AUC PHILOSOPHICA ET HISTORICA
AUC PHILOSOPHICA ET HISTORICA

AUC Philosophica et Historica je víceoborový akademický časopis zaměřený na humanitní a společenskovědné obory (filozofie, psychologie, pedagogika, sociologie, obecné, české a hospodářské dějiny, pomocné vědy historické a archivnictví, etnologie).

Časopis je indexován v databázích CEEOL, DOAJ a EBSCO.

AUC PHILOSOPHICA ET HISTORICA, Vol 2017 No 2 (2017), 7–26

Logical space and the origins of pluralism in logic

Pavel Arazim

DOI: https://doi.org/10.14712/24647055.2017.12
zveřejněno: 14. 11. 2017

Abstract

The fact that there is a plurality of systems that we call logics makes it requisite to attempt an explanation and thorough evaluation of the role of logic. I exploit the analogical development towards the pluralism of geometry to show that both disciplines are about some kinds of space which they explicate and that we can choose with some freedom the tools for engaging in an enterprise of these disciplines. After revisiting the development of non-classical (i.e. non-Euclidian) geometries, I present logical expressivism, as coined by Robert Brandom, and, returning again to geometry, show that an analogous doctrine of geometrical expressivism can also provide a viable account of the nature and purpose of the discipline and the reasons for plurality of both geometries and logics.

klíčová slova: pluralism; expressivism; logical space; geometry; holism

reference (30)

1. Arazim, P. (2013). Pluralism in geometry. Acta Universitatis Carolinae – Philosophica et Historica, 2(2010), 7–21.

2. Beall, G., Restall, J. (2006). Logical Pluralism. Oxford: Oxford University Press.

3. Beltrami, E. (1868). Saggio di interpretazione della geometria non euclidea. Giornale di Matematiche, 6, 284–312. (English translation in J. Stillwell, 1996, Sources of Hyperbolic Geometry (History of Mathematics 10), American and London Mathematical Societies, p. 7–34).

4. Brandom, R. (1994). Making it explicit. Cambridge: Harvard University Press.

5. Brandom, R. (2000). Articulating Reasons. Cambridge: Harvard University Press.

6. Coffa, A. J. (1993). The Semantic Tradition from Kant to Carnap: To the Vienna Station. Cambridge: Cambridge University Press.

7. Descartes, R. (1965). Discourse on Method, Optics, Geometry, and Meteorology, trans. Paul J. Olscamp. Indianapolis: Bobbs-Merrill.

8. Došen, K. (1989). Logical constants as punctuation marks. Notre Dame Journal of Formal Logic, 30, 362–381. CrossRef

9. Dubucs, J. (2008). Truth and experience of truth. In M. van Atten (Ed.), One hundred years of intuitionism pp. 49–58). Basel: Birkhäuser Verlag. CrossRef

10. Dummett, M. (1977). Elements of Intuitionism. Oxford: Clarendon Press.

11. Haack, S. (1978). Philosophy of Logics. Cambridge: Cambridge University Press. CrossRef

12. Hacking, I. (1979). What is logic? Journal of Philosophy, 76(6), 285–319. CrossRef

13. Helmholtz, H. v. (1870). Über den ursprung und die bedeutung der geometrischen axiome. Vorträge und Reden, 2, 1–31.

14. Kant, I. (1954). Kritik der reinen vernunft. Hamburg: Felix Meiner.

15. Kripke, S. (1982). Wittgenstein on rules and private language: an elementary exposition. Cambridge: Harvard University Press.

16. Kuhn, T. S. (1962). The structure of scientific revolutions. Chicago: University of Chicago Press.

17. Peregrin, J. (2000). The "natural" and the "formal". Journal of Philosophical Logic, 29(1), 75–101. CrossRef

18. Peregrin, J. (2014). Inferentialism: Why Rules Matter. New York: Palgrave Macmillan. CrossRef

19. Putnam, H. (1968). Is logic empirical? Boston Studies in the Philosophy of Science, (5).

20. Quine, W. v. O. (1951). Two dogmas of empiricism. Philosophical Review, 60(1), 20–43. CrossRef

21. Quine, W. v. O. (1960). Word and Object. Cambridge, Mass.: M.I.T. Press.

22. Quine, W. v. O. (1986). Philosophy of Logic. Cambridge: Harvard University Press.

23. Shapiro, S. (1996). Space, number and structure: A tale of two debates. Philosophia Mathematica, 148–173. CrossRef

24. Sher, G. (1991). The Bounds of Logic: a Generalized Viewpoint. Cambridge, Mass.: M.I.T. Press.

25. Triplett, T. (1988). Azande logic versus werstern logic? British Journal for the Philosophy of Science, 39, 361–366. CrossRef

26. Wittgenstein, L. (1984). Über Gewißheit. Frankfurt am Main: Suhrkamp.

27. Wittgenstein, L. (2001). Philosophische Untersuchungen. Frankfurt am Main: Suhrkamp.

28. Wittgenstein, L. (2003). Tractatus logico-philosophicus, Logisch-philosophische Abhandlung. Frankfurt am Main: Suhrkamp.

29. Wolff, M. (1995). Die Vollständigkeit der kantischen Urteilstafel. Frankfurt am Main: Klostermann. CrossRef

30. Zach, R. (2006). Hilbert's programme then and now. In: Dale Jacquette (Ed.), Philosophy of Logic. Handbook of the Philosophy of Science, vol. 5. Amsterdam: Elsevier, 411–447.

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vychází: 2 x ročně
ISSN: 0567-8293
E-ISSN: 2464-7055

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