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THE FUNCTIONS OF RUSSELL’S NO CLASS THEORY

Published online by Cambridge University Press:  30 September 2010

KEVIN C. KLEMENT
KEVIN C. KLEMENT*
Affiliation:
University of Massachusetts—Amherst
*
*PHILOSOPHY DEPARTMENT, UNIVERSITY OF MASSACHUSETTS—AMHERST, 352 BARTLETT HALL, 130 HICKS WAY, AMHERST, MA 01003. E-mail: klement@philos.umass.edu, Webpage: http://people.umass.edu/klement/
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Abstract

Certain commentators on Russell’s “no class” theory, in which apparent reference to classes or sets is eliminated using higher-order quantification, including W. V. Quine and (recently) Scott Soames, have doubted its success, noting the obscurity of Russell’s understanding of so-called “propositional functions.” These critics allege that realist readings of propositional functions fail to avoid commitment to classes or sets (or something equally problematic), and that nominalist readings fail to meet the demands placed on classes by mathematics. I show that Russell did thoroughly explore these issues, and had good reasons for rejecting accounts of propositional functions as extralinguistic entities. I argue in favor of a reading taking propositional functions to be nothing over and above open formulas which addresses many such worries, and in particular, does not interpret Russell as reducing classes to language.

Type
Research Article
Information
The Review of Symbolic Logic , Volume 3 , Issue 4 , December 2010 , pp. 633 - 664
Copyright
Copyright © Association for Symbolic Logic 2010

