Journal of Philosophical Logic

, Volume 29, Issue 1, pp 75–101 | Cite as

The "Natural" and the "Formal"

  • Jaroslav Peregrin
Article

Abstract

The paper presents an argument against a “metaphysical” conception of logic according to which logic spells out a specific kind of mathematical structure that is somehow inherently related to our factual reasoning. In contrast, it is argued that it is always an empirical question as to whether a given mathematical structure really does captures a principle of reasoning. (More generally, it is argued that it is not meaningful to replace an empirical investigation of a thing by an investigation of its a priori analyzable structure without paying due attention to the question of whether it really is the structure of the thing in question.) It is proposed to elucidate the situation by distinguishing two essentially different realms with which our reason must deal: “the realm of the natural”, constituted by the things of our empirical world, and “the realm of the formal”, constituted by the structures that we use as “prisms” to view, to make sense of, and to reconstruct the world. It is suggested that this vantage point may throw light on many foundational problems of logic.

philosophy of logic logical form logical truth structuralism mathematical models 

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

REFERENCES

  1. Boolos, G. S. and Jeffrey, R. C. (1974): Computability and Logic, Cambridge University Press, Cambridge.Google Scholar
  2. Brandom, R. (1994): Making it Explicit, Harvard University Press, Cambridge, MA.Google Scholar
  3. Brouwer, L. E. J. (1907): Over de grondslagen der wiskunde, Thesis, Amsterdam; reprinted in A. Heyting (ed.), Brouwer: Collected Works I: Philosophy and Foundations of Mathematics, North-Holland, Amsterdam, 1975.Google Scholar
  4. Davidson, D. (1989): What is present to the mind?, in J. Brandl and W. L. Gombocz (eds), The Mind of Donald Davidson, Rodopi, Amsterdam, pp. 3–18.Google Scholar
  5. Davidson, D. (1990): The structure and contents of truth, J. Philos. 87: 279–328.Google Scholar
  6. Einstein, A. (1983): Geometry and Experience, Sidelights on Relativity, Dover, New York (translation of the German original ‘Geometrie und Erfahrung’ from 1921).Google Scholar
  7. Etchemendy, J. (1988): Tarski on truth and logical consequence, J. Symbolic Logic 53: 51–79.Google Scholar
  8. Frege, G. (1879): Begriffsschrift, Nebert, Halle; English translation in van Heijenoort (1971), pp. 1–82.Google Scholar
  9. Frege, G. (1976): Wissenschaftlicher Briefwechsel (ed. by G. Gabriel et al.), Meiner, Hamburg; English translations in Frege: Philosophical and Mathematical Correspondence, Blackwell, Oxford, 1980.Google Scholar
  10. García-Carpintero, M. (1999): The explanatory value of truth theories embodying the semantic conception, in Peregrin (1999b), pp. 185–212.Google Scholar
  11. Gödel, K. (1931): Ñber formal unentscheidbare Sätze der Principia Mathematica und verwandter Systeme I, Monatsh. Math. Phys. 38: 173–198.Google Scholar
  12. van Heijenoort, J. (ed.) (1971): From Frege to Gödel: A Source Book in Mathematical Logic, Harvard University Press, Cambridge, MA.Google Scholar
  13. Hilbert, D. (1899): Grundlagen der Geometrie, Teubner, Leipzig.Google Scholar
  14. Hintikka, J. and Mutanen, A. (1998): An alternative concept of computability, in J. Hintikka (ed.), Language, Truth and Logic in Mathematics (Selected Papers 3), Kluwer Acad. Publ., Dordrecht.Google Scholar
  15. Hofman, A. (1995): On the nature of meaning and its indeterminacy: Davidson's view in perspective, Erkenntnis 42: 15–40.Google Scholar
