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Theory of Concepts

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Abstract

The word ‘concept’ is sometimes used as a synonym for ‘property’, but many authors use it in a more specific sense, for example as standing for unsaturated entities whose extensions are sets and classes, for Fregean senses, or for abstract objects. Although there is no universal agreement on a definition of concepts, a viable theory of concepts has to address a number of formal issues: How to deal with counterfactual and possibly contradictory concepts, how to restrict comprehension schemes in higher-order logic to avoid semantic paradoxes like the Paradox of Predication, how to nominalize concepts, and how to express similarity and typicality of concepts. The article gives a brief survey of the most important problems in concept theory and their possible solutions.

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References and Recommended Readings

Asterisks (∗) indicate recommended readings.

  1. *Andrews, P. B. (2002). An introduction to mathematical logic and type theory: To truth through proof. New York: Academic Press. [Contains an introduction to higher-order logic suitable for beginners].

    Google Scholar 

  2. Benzmüller, C., Brown, C. E., Siekmann, J., & Stratman, R. (Eds.). (2008). Reasoning in simple type theory (Studies in logic, Vol. 17). London: College Publications.

    Google Scholar 

  3. Burgess, J. P. (2005). Fixing Frege. Princeton: Princeton University Press.

    Google Scholar 

  4. Castañeda, H. -N. (1989). Thinking, language, experience. Minneapolis: University of Minnesota Press.

    Google Scholar 

  5. Cocchiarella, N. B. (1994). Philosophical perspectives on formal theories of predication. In F. Guenthner & D. Gabbay (Eds.), Handbook of philosophical logic (Vol. 4, pp. 253–326). Dordrecht: Kluwer.

    Google Scholar 

  6. *Cocchiarella, N. B. (2007). Formal ontology and conceptual realism (Synthese library, Vol. 339). Dordrecht: Springer. [Intermediate-level text that lays out fine-grained philosophical distinctions between systems of higher-order logic].

    Google Scholar 

  7. Ganter, B., & Wille, R. (1998). Formal concept analysis: Mathematical foundations. Berlin/Heiderlberg/New York: Springer.

    Google Scholar 

  8. Ganter, B., Stumme, G., & Wille, R. (Eds.). (2005). Formal concept analysis. Berlin/New York: Springer.

    Google Scholar 

  9. *Gärdenfors, P. (2004). Conceptual spaces: The geometry of thought. Cambridge, MA: MIT Press. [Reference work on the theory of conceptual spaces].

    Google Scholar 

  10. Henkin, L. (1950). Completeness in the theory of types. The Journal of Symbolic Logic, 15(2), 81–91.

    Article  Google Scholar 

  11. Hintikka, J. (1955). Reductions in the theory of types. In K. Jaakko & J. Hintikka (Eds.), Two papers on symbolic logic (Acta philosophica fennica, Vol. 8, pp. 57–115). Helsinki: Soc. Philosophica.

    Google Scholar 

  12. Mormann, T. (1995). Trope sheaves: A topological ontology of tropes. Logic and Logical Philosophy, 3, 129–150.

    Article  Google Scholar 

  13. Muskens, R. (2007). Intensional models for the theory of types. Journal of Symbolic Logic, 72(1), 98–118.

    Article  Google Scholar 

  14. Parsons, T. (1980). Existence. New Haven: Yale University Press.

    Google Scholar 

  15. *Priest, G. (2005). Towards non-being: The logic and metaphysics of intentionality. Oxford: Clarendon. [Seminal recent work on non-existence].

    Google Scholar 

  16. Rapaport, W. J. (1978). Meinongian theories and a Russellian paradox. Noûs, 12(2), 153–180.

    Article  Google Scholar 

  17. Shapiro, S. (1991). Foundations without foundationalism: A case for second-order logic. Oxford: Clarendon Press.

    Google Scholar 

  18. *Zalta, E. (1983). Abstract objects. Dordrecht/Boston/Lancaster: D. Reidel. [Older, yet important work on abstract object theory].

    Google Scholar 

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Author information

Authors and Affiliations

  1. IFILNOVA Institute of Philosophy, New University of Lisbon, Lisbon, Portugal

    Erich Rast

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  1. Erich Rast
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Correspondence to Erich Rast .

Editor information

Editors and Affiliations

  1. Division of Philosophy, Royal Institute of Technology (KTH), Stockholm, Sweden

    Sven Ove Hansson

  2. Center for Information and Bubble Studies, University of Copenhagen, Copenhagen, Denmark

    Vincent F. Hendricks

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Rast, E. (2018). Theory of Concepts. In: Hansson, S., Hendricks, V. (eds) Introduction to Formal Philosophy. Springer Undergraduate Texts in Philosophy. Springer, Cham. https://doi.org/10.1007/978-3-319-77434-3_10

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