Hostname: page-component-8448b6f56d-42gr6 Total loading time: 0 Render date: 2024-04-23T16:14:38.555Z Has data issue: false hasContentIssue false
  • English
  • Français

THE CONCEPT HORSE IS A CONCEPT

Published online by Cambridge University Press:  21 December 2017

ANSTEN KLEV
ANSTEN KLEV*
Affiliation:
Institute of Philosophy, Czech Academy of Sciences
*
*INSTITUTE OF PHILOSOPHY CZECH ACADEMY OF SCIENCES JILSKÁ 1 110 00 PRAGUE 1 CZECH REPUBLIC E-mail: anstenklev@gmail.com
Get access Rights & Permissions [Opens in a new window]

Abstract

I offer an analysis of the sentence ‘the concept horse is a concept’. It will be argued that the grammatical subject of this sentence, ‘the concept horse’, indeed refers to a concept, and not to an object, as Frege once held. The argument is based on a criterion of proper-namehood according to which an expression is a proper name if it is so rendered in Frege’s ideography. The predicate ‘is a concept’, on the other hand, should not be thought of as referring to a function. It will be argued that the analysis of sentences of the form ‘C is a concept’ requires the introduction of a new form of statement. Such statements are not to be thought of as having function–argument form, but rather the structure subject–copula–predicate.

Keywords

03A0503B15Gottlob Fregetype theorypredication
Type
Research Article
Information
The Review of Symbolic Logic , Volume 11 , Issue 3 , September 2018 , pp. 547 - 572
Copyright
Copyright © Association for Symbolic Logic 2017 