  16. Katz, J. J. and Postal, P. M. (1991): Realism vs. conceptualism in linguistics', Linguistics and Philosophy 14: 515–554.Google Scholar
  17. Kreisel, G. (1967): Informal rigour and completeness proofs, in I. Lakatos (ed.), Problems in the Philosophy of Mathematics, North-Holland, Amsterdam; reprinted in J. Hintikka (ed.), The Philosophy of Mathematics, Oxford University Press, Oxford, 1969, pp. 78–94.Google Scholar
  18. Malcolm, N. (1940): Are necessary propositions really verbal?, Mind 49: 189–203.Google Scholar
  19. Montague, R. (1974): Formal Philosophy: Selected Papers of R. Montague (ed. R. Thomason), Yale University Press, New Haven.Google Scholar
  20. Penrose, R. (1990): The Emperor's New Mind, Vintage, London.Google Scholar
  21. Peregrin, J. (1995): Doing Worlds with Words, Kluwer Acad. Publ., Dordrecht.Google Scholar
  22. Peregrin, J. (1997): Language and its models, Nordic J. Philos. Logic 2: 1–23.Google Scholar
  23. Peregrin, J. (1998): Linguistics and philosophy, Theoretical Linguistics 24: 245–264.Google Scholar
  24. Peregrin, J. (1999a): The pragmatization of semantics, in K. Turner (ed.), The Semantics/ Pragmatics Interface from Different Points of View, Elsevier, Amsterdam, pp. 419–442.Google Scholar
  25. Peregrin, J. (ed.) (1999b): Truth and its Nature (if Any), Kluwer Acad. Publ., Dordrecht.Google Scholar
  26. Poincaré, H. (1908): Science and method (English translation), in Foundations of Science, Science Press, New York, 1921, pp. 359–546.Google Scholar
  27. Putnam, H. (1985): A comparison of something with something else, New Literary History 17: 61–79.Google Scholar
  28. Putnam, H. (1994): Rethinking mathematical necessity, in J. Conant (ed.), Words and Life, Harvard University Press, Cambridge, MA.Google Scholar
  29. Quine, W. V. O. (1960): Word and Object, MIT Press, Cambridge, MA.Google Scholar
  30. Reichenbach, H. (1920): Relativitätstheorie und Erkenntnis Apriori, Springer, Berlin.Google Scholar
  31. Russell, B. (1905): On denoting, Mind 14: 479–493.Google Scholar
  32. Sellars, W. (1963): Science, Perception and Reality, Routledge, New York.Google Scholar
  33. Shapiro, S. (1996): Space, number and structure: A tale of two debates, Philos. Math. 4: 148–173.Google Scholar
  34. Stekeler-Weithofer, P. (1986): Grundprobleme der Logik, de Gruyter, Berlin.Google Scholar
  35. Stekeler-Weithofer, P. (1992): Hegels Analytische Philosophie, Schöningh, Paderborn.Google Scholar
  36. Stekeler-Weithofer, P. (1994): Ideation und Projektion, Deutsche Zeitschrift für Philosophie 42: 783–798.Google Scholar
  37. Tarski, A. (1932): Der Wahrheitsbegriff in den Sprachen der deduktiven Disziplinen, in Akademischer Anzeiger der Akademie der Wissenschaften in Wien 69; English translation ‘The Concept of Truth in Formalized Languages’ in Tarski (1956), pp. 152–278.Google Scholar
  38. Tarski, A. (1944): The semantic conception of truth, Philosophy and Phenomenological Research 4: 341–375.Google Scholar
  39. Tarski, A. (1956): Logic, Semantics, Metamathematics, Clarendon Press, Oxford.Google Scholar
  40. Wittgenstein, L. (1953): Philosophische Untersuchungen, Blackwell, Oxford; English translation Philosophical Investigations, Blackwell, Oxford, 1953.Google Scholar
  41. Wittgenstein, L. (1956): Bemerkungen über die Grundlagen der Mathematik, Blackwell, Oxford; English translation Remarks on the Foundations of Mathematics, Blackwell, Oxford, 1956.Google Scholar

Copyright information

© Kluwer Academic Publishers 2000

Authors and Affiliations

  • Jaroslav Peregrin
    • 1
  1. 1.Institute of PhilosophyAcademy of Sciences, JilskaPrahaCzech Republic

Personalised recommendations