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Inconsistency in Science: A Partial Perspective

Chapter
Part of the Origins book series (ORIN, volume 2)

Abstract

The prevalence of inconsistency in both our scientific and ‘everyday’ belief structures is something which is being increasingly recognised.1 In the world of scientific representations, Bohr’s theory, of course, is one of the more well known examples, described by Lakatos as ‘... sat like a baroque tower upon the Gothic base of classical electrodynamics’ (Lakatos 1970, 142; see also Brown 1992); others that have been put forward include the old quantum theory of black-body radiation, the Everett-Wheeler interpretation of quantum mechanics, Newtonian cosmology, the (early) theory of infinitesimals in calculus, the Dirac δ-function, Stokes’ analysis of pendulum motion and Michelson’s ‘single-ray’ analysis of the Michelson-Morley interferometer arrangement. The problem, of course, is how to accommodate this aspect of scientific practice given that within the framework of classical logic an inconsistent set of premises yields any well-formed statement as a consequence. The result is disastrous: the set of consequences of an inconsistent theory will explode into triviality and the theory is rendered useless. Another way of expressing this descent into logical anarchy which will be useful for our discussion to follow is to say that under classical logic the closure of any inconsistent set of sentences includes every sentence. It is this which lies behind Popper’s famous declaration that the acceptance of inconsistency ‘... would mean the complete breakdown of science’ since an inconsistent system is ultimately uninformative (Popper 1940, 408; 1972, 91–92).

Keywords

Quantum Theory Classical Logic Epistemic Attitude Paraconsistent Logic Doxastic Attitude 
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.

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References

  1. Arruda, A. I. (1980), A Survey of Paraconsistent Logic. In Mathematical Logic in Latin America A. I. Arruda, R. Chuaqui and N. C. A. da Costa (eds.), North-Holland, pp. 1–41.Google Scholar
  2. Arruda, A. I. (1989), Aspects of the Historical Development of Paraconsistent Logic. In Paraconsistent Logic: Essays on the Inconsistent G. Priest, R. Routley, and J. Norman (eds.), Munich: Philosophia, 1989, pp. 99–130.Google Scholar
  3. Bartelborth, T. (1989), Is Bohr’s Model of the Atom Inconsistent? In Philosophy of the Natural Sciences, Proceedings of the 13th International Wittgenstein Symposium P. Weingartner and G. Schurz (eds.), HPT, pp. 220–223.Google Scholar
  4. Bohr, N. (1972), Collected Works Elsevier.Google Scholar
  5. Brown, B. (1990), How to be Realistic about Inconsistency in Science. Studies in History and Philosophy of Science 21 281–294.CrossRefGoogle Scholar
  6. Brown, B. (1992), Old Quantum Theory: A Paraconsistent Approach. PSA 1992 Vol. 2, Philosophy of Science Association, pp. 397–411.Google Scholar
  7. Bueno, O. (1997), Empirical Adequacy: A Partial Structures Approach. Studies in History and Philosophy of Science 28 585–610.CrossRefGoogle Scholar
  8. da Costa, N. C. A.(1989), Logic and Pragmatic Truth. In Logic, Methodology and Philosophy of Science VIII J. E. Fenstad et al. (eds.), Elsevier, pp. 247–261.Google Scholar
  9. da Costa, N. C. A., O. Bueno, and S. French (1998), The Logic of Pragmatic Truth. The Journal of Philosophical Logic 27 603–620.CrossRefGoogle Scholar
  10. da Costa, N. C. A. and S. French (1989a), Pragmatic Truth and the Logic of Induction. The British Journal for the Philosophy of Science 40 333–356.CrossRefGoogle Scholar
  11. da Costa, N. C. A. and S. French (1989b), Critical Study of ‘In Contradiction’. Philosophical Quarterly 39 498–501.CrossRefGoogle Scholar
  12. da Costa, N. C. A. and S. French (1990), The Model-Theoretic Approach in the Philosophy of Science. Philosophy of Science 57 248–265.CrossRefGoogle Scholar
  13. da Costa, N. C. A. and S. French (1993a), Towards an Acceptable Theory of Acceptance. In Correspondence, Invariance and Heuristics S. French and H. Kamminga (eds.), Dordrecht: Reidel, pp. 137–158.Google Scholar
  14. da Costa, N. C. A. and S. French (1993b), A Model Theoretic Approach to ‘Natural Reasoning’. International Studies in Philosophy of Science 7 177–190.CrossRefGoogle Scholar
  15. da Costa, N. C. A. and D. Marconi (1989), An Overview of Paraconistent Logic in the ‘80’s. The Journal of Non-Classical Logic 6 5–31.Google Scholar
  16. French, S. (1991), Rationality, Consistency and Truth. The Journal of Non-Classical Logic 7 51–71.Google Scholar
  17. French, S. and J. Ladyman (1997), Superconductivity and Structures: Revisiting The London Approach. Studies in History and Philosophy of Modern Physics 28 363–393.CrossRefGoogle Scholar
  18. French, S. and J. Ladyman (1999), Reinflating the Semantic Approach. International Studies in the Philosophy of Scienc 13 103–121.CrossRefGoogle Scholar
  19. Gotesky, R. (1968), The Uses of Inconsistency. Philosophy and Phenomenological Research 28 471–500.CrossRefGoogle Scholar
  20. Hettema, H. (1995), Bohr’s Theory of the Atom 1913–1923: A Case Study in the Progress of Scientific Research Programmes. Studies in History and Philosophy of Modern Physics 26 307–323.CrossRefGoogle Scholar
  21. Jammer, M. (1966), The Conceptual Development of Quantum Mechanics McGraw-Hill.Google Scholar
  22. Klein, M. (1970), Paul Ehrenfest Vol. I, North-Holland.Google Scholar
  23. Lakatos, I. (1970), Falsification and the Methodology of Scientific Research Programs. In Criticism and the Growth of Knowledge I. Lakatos and A. Musgrave (eds.), Cambridge: Cambridge University Press, pp. 91–195.Google Scholar
  24. Laymon, R. (1985), Idealizations and the Testing of Theories by Experimentation. In Experiment and Observation in Modern Science P. Achinstein and O. Hannaway (eds.), Boston: MIT Press, pp. 147–173.Google Scholar
  25. Laymon, R. (1988), The Michelson-Morley Experiment and the Appraisal of Theories. In Scrutinizing Science A. Donovan et al. (eds.), Dordrecht: Kluwer, 1988, pp. 245–266.CrossRefGoogle Scholar
  26. Madan, D. B. (1983), Inconsistent Theories as Scientific Objectives. Philosophy ofScience 50 453–470.Google Scholar
  27. Mikenberg, I., N. C. A. da Costa, and R. Chuaqui (1986), Pragmatic Truth and Approximation to Truth. Journal of Symbolic Logic 51 201–221.CrossRefGoogle Scholar
  28. Norton, J. (1987), The Logical Inconsistency of the Old