Reasons from Science for Limiting Classical Logic

  • Paul Weingartner


As is clear from the title, the paper defends the view that there are reasons from Science for limiting Classical Logic (CL). In this paper such reasons are especially given from physics; even if I think that other areas (Philosophy of Science, Epistemology, Action theory, Ethics... etc.) lead to similar or to the same limitations which are proposed here.1 In general problems arise when logic is applied to fields outside logic and mathematics. These problems are of different kinds but many of them have the same source. The source is what I have called elsewhere “replaceable and reducible parts in the consequence class”. In other words: Classical valid inferences, (arguments) which have replaceable or reducible parts in their consequence class lead to paradoxical or incorrect results when applied to the respective area. Replaceable parts are parts which can be replaced by an arbitrary part (sentence, predicate) salva validitate of the argument. And reducible parts are parts which can be reduced to smaller parts salva validitate of the argument. In this paper I shall concentrate on problems which arise when logic is applied to physics. The paper is divided into 4 chapters. In the first chapter I want to deal with the problems of commensurability and to show that this problem is not specific to physics, but is much more general. The second chapter deals with commensurability in Quantum logic. In the third chapter special restrictions (filters) on CL are proposed for a solution of the above mentioned problems. In the fourth chapter it is shown how these restrictions can solve the problems concerning commensurability and distributivity when logic is applied to Quantum Theory.


Classical Logic Observable State Consequence Class Quantum Logic Reducible Part 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. 1.
    G. Birkhoff, J. v. Neumann: ‘The Logic of Quantum Mechanics’. In: Annals of Mathematics 37 (1936) pp. 823–843Google Scholar
  2. 2.
    D. Finkelstein: ‘Matter, Space and Logic’. In: Hooker (ed.): II (1979) pp. 123139Google Scholar
  3. 3.
    J. Hintikka: ‘The Principles of Mathematics Revisited’. ( Cambridge University Press, Cambridge 1996 )MATHCrossRefGoogle Scholar
  4. 4.
    J. Hintikka: A Logic for Quantum Theory. Unpublished manuscriptGoogle Scholar
  5. 5.
    J.M. Jauch, C. Piron: ‘What is Quantum Logic?’ In: Quanta ed. by P. Freund et al. (Univ. of Chicago Press, Chicago 1970) p. 166ffGoogle Scholar
  6. 6.
    P. Mittelstaedt: ‘On the Interpretation of the Lattice of Subspaces of the Hilbert Space as a Propositional Calculus’. In: Zeitschrift für Naturforschung 27a (1972) p. 1358 ffGoogle Scholar
  7. 7.
    P. Mittelstaedt: Quantum Logic ( Reidel, Dordrecht 1978 )MATHCrossRefGoogle Scholar
  8. 8.
    G. Schurz: ‘Relevant Deduction. From Solving Paradoxes towards a General Theory’. In: Erkenntnis 35 (1991) pp. 391–437Google Scholar
  9. 9.
    G. Schurz: ‘Relevance in Deductive Reasoning: A Critical Overview’. In: Beyond Classical Logic Conceptus-Studien. Ed. by G. Schurz and M. Ursic. ( Academie-Verlag, St. Augustin 1998 )Google Scholar
  10. 10.
    G. Schurz, P. Weingartner: ‘Verisimilitude Defined by Relevant Consequence Elements. A new Reconstruction of Popper’s Original Idea’. In: What is Closer to the Truth? ed. by Th. Kuipers. (Rodopi, Amsterdam 1987 )Google Scholar
  11. 11.
    P. Suppes: Probabilistic Metaphysics ( Blackwells, Oxford 1984 )Google Scholar
  12. 12.
    P. Weingartner: ‘Remarks on the Consequence-Class of Theories’. In: The Role of Experience in Science ed. by E. Scheibe. (de Gruyter, Berlin 1988) pp. 161180Google Scholar
  13. 13.
    P. Weingartner: ‘A Logic for QM Based on Classical Logic’. In: L’art, la science et la metaphysique. Essays in Honor of André Mercier ed. by M. de la Luiz Garcia Alonso, E. Montsopoulos, G. Seel ( Peter Lang, Bern 1993 ) pp. 439–458Google Scholar
  14. 14.
    P. Weingartner: ‘Can there be Reasons for Putting Limitations on Classical Logic?’ In: Patrick Suppes, Scientific Philosopher, Vol. 3. ed. by P. Humphries. ( Kluwer, Dordrecht 1994 ) pp. 89–124Google Scholar
  15. 15.
    P. Weingartner: ‘Language and Coding Dependencies of Results in Logic and Mathematics’. In: Philosophy of Mathematics Today ed. by Agazzi, E. and György Darvas. (Kluwer, Dordrecht 1997 ) pp. 73–87Google Scholar
  16. 16.
    P. Weingartner, G. Schurz: ‘Paradoxes Solved by Simple Relevance Criteria’. In: Logique et Analyse 113 (1986), pp. 3–40Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2004

Authors and Affiliations

  • Paul Weingartner

There are no affiliations available

Personalised recommendations