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References

BIBLIOGRAPHY

Baldwin, T. (1979). Interpretations of quantifiers. Mind, 88, 215–240.CrossRefGoogle Scholar
Bostock, D. (2008). Russell on ‘the’ in the plural. In Griffin, N. and Jacquette, D., editors. Russell vs. Meinong: The Legacy of “On Denoting”. New York: Routledge, pp. 113–143.Google Scholar
Cartwright, R. (2005). Remarks on propositional functions. Mind, 114, 915–927.CrossRefGoogle Scholar
Church, A. (1976). Comparison of Russell’s resolution of the semantical antinomies with that of Tarski. Journal of Symbolic Logic, 41, 747–760.CrossRefGoogle Scholar
Deutsch, H. (2008). Review of J. C. King, The Nature and Structure of Content. Notre Dame Philosophical Reviews. Available from: http://ndpr.nd.edu/review.cfm?id=13165.Google Scholar
Frege, G. (1980). Philosophical and Mathematical Correspondence (McGuinness, B., translator; Hans, Kaal, editor). Chicago: University of Chicago Press.Google Scholar
Frege, G. (1984). On concept and object. In McGuinness, B., editor. Collected Papers on Mathematics, Logic and Philosophy. New York: Basil Blackwell, pp. 182–194. (First published 1892).Google Scholar
Geach, P. (1972). Logic Matters. Oxford: Blackwell.Google Scholar
Gödel, K. (1944). Russell’s mathematical logic. In Schilpp, P., editor. The Philosophy of Bertrand Russell, Vol. I. New York: Harper & Row, pp. 123–153.Google Scholar
Grattan-Guinness, I., editor. (1977). Dear Russell–Dear Jourdain. New York: Columbia University Press.Google Scholar
Hazen, A. P. (2004). A “constructive” proper extension of ramified type theory. In Link, G., editor. One Hundred Years of Russell’s Paradox. Berlin: Walter de Gruyter, pp. 449–480.CrossRefGoogle Scholar
Klement, K. C. (2002). Frege and the Logic of Sense and Reference. New York: Routledge.Google Scholar
Klement, K. C. (2003). Russell’s 1903-05 anticipation of the lambda calculus. History and Philosophy of Logic, 24, 15–37.CrossRefGoogle Scholar
Klement, K. C. (2004). Putting form before function: Logical grammar in Frege, Russell and Wittgenstein. Philosopher’s Imprint, 4, 1–47.Google Scholar
Klement, K. C. (2005). The origins of the propositional functions version of Russell’s paradox. Russell, 24, 101–32.CrossRefGoogle Scholar
Klement, K. C. (2010). Russell, his paradoxes, and Cantor’s theorem: Part 2. Philosophy Compass, 5, 29–41.CrossRefGoogle Scholar
Klement, K. C. (forthcoming). PM’s circumflex, syntax and philosophy of types. In Linsky, B., and Griffin, N., editors. Principia Mathematica at 100.Google Scholar
Kremer, M. (2006). Review of Scott Soames, Philosophical Analysis in the Twentieth Century. Notre Dame Philosophical Reviews. Available at: http://ndpr.nd.edu/review.cfm?id=4061.Google Scholar
Kremer, M. (2008). Soames on Russell’s logic: A reply. Philosophical Studies, 139, 209–212.CrossRefGoogle Scholar
Kripke, S. (1976). Is there a problem about substitutional quantification? In Evans, G., and McDowell, J., editors. Truth and Meaning. Oxford: Clarendon Press, pp. 325–419.Google Scholar
Landini, G. (1998). Russell’s Hidden Substitutional Theory. Oxford: Oxford University Press.CrossRefGoogle Scholar
Linsky, B. (1988). Propositional functions and universals in Principia Mathematica. Australasian Journal of Philosophy, 66, 447–460.CrossRefGoogle Scholar
Linsky, B. (1999). Russell’s Metaphysical Logic. Stanford, CA: CSLI Publications.Google Scholar
Linsky, B. (2002). The substitutional paradox in Russell’s 1907 letter to Hawtrey [corrected reprint]. Russell, 22, 151–160.CrossRefGoogle Scholar
Linsky, B. (2004). Russell’s marginalia in his copies of Frege’s works. Russell, 24, 5–36.CrossRefGoogle Scholar
Pincock, C. (2005–2006). Review of Scott Soames, Philosophical Analysis in the Twentieth Century. Russell n.s. 25, 167–172.CrossRefGoogle Scholar
Proops, I. (2006). Soames on the metaphysics and epistemology of Moore and Russell. Philosophical Studies, 129, 627–35.CrossRefGoogle Scholar
Quine, W. V. (1980). Logic and the reification of universals. In From a Logical Point of View (second edition). Cambridge, MA: Harvard University Press, pp. 102–129. (First edition 1953).CrossRefGoogle Scholar
