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Frege's Theory of Incomplete Entities

Published online by Cambridge University Press:  14 March 2022

Michael David Resnik
Michael David Resnik*
Affiliation:
University of Hawaii
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Abstract

This paper examines four arguments in support of Frege's theory of incomplete entities, the heart of his semantics and ontology. Two of these arguments are based upon Frege's contributions to the foundations of mathematics. These are shown to be question-begging. Two are based upon Frege's solution to the problem of the relation of language to thought and reality. They are metaphysical in nature and they force Frege to maintain a theory of types. The latter puts his theory of incomplete entities in the paradoxical position of maintaining that it is no theory at all. Moreover, his metaphysics rules out well-known suggestions for avoiding this difficulty.

Type
Research Article
Information
Philosophy of Science , Volume 32 , Issue 4 , October 1965 , pp. 329 - 341
Copyright
Copyright © 1965 by The Philosophy of Science Association

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Footnotes

**

I would like to thank Professor Burton Dreben for the suggestions which led to this article. Professors Chung-ying Cheng, Dagfinn F⊘lesdal, Richard P. Haynes, and Charles D. Parsons have commented on various manuscripts of this article and I am grateful to them. Much of the research reported here was done while I was employed by the U.S. Air Force Cambridge Research Laboratories, and I would like to acknowledge their support. This article is adapted from a dissertation submitted to the Department of Philosophy of Harvard University in partial fulfillment of the requirements for the Ph. D.

