 1981).
Forbes, Graeme: 1990, ‘The Indispensability of Sinn’, The Philosophical Review 99, 535-563.
Frege, Gottlob: 1891, ‘Function and Concept’, in Frege 1997, pp. 130-148.
Frege, Gottlob: 1892a, ‘On Sinn and Bedeutung’, in Frege 1997, pp. 151-171.
Frege, Gottlob: 1892b, ‘Comments on Sinn and Bedeutung’, in Frege 1997, pp. 172-181.
Frege, Gottlob: 1892c, ‘On Concept and Object’, in Frege 1997, pp. 181-193.
Frege, Gottlob: 1897, ‘Logic’, in Frege 1997, pp. 227-250.
Frege, Gottlob: 1918, ‘Thought’, in Frege 1997, pp. 325-345.
Frege, Gottlob: 1980, Philosophical and Mathematical Correspondence, University of Chicago Press, Chicago.
Frege, Gottlob: 1997, in M. Beaney (ed.), The Frege Reader, Blackwell, Oxford.
Jeshion, Robin: 2000, ‘Ways of Taking a Meter’, Philosophical Studies 99, 297-318.
Kaplan, David: 1995, ‘A Problem in Possible World Semantics’, in Walter Sinnott-Armstrong et al. (eds.), Modality, Morality and Belief: Essays in Honor of Ruth Barcan Marcus, Cambridge University Press, Cambridge, pp. 41-52.
Katz, Jerrold: 1981, Languages and Other Abstract Objects, Rowman and Littlefield, Totowa, NJ.
Katz, Jerrold: 1990, The Metaphysics of Meaning, MIT Press, Cambridge, MA.
Katz, Jerrold: 2001, ‘The End of Millianism’, Journal of Philosophy 98, 137-166.
Klement, Kevin C.: 2002a, Frege and the Logic of Sense and Reference, Routledge, New York.
Klement, Kevin C.: 2002b, ‘Russell's Paradox from Appendix B of the Principles of Mathematics: Was Frege's Reply Adequate?’, History and Philosophy of Logic, forthcoming.
Myhill, John: 1958, ‘Problems Arising in the Formalization of Intensional Logic’, Logique et Analyse 1, 78-82.
Parsons, Terence: 1980, ‘Frege's Hierarchies of Indirect Senses and the Paradox of Analysis’, in Midwest Studies in Philosophy, vol. 4, The Foundations of Analytical Philosophy, University of Minnesota Press, Minneapolis, pp. 37-57.
Quine, Willard: 1937, ‘New Foundations for Mathematical Logic’, reprinted in From a Logical Point of View, Harvard University Press, Cambridge, MA, pp. 80-101.
Russell, Bertrand: 1903, The Principles of Mathematics, W. W. Norton, New York (paperback edition 1996).
Russell, Bertrand: 1908, ‘Mathematical Logic As Based on The Theory of Types’, reprinted in R. Marsh (ed.), Logic and Knowledge, Allen & Unwin, London, 1956, pp. 57-102.
Searle, John: 1983, Intentionality, Cambridge University Press, Cambridge.
Tichy, Pavel: 1988, The Foundations of Frege's Logic, de Gruyter, Berlin.
Author information
Authors and Affiliations
Rights and permissions
About this article
Cite this article
Klement, K.C. The Number of Senses. Erkenntnis 58, 303–323 (2003). https://doi.org/10.1023/A:1022619903237
Issue Date:
DOI: https://doi.org/10.1023/A:1022619903237