Quine, W. V. (1981). Russell’s ontological development. In Theories and Things. Cambridge, MA: Harvard University Press, pp. 73–85. (First published 1966).Google Scholar
Quine, W. V. (1995). Whitehead and the rise of modern logic. In Selected Logic Papers. Cambridge, MA: Harvard University Press, pp. 3–36. (First published 1941).Google Scholar
Russell, B. (1903a). Dependent variables and denotation. In Urquhart, A., editor. The Collected Papers of Bertrand Russell, Vol. 4. London: Routledge, pp. 297–304.Google Scholar
Russell, B. (1903b). Functions. In Urquhart, A., editor. The Collected Papers of Bertrand Russell, Vol. 4. London: Routledge, pp. 49–74.Google Scholar
Russell, B. (1903c). On meaning and denotation. In Urquhart, A., editor. The Collected Papers of Bertrand Russell, Vol. 4. London: Routledge, pp. 314–358.Google Scholar
Russell, B. (1903d). On the meaning and denotation of phrases. In Urquhart, A., editor. The Collected Papers of Bertrand Russell, Vol. 4. London: Routledge, pp. 283–296.Google Scholar
Russell, B. (1903e). Points about denoting. In Urquhart, A., editor. The Collected Papers of Bertrand Russell, Vol. 4. London: Routledge, pp. 305–313.Google Scholar
Russell, B. (1903f). The Principles of Mathematics. Cambridge, UK: Cambridge University Press. (Second edition 1931).Google Scholar
Russell, B. (1904a). Fundamental notions. In Urquhart, A., editor. The Collected Papers of Bertrand Russell, Vol. 4. London: Routledge, pp. 111–263.Google Scholar
Russell, B. (1904b). Meinong’s theory of complexes and assumptions. In Urquhart, A., editor. The Collected Papers of Bertrand Russell, Vol. 4. London: Routledge, pp. 431–474.Google Scholar
Russell, B. (1904c). On functions. In Urquhart, A., editor. The Collected Papers of Bertrand Russell, Vol. 4. London: Routledge, pp. 96–110.Google Scholar
Russell, B. (1904d). On functions, classes and relations. In Urquhart, A., editor. The Collected Papers of Bertrand Russell, Vol. 4. London: Routledge, pp. 85–95.Google Scholar
Russell, B. (1904e). On the nature of functions. In Urquhart, A., editor. The Collected Papers of Bertrand Russell, Vol. 4. London: Routledge, pp. 265–272.Google Scholar
Russell, B. (1905a). The nature of truth. In Urquhart, A., editor. The Collected Papers of Bertrand Russell, Vol. 4. London: Routledge, pp. 492–493.Google Scholar
Russell, B. (1905b). On classes and relations. In Urquhart, A., editor. The Collected Papers of Bertrand Russell, Vol. 4. London: Routledge, pp. 273–279.Google Scholar
Russell, B. (1905c). On denoting. In Urquhart, A., editor. The Collected Papers of Bertrand Russell, Vol. 4. London: Routledge, pp. 414–427.Google Scholar
Russell, B. (1905d). On fundamentals. In Urquhart, A., editor. The Collected Papers of Bertrand Russell, Vol. 4. London: Routledge, pp. 359–413.Google Scholar
Russell, B. (1906a). On ‘insolubilia’ and their solution by symbolic logic. In Lackey, D., editor. Essays in Analysis. New York: George Braziller, pp. 190–214.Google Scholar
Russell, B. (1906b). The substitutional theory of classes and relations. In Lackey, D., editor. Essays in Analysis. New York: George Braziller, pp. 165–189.Google Scholar
Russell, B. (1907a). Logic in Which Propositions Are Not Entities. Unpublished manuscript, Bertrand Russell Archives, McMaster University.Google Scholar
Russell, B. (1907b). On the nature of truth. Proceedings of the Aristotelian Society, 7, 28–49.CrossRefGoogle Scholar
Russell, B. (1907c). The Paradox of the Liar. Unpublished manuscript, Bertrand Russell Archives, McMaster University.Google Scholar
Russell, B. (1908). Mathematical logic as based on the theory of types. American Journal of Mathematics, 30, 222–262.CrossRefGoogle Scholar
Russell, B. (1910a). On the nature of truth and falsehood. In Philosophical Essays. New York: Longmans & Green, pp. 140–151.Google Scholar
Russell, B. (1910b). Some explanations in reply to Mr. Bradley. Mind, 19, 373–378.CrossRefGoogle Scholar
Russell, B. (1911a). Analytic realism. In Mumford, S., editor. Russell on Metaphysics. London: Routledge, pp. 91–96.Google Scholar
Russell, B. (1911b). On the relations of universals and particulars. In Marsh, R. C., editor. Logic & Knowledge. London: George Allen & Unwin, pp. 105–124.Google Scholar
Russell, B. (1912a). The Problems of Philosophy. London: Home University Library.Google Scholar
Russell, B. (1912b). What is logic? In Slater, J. G., editor. The Collected Papers of Bertrand Russell, Vol. 6. London: Routledge, pp. 54–56.Google Scholar
Russell, B. (1914). Our Knowledge of the External World. Chicago: Open Court.Google Scholar
Russell, B. (1918a). On the notion of cause. In Mysticism and Logic. London: George Allen & Unwin, pp. 132–151. (First published 1912).Google Scholar
Russell, B. (1918b). The philosophy of logical atomism. In Marsh, R. C., editor. Logic & Knowledge. London: George Allen & Unwin, pp. 175–281.Google Scholar
Russell, B. (1919a). Introduction to Mathematical Philosophy. London: George Allen & Unwin.Google Scholar
Russell, B. (1919b). On propositions: what they are and how they mean. In Marsh, R. C., editor. Logic & Knowledge. London: George Allen & Unwin, pp. 283–320.Google Scholar
Russell, B. (1921). The Analysis of Mind. London: Allen & Unwin.Google Scholar
Russell, B. (1923). Vagueness. In Slater, J. G., editor. The Collected Papers of Bertrand Russell, Vol. 9. London: Unwin Hyman, pp. 147–154.Google Scholar
Russell, B. (1924). Logical atomism. In Marsh, R. C., editor. Logic & Knowledge. London: George Allen & Unwin, pp. 323–343.Google Scholar
Russell, B. (1931). Review of Ramsey, The Foundations of Mathematics. In Slater, J. G., editor. The Collected Papers of Bertrand Russell, Vol. 10. London: Routledge, pp. 107–114.Google Scholar
Russell, B. (1932). [Another] Review of Ramsey, The Foundations of Mathematics. In Slater, J. G., editor. The Collected Papers of Bertrand Russell, Vol. 10. London: Routledge, pp. 114–117.Google Scholar
Russell, B. (1940). Inquiry into Meaning and Truth. London: George Allen & Unwin.Google Scholar
Russell, B. (1946). The problem of universals. In Mumford, S., editor. Russell on Metaphysics. London: Routledge, pp. 143–159.Google Scholar
Russell, B. (1950). Logical positivism. In Marsh, R. C., editor. Logic & Knowledge. London: George Allen & Unwin, pp. 365–382.Google Scholar
Russell, B. (1958). My Philosophical Development. London: George Allen & Unwin.Google Scholar
Russell, B. (date unknown). Types (draft). Unpublished manuscript, Bertrand Russell Archives, McMaster University.Google Scholar
Sainsbury, R. M. (1979). Russell. London: Routledge and Kegan Paul.Google Scholar
Sainsbury, R. M. (2006). Review of Scott Soames, Philosophical Analysis in the Twentieth Century. Philosophical Studies, 129, 637–43.CrossRefGoogle Scholar
Soames, S. (2003). Philosophical Analysis in the Twentieth Century: Volume 1: The Dawn of Analysis. Princeton, NJ: Princeton University Press.CrossRefGoogle Scholar
Soames, S. (2006). What is history for? Reply to critics of The Dawn of Analysis. Philosophical Studies, 129, 645–665.CrossRefGoogle Scholar
Soames, S. (2008). No class: Russell on contextual definition and the elimination of sets. Philosophical Studies, 139, 213–218.CrossRefGoogle Scholar
Soames, S. (forthcoming). Propositions. In Graff Fara, D., and Russell, G., editors. The Routledge Companion to the Philosophy of Language. Abingdon: Routledge.Google Scholar
Stevens, G. (2005). The Russellian Origins of Analytical Philosophy. London: Routledge.Google Scholar
Whitehead, A. N. (1898). A Treatise on Universal Algebra. Cambridge, UK: Cambridge University Press.Google Scholar
Whitehead, A. N., & Russell, B. (1910). Principia Mathematica (3 Volumes, first edition). Cambridge: Cambridge University Press.Google Scholar
Whitehead, A. N., & Russell, B. (1925). Principia Mathematica (3 Volumes, second edition). Cambridge: Cambridge University Press.Google Scholar
Wittgenstein, L. (1961). Tractatus Logico-Philosophicus. London: Routledge. Translator Pears, D. and McGuinness, B.. (First published 1921).Google Scholar