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

BIBLIOGRAPHY

Aczel, P. (1980). Frege structures and the notions of proposition, truth and set. In Barwise, J., Keisler, H. J., and Kunen, K., editors. The Kleene Symposium. Amsterdam: North-Holland, pp. 31–59.CrossRefGoogle Scholar
Barnes, J. (2002). What is a Begriffsschrift? Dialectica, 56, 65–80.CrossRefGoogle Scholar
Bostock, D. (1974). Logic and Arithmetic. Natural Numbers. Oxford: Clarendon Press.Google Scholar
de Bruijn, N. G. (1975). Set theory with type restrictions. In Hajnal, A., Rado, R., and Sós, T., editors. Infinite and Finite Sets: To Paul Erdős on his 60th Birthday. Amsterdam: North-Holland, pp. 205–214.Google Scholar
de Bruijn, N. G. (1980). A survey of the project AUTOMATH. In Hindley, J. R. and Seldin, J. P., editors. To H.B. Curry: Essays on Combinatory Logic, Lambda Calculus and Formalism. London: Academic Press, pp. 579–606.Google Scholar
Carnap, R. (1929). Abriss der Logistik. Vienna: Springer.CrossRefGoogle Scholar
Carnap, R. (1937). Logical Syntax of Language. London: Routledge & Kegan Paul.Google Scholar
Church, A. (1940). A formulation of the simple theory of types. Journal of Symbolic Logic, 5, 56–68.CrossRefGoogle Scholar
Dedekind, R. (1888). Was sind und was sollen die Zahlen? Braunschweig: Vieweg und Sohn.Google Scholar
Dummett, M. (1973). Frege. Philosophy of Language. London: Duckworth. Cited from the second edition (1981).Google Scholar
Dummett, M. (1991). Frege. Philosophy of Mathematics. London: Duckworth.Google Scholar
Eilenberg, S. & MacLane, S. (1942). Natural isomorphisms in group theory. Proceedings of the National Academy of Sciences, 28, 537–543.CrossRefGoogle ScholarPubMed
Frege, G. (1879). Begriffsschrift. Halle: Louis Nebert.Google Scholar
Frege, G. (1881). Booles rechnende Logik und die Begriffsschrift. Cited from Frege (1983).Google Scholar
Frege, G. (1884). Grundlagen der Arithmetik. Breslau: Verlag von Wilhelm Koebner.Google Scholar
Frege, G. (1891). Funktion und Begriff. Jena: Hermann Pohle.Google Scholar
Frege, G. (1892a). Über Begriff und Gegenstand. Vierteljahrsschrift für wissenschaftliche Philosophie, 16, 192–205.Google Scholar
Frege, G. (1892b). Über Sinn und Bedeutung. Zeitschrift für Philosophie und philosophische Kritik, NF 100, 25–50.Google Scholar
Frege, G. (1893). Grundgesetze der Arithmetik I. Jena: Hermann Pohle.Google Scholar
Frege, G. (1903). Über die Grundlagen der Geometrie. Jahresbericht der Deutschen Mathematiker-Vereinigung, 12, 319–324, 368–375.Google Scholar
Frege, G. (1904). Was ist eine Funktion? In Festschrift Ludwig Boltzmann. Gewidmet zum sechzigsten Geburtstage. Leipzig: Johann Ambrosius Barth, pp. 656–666.Google Scholar
Frege, G. (1906). Über Schoenflies: Die logischen Paradoxien der Mengenlehre. Cited from Frege (1983).Google Scholar
Frege, G. (1914). Logik in der Mathematik. Cited from Frege (1983).Google Scholar
Frege, G. (1924). Erkenntnisquellen der Mathematik und der mathematischen Naturwissenschaften. Cited from Frege (1983).Google Scholar
Frege, G. (1976). Wissenschaftlicher Briefwechsel. Hamburg: Felix Meiner Verlag.Google Scholar
Frege, G. (1983). Nachgelassene Schriften. Hamburg: Felix Meiner Verlag.Google Scholar
Gaskin, R. (2008). The Unity of the Proposition. Oxford: Oxford University Press.CrossRefGoogle Scholar
Geach, P. T. (1976). Saying and showing in Frege and Wittgenstein. In Essays in Honour of G. H. von Wright. Acta Philosophica Fennica, Vol. 28. Amsterdam: North-Holland, pp. 54–70.Google Scholar
Granström, J. G. (2011). Treatise on Intuitionistic Type Theory. Dordrecht: Springer.CrossRefGoogle Scholar
Hacker, P. (1986). Insight and Illusion (second revised edition). Oxford: Clarendon Press.Google Scholar
Hale, B. (1994). Singular terms (2). In McGuinness, B. and Oliveri, G., editors. The Philosophy of Michael Dummett. Dordrecht: Kluwer, pp. 17–44. Reprinted in (Hale & Wright, 2001).CrossRefGoogle Scholar
Hale, B. (1996). Singular terms (1). In Schirn, M., editor. Frege: Importance and Legacy. Berlin: Walter de Grutyer, pp. 438–457. Reprinted in (Hale & Wright, 2001).Google Scholar
Hale, B. (2010). The bearable lightness of being. Axiomathes, 20, 399–420.CrossRefGoogle Scholar
Hale, B. & Wright, C. (2001). The Reason’s Proper Study. Oxford: Oxford University Press.CrossRefGoogle Scholar
Hale, B. & Wright, C. (2012). Horse sense. Journal of Philosophy, 109, 85–131.CrossRefGoogle Scholar
Hamlyn, D. W. (1959). Categories, formal concepts and metaphysics. Philosophy, 34, 111–124.Google Scholar
Hindley, J. R. (1997). Basic Simple Type Theory. Cambridge: Cambridge University Press.CrossRefGoogle Scholar
Hodes, H. (1984). Logicism and the ontological commitments of arithmetic. Journal of Philosophy, 81, 123–149.CrossRefGoogle Scholar
