Can concepts be defined in terms of sets?

Marie Duží, Pavel Materna

DOI: http://dx.doi.org/10.12775/LLP.2010.008

Abstract


The goal of this paper is a philosophical explication and logical rectification of the notion of concept. We take into account only those contexts that are relevant from the logical point of view. It means that we are not interested in contexts characteristic of cognitive sciences, particularly of psychology, where concepts are conceived of as some kind of mental objects or representations. After a brief recapitulation of various theories of concept, in particular Frege’s and Church’s ones, we propose our own theory based on procedural semantics of Transparent Intensional Logic (TIL) and explicate concept in terms of the key notion of TIL, namely construction viewed as an abstract, algorithmically structured procedure.

Keywords


procedural semantics; Transparent Intensional Logic; concepts; structured meanings

Full Text:

PDF

References


Anderson, C. A., 1998, “Alonzo Church’s contributions to philosophy and intensional logic”, The Bulletin of Symbolic Logic 4 (2),:129–171.

Bealer, G., 1982, Quality and Concept, Oxford: Clarendon Press.

Bolzano, B., 1837, Wissenschaftslehre, vols. I, II. Sulzbach.

Carnap, R., 1947, Meaning and Necessity, Chicago: Chicago University Press.

Church, A., 1956, Introduction to Mathematical Logic, Princeton: Princeton University Press.

Church, A., 1985, “Intensional semantics”, pp. 40–47 in: A.P. Martinich (ed.), The Philosophy of Language, Oxford University Press.

Church, A., 1993, “A revised formulation of the logic of sense and denotation. Alternative (1)”, Noûs 27: 141–157.

Cresswell, M.J., 1975, “Hyperintensional logic”, Studia Logica 34: 25–38.

Cresswell, M.J., 1985, Structured Meanings, Cambridge: MIT Press.

Duží, M., 2004, “Intensional logic and the irreducible contrast between de dicto and de re”, ProFil 5: 1–34. http://profil.muni.cz/01_2004/duzi_de_dicto_de_re.pdf

Duží, M., B. Jespersen and P. Materna, 2010, Procedural Semantics for Hyper-intensional Logic. Foundations and Applications of Transparent Intensional Logic, Springer Verlag.

Fodor, Jerry A., 1998, Concepts, Oxford: Clarendon Press.

Frege, G, 1884, Die Grundlagen der Arithmetik, Breslau: W. Koebner.

Frege, G., 1891, Funktion und Begriff, H. Pohle, Jena. (Vortrag, gehalten in der Sitzung vom 9. Januar 1891 der Jenaischen Gesellschaft für Medizin und Naturwissenschaft, Jena, 1891).

Frege, G., 1892, “Über Begriff und Gegenstand”, Vierteljahrschrift für wissenschaftliche Philosophie 16: 192–205.

Frege, G., 1952: P. Geach and M. Black, M. (eds), Translations from the Philosophical Writings of Gottlob Frege, B. Blackwell, Oxford.

Frege, G., 1971: G. Gabriel, Schriften zur Logik und Sprachphilosophie, Felix Meiner Verlag, Hamburg.

Gödel, K., 1944, “Russell’s mathematical logic”, pp. 119–141 in: Kurt Gödel: Collected Works, Vol.II., Feferman, S. et alii (eds.). Oxford University Press 1990.

Horák, A., 2002, The Normal Translation Algorithm in Transparent Intensional Logic for Czech, PhD Thesis, Masaryk University, Brno, retrievable at http://www.fi.muni.cz/ hales/disert/

Jespersen, B., 2003, “Why the tuple theory of structured propositions isn’t a theory of structured propositions”, Philosophia 31: 171–183.

Jespersen, B., 2010,“ How hyper are hyperpropositions?”, Language and Linguistics Compass 4:, 96–106.

Jespersen, B., 2010a: “Hyperintensions and procedural isomorphism: Alternative (1/2)”, pp. 299–320 in: The Analytical Way. Proceedings of the 6th European Congress of Analytic Philosophy, T. Czarnecki, K. Kijania-Placek, O. Poller and J. Woleński (eds.), College Publications, London.

King, J.C., 2001, “Structured propositions”. http://plato.stanford.edu/entries/

propositions-structured/, version as of 8 August 2001.

Materna, P., 1998, Concepts and Objects, Acta Philosophica Fennica, vol. 63, Helsinki.

Materna, P., 2004, Conceptual Systems, Berlin: Logos.

Materna, P., 2007, “Properties of mathematical objects (Gödel on classes, properties and Concepts)”, Journal of Physics: Conference Series 82: 012007.

Materna, P., 2007a, “Once more on analytic vs. synthetic”, Logic and Logical Philosophy16: 3–43.

Montague, R., 1970, “Universal grammar”. Theoria 36: 373–398.

Moschovakis, Y.N., 1994, “Sense and denotation as algorithm and value”, pp. 210-249 in: Lecture Notes in Logic, J. Väänänen and J. Oikkonen (eds.), vol. 2, Berlin: Springer.

Moschovakis, Y.N, 2006, “A logical calculus of meaning and synonymy”, Linguistics and Philosophy 29: 27–89.

Parsons, Ch., 1990, “Introductory note to 1944”, pp. 02–118 in: Kurt Gödel: Collected Works, Vol.II.

Quine, W.v.O., 1953, “Two dogmas of empiricism”, pp. 20–46 in: From a Logical Point of View, Harvard University Press, Cambridge (Mass.).

Tichý, P., 1968, “Smysl a procedura”, Filosofický časopis 16: 222-232. Translated as “Sense and procedure” in Tichý [2004], pp. 77–92.

Tichý, P., 1988, The Foundations of Frege’s Logic, Berlin, New York: De Gruyter.

Tichý, P., 1995, “Constructions as the subject-matter of mathematics”, pp. 175–185 in: The Foundational Debate: Complexity and Constructivity in Mathematics and Physics, W. DePauli-Schimanovich, E. Köhler and F. Stadler (eds.), Dordrecht, Boston, London, and Vienna: Kluwer. Reprinted in Tichý [2004], pp. 873–885.

Tichý, P., 2004, Collected Papers in Logic and Philosophy, V. Svoboda, B. Jespersen and C. Cheyne (eds.), Prague: Filosofia, Czech Academy of Sciences, and Dunedin: University of Otago Press.








ISSN: 1425-3305 (print version)

ISSN: 2300-9802 (electronic version)

Partnerzy platformy czasopism