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Journal for General Philosophy of Science

, Volume 35, Issue 1, pp 129–145 | Cite as

Wie Natürlich ist das System der Natürlichen Deduktion?

  • Roger Schmit
Article
  • 59 Downloads

Abstract

How natural is natural deduction?– Gentzen's system of natural deduction intends to fit logical rules to the effective mathematical reasoning in order to overcome the artificiality of deductions in axiomatic systems (¶ 2). In spite of this reform some of Gentzen's rules for natural deduction are criticised by psychologists and natural language philosophers for remaining unnatural. The criticism focuses on the principle of extensionality and on formalism of logic (¶ 3). After sketching the criticism relatively to the main rules, I argue that the criteria of economy, simplicity, pertinence etc., on which the objections are based, transcend the strict domain of logic and apply to arguments in general (¶ 4). (¶ 5) deals with Frege's critique of the concept of naturalness as regards logic. It is shown that this concept means a regression into psychologism and is exposed to the same difficulties as are: relativity, lack of precision, the error of arguing from `is' to `ought' (the naturalistic fallacy). Despite of these, the concept of naturalness plays the role of a diffuse ideal which favours the construction of alternative deductive systems in contrast to the platonic conception of logic (¶ 6).

argument constructivism extensionality formalism logical consequence natural deduction natural language platonism principle of conditionalisation psychologism truth-functions 

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LITERATUR

  1. Bar-Hillel, Y. and Carnap, R.: 1953-54, 'Semantic Information', The British Journal for the Philosophy of Science 4, 147–57.Google Scholar
  2. Braine, M. D. S.: 1978, 'On the Relation Between the Natural Logic of Reasoning and Standard Logic', Psychological Review 85(1), 1–21.CrossRefGoogle Scholar
  3. Dummett, M.: 1973, Frege. Philosophy of Language, Duckworth, London.Google Scholar
  4. Falmagne, R. J.: 1975 (ed.), Reasoning: Representation and Process in Children and Adults, Erlbaum, Hillsdale, N.J.Google Scholar
  5. Frege, G.: 1879-1891, 'Logik', in Frege 1969, 1–8.Google Scholar
  6. Frege, G.: 1882, 'Über die wissenschaftliche Berechtigung einer Begriffsschrift', Zeitschrift für Philosophie und philosophische Kritik 81, 48–56.Google Scholar
  7. Frege, G.: 1897, 'Logik', in Frege 1969, 137–163.Google Scholar
  8. Frege, G.: 1906, 'Brief an Husserl. 30.10.-1.11. 1906', in Frege 1976, 101–105.Google Scholar
  9. Frege, G.: 1969, Nachgelassene Schriften, hrsg. von H. Hermes, F. Kambartel, F. Kaulbach, Felix Meiner Verlag, Hamburg.Google Scholar
  10. Frege, G.: 1976, Wissenschaftlicher Briefwechsel, hrsg. von G. Gabriel, H. Hermes, F. Kambartel, Ch. Thiel, A. Veraart, Felix Meiner Verlag, Hamburg.Google Scholar
  11. Gentzen, G.: 1934-35, 'Untersuchungen über das logische Schließen', Mathematische Zeitschrift 39, 176–210 und 405-431.CrossRefGoogle Scholar
  12. Grice, H. P.: 1967, Logic and Conversation. William James Lectures, Harvard University Press, Cambridge, Mass.Google Scholar
  13. Husserl, E.: 1980, Logische Untersuchungen, Bd.I: Prolegomena zur reinen Logik, Max Niemeyer Verlag, Tübingen.Google Scholar
  14. Jaskowski, S.: 1934, 'On the Rules of Suppositions in Formal Logic', Studia logica 1, 5–32.Google Scholar
  15. Johnson-Laird, P. N.: 1983, Mental Models. Towards a Cognitive Science of Language, Inference, and Consciousness, University Press, Cambridge.Google Scholar
  16. Lorenzen, P.: 1968, 'Collegium Logicum', in Methodisches Denken,Suhrkamp Verlag, Frankfurt a. M., 7–23.Google Scholar
  17. Osherson, D.: 1975, 'Logic and Models of Logical Thinking', in Falmagne 1975, 81–91.Google Scholar
  18. Popper, K.: 1972, Objective Knowledge, Clarendon Press, Oxford.Google Scholar
  19. Rips, L. J.: 1983, 'Cognitive Processes in Propositional Reasoning', Psychological Review 90(1), 38–71.CrossRefGoogle Scholar
  20. Seebohm, T.: 1984, Philosophie der Logik, Verlag Karl Alber, Freiburg-München.Google Scholar
  21. Strawson, P. F.: 1952, Introduction to Logical Theory, Methuen & CO LTD, Oxford.Google Scholar
  22. Wittgenstein, L.: 1971, Philosophische Untersuchungen, Suhrkamp Verlag, Frankfurt a.M.Google Scholar

Copyright information

© Kluwer Academic Publishers 2004

Authors and Affiliations

  • Roger Schmit
    • 1
  1. 1.Section de Philosophie, Département des LettresCentre Universitaire de LuxembourgLuxembourg

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