Jones, N. K. (2016). A higher-order solution to the problem of the concept horse. Ergo, 3, 132–166.Google Scholar
Kemp, A. (1987). The Tekhnē Grammatikē of Dionysius Thrax: English translation with introduction and notes. In Taylor, D. J., editor. The History of Linguistics in the Classical Period. Amsterdam: John Benjamins, pp. 169–190.CrossRefGoogle Scholar
Kim, J. (2013). What are numbers? Synthese, 190, 1099–1112.CrossRefGoogle Scholar
Kim, J. (2015). A logical foundation of arithmetic. Studia Logica, 103, 113–144.CrossRefGoogle Scholar
Klein, C. (2004). Carnap on categorial concepts. In Awodey, S. and Klein, C., editors. Carnap Brought Home: The View from Jena. Chicago: Open Court, pp. 295–316.Google Scholar
Kretzmann, N. (1966). William of Sherwood’s Introduction to Logic. Translated with an introduction and notes. Minneapolis: University of Minnesota Press.Google Scholar
Lambek, J. (1958). The mathematics of sentence structure. The American Mathematical Monthly, 65, 154–170.CrossRefGoogle Scholar
Liebesman, D. (2015). Predication as ascription. Mind, 124, 517–569.CrossRefGoogle Scholar
Linnebo, O. (2010). Pluralities and sets. Journal of Philosophy, 107, 144–164.CrossRefGoogle Scholar
Martin-Löf, P. (1982). Constructive mathematics and computer programming. In Cohen, J. L., Łoś, J., Pfeiffer, H., and Podewski, K.-P., editors. Logic, Methodology and Philosophy of Science VI, 1979. Amsterdam: North-Holland, pp. 153–175.Google Scholar
Martin-Löf, P. (1984). Intuitionistic Type Theory. Naples: Bibliopolis.Google Scholar
Martin-Löf, P. (2006). Comments on Prof. Kazuyuki Nomoto’s paper. Annals of the Japan Association for Philosophy of Science, 14, 98–99.Google Scholar
Mulligan, K. (2006). Ascent, propositions and other formal objects. Grazer Philosophische Studien, 72, 29–48.Google Scholar
Noonan, H. (2006). The concept horse. In Strawson, P. F. and Chakrabarti, A., editors. Universal, Concepts and Qualities. Aldershot: Ashgate, pp. 155–176.Google Scholar
Parsons, T. (1979). Type theory and ordinary language. In Davis, S. and Mithun, M., editors. Linguistics, Philosophy, and Montague Grammar. Austin: University of Texas Press, pp. 127–151.Google Scholar
Parsons, T. (1986). Why Frege should not have said “The concept horse is not a concept”. History of Philosophy Quarterly, 3, 449–465.Google Scholar
Paseau, A. C. (2015). Did Frege commit a cardinal sin? Analysis, 75, 379–386.CrossRefGoogle Scholar
Proops, I. (2013). What is Frege’s ‘concept horse problem’? In Sullivan, P. and Potter, M., editors. Wittgenstein’s Tractatus. History and Interpretation. Oxford: Oxford University Press, pp. 76–96.CrossRefGoogle Scholar
Quine, W. v. O. (1986). Philosophy of Logic (second edition). Cambridge, Massachusetts: Harvard University Press.Google Scholar
Rayo, A. (2002). Frege’s unofficial arithmetic. Journal of Symbolic Logic, 67, 1623–1638.CrossRefGoogle Scholar
Reynolds, J. C. (1998). Theories of Programming Languages. Cambridge: Cambridge University Press.CrossRefGoogle Scholar
Robins, R. H. (1966). The development of the word class system of the European grammatical tradition. Foundations of Language, 2, 3–19.Google Scholar
Russell, B. (1905). On denoting. Mind, 14, 479–493.CrossRefGoogle Scholar
Russell, B. (1919). The philosophy of logical atomism. The Monist, 30, 345–380. Part of a series of papers of the same title. Cited from Russell (1956).CrossRefGoogle Scholar
Russell, B. (1944). Reply to criticisms. In Schilpp, P. A., editor. The Philosophy of Bertrand Russell. The Library of Living Philosophers. Evanston, IL: Northwestern University Press, pp. 681–741.Google Scholar
Russell, B. (1956). Logic and Knowledge. Essays 1901–1950. London: George Allen & Unwin.Google Scholar
Russell, B. & Whitehead, A. N. (1910). Principia Mathematica, Vol. 1. Cambridge: Cambridge University Press.Google Scholar
Schwartzkopff, R. (2016). Singular terms revisited. Synthese, 193, 909–936.CrossRefGoogle Scholar
Sundholm, B. G. (2009). A century of judgement and inference, 1837–1936: Some strands in the development of logic. In Haaparanta, L., editor. The Development of Modern Logic. Oxford: Oxford University Press, pp. 263–317.CrossRefGoogle Scholar
Textor, M. (2010). Frege’s concept paradox and the mirroring principle. The Philosophical Quarterly, 60, 126–148.CrossRefGoogle Scholar
Trueman, R. (2015). The concept horse with no name. Philosophical Studies, 172, 1889–1906.CrossRefGoogle Scholar
Wittgenstein, L. (1922). Tractatus Logico-Philosophicus. London: Routledge & Kegan Paul.Google Scholar
Wright, C. (1983). Frege’s Conception of Numbers as Objects. Aberdeen: Aberdeen University Press.Google Scholar
Wright, C. (1998). Why Frege does not deserve his grain of salt. Grazer Philosophische Studien, 55, 239–263. Cited from the reprint in Hale & Wright (2001).CrossRefGoogle Scholar