References

[1] Frege, Gottlob, Begriffsschrift, eine der arithmetischen nachgebildete Formelsprachen des reinen Denkens, Halle: Louis Nebert, 1879. (Reprinted Hildesheim I. Ensch, 1962.)Google Scholar
[2] Frege, Gottlob, “Über die wissenschaftliche Berechtigung einer Begriffsschrift”, Zeitschrift für Philosophie und Philosophische Kritik 81, 1882, pp. 48–56.Google Scholar
[3] Frege, Gottlob, Die Grundlagen der Arithmetik, Breslau, Wilhelm Koebner, 1884. (Reprinted Breslau 1934 and Darmstadt and Hildesheim 1961.)Google Scholar
[4] Frege, Gottlob, Funktion und Begriff, Jena: Hermann Pohle 1891.Google Scholar
[5] Frege, Gottlob, “Über Begriff und Gegenstand” Vierteljahrsheft für wissenschaftliche Philosophie 16, 1892, pp. 192–205.Google Scholar
[6] Frege, Gottlob, “Über Sinn und Bedeutung,” Zeitschrift für Philosophie und Philosophische Kritik 100, 1892, pp. 25–50.Google Scholar
[7] Frege, Gottlob, Grundgesetze der Arithmetik I, Jena: Hermann Pohle 1893. II, Jena: Hermann Pohle 1903. (Reprinted Hildescheim: Georg Olms Verlagsbuchhandlung, 1962.)Google Scholar
[8] Frege, Gottlob, Review of Husserl's Philosophie der Arithmetik, Zeitschrift für Philosophie und philosophische Kritik 103, 1894, pp. 313–332.Google Scholar
[9] Frege, Gottlob, “Lettera del sig. G. Frege all’ Editore,” (Dated Sept. 29, 1896), Revue de Mathématique 7 No. 2, 1898, pp. 53–59.Google Scholar
[10] Frege, Gottlob, “Über die Grundlagen der Geometrie.” (First series.) Jahresbericht der deutschen Mathematikvereinigung 12, 1903, pp. 319–324, pp. 368-375.Google Scholar
[11] Frege, Gottlob, “Was ist ein Funktion?” Festschrift für Ludwig Boltsmann gewidmet zum sechzigsten Geburtstage, 20 Februar, 1904, Leipzig: Ambrosius Barth, 1904, pp. 656–666.Google Scholar
[12] Frege, Gottlob, “Über de Grundlagen der Geometrie,” (Second series). Jahresbericht der deutschen Mathematikervereinigung 15, 1906, pp. 293–309, pp. 377-403, pp. 423-430.Google Scholar
[13] Frege, Gottlob, “Der Gedanke. Eine logische Untersuchung,” Beiträge zur Philosophie des deutschen Idealismus 1, 1918, pp. 58–77.Google Scholar
[14] Frege, Gottlob, “Die Verneinung,” Beiträge zur Philosophie des deutschen Idealismus 1, 1918, pp. 143–157.Google Scholar
[15] Frege, Gottlob, “Gedankengefüge,” Beiträge zur Philosophie des deutschen Idealismus 3, 1923, pp. 36–51.Google Scholar
[16] Frege, Gottlob, Correspondence with Bertrand Russell (unpublished).Google Scholar
[17] Frege, Gottlob, Translations of the Philosophical Writings of Gottlob Frege. P. T. Geach and Max Black (eds.). Oxford, 1952. Second edition, Oxford: Basil Blackwell, 1960. (Contains translations of [1], [4], [5], [6], [7], [8], [11], [14].)Google Scholar
[18] Frege, Gottlob, The Foundations of Arithmetic, trans. J. L. Austin, Oxford, 1950. Second edition, Oxford: Basil Blackwell, 1953. (English-German edition of [3].)Google Scholar
[19] Frege, Gottlob, “The Thought: A Logical Inquiry,” trans. A. N. and Marceli Quinton. Mind 65, 1956, pp. 289–311.CrossRefGoogle Scholar
[20] Frege, Gottlob, “Compound Thoughts,” trans. R. H. Stoothoff, Mind 72, 1963, pp. 1–17.CrossRefGoogle Scholar
[21] Anscombe, G. E. M. and Geach, P. T., Three Philosophers. Ithaca: Cornell University Press, 1961.Google Scholar
[22] Bartlett, J. M., Funktion und Gegenstand. Dissertation, Munich, 1961. (Contains passages from the Frege Nachlass.)Google Scholar
[23] Black, M., “Frege on Functions,” Problems of Analysis by Max Black. Ithaca: Cornell University Press, 1954, pp. 229–254, pp. 297-298.Google Scholar
[24] Caton, C., “An apparent difficulty in Frege's ontology,” The Philosophical Review 71, 1962, pp. 462–475.CrossRefGoogle Scholar
[25] Church, A., “A Formulation of the Logic of Sense and Denotation,” Structure, Method, and Meanings: Essays in Honor of H. M. Sheffer. Kallen, P. Henle, and S. K. Langer (eds.) New York: Liberal Arts Press, 1951.Google Scholar
[26] Dummett, M., “Frege on Functions: A Reply,” The Philosophical Review 64, 1955, pp. 96–107.CrossRefGoogle Scholar
[27] Dummett, M., “Note: Frege on Functions,” The Philosophical Review 65, 1956, pp. 229–230.CrossRefGoogle Scholar
[28] Fisk, M., “A paradox in Frege's Semantics,” Philosophical Studies 14, 1963, pp. 56–62.CrossRefGoogle Scholar
[29] Fitch, F. B., “Self-reference in Philosophy,” Symbolic Logic. New York: Ronald Press, 1952.Google Scholar
[30] Geach, P. T., “Subject and Predicate,” Mind 59, 1950, pp. 461–482.CrossRefGoogle Scholar
[31] Geach, P. T., “Frege's Grundlagen,” The Philosophical Review 62, 1953, pp. 535–544.Google Scholar
[32] Jackson, H., “Frege on sense-functions,” Analysis 23, 1963, pp. 84–87.CrossRefGoogle Scholar
[33] Patzig, G., (ed.) Funktion, Begriff, Bedeutung. Gottingen: Vandenhoech and Ruprecht, 1962. (Contains reprints of [2], [4], [5], [6], [11].)Google Scholar
[34] Quine, W. V., “Unification of Universes in Set Theory,” Journal of Symbolic Logic 21, 1956, pp. 267–279.CrossRefGoogle Scholar
[35] Resnik, M. D., Frege's Methodology, Dissertation, Harvard, 1963.Google Scholar
[36] Wells, R., “Is Frege's Concept of Function Valid ?” The Journal of Philosophy 60, No. 23, 1963.CrossRefGoogle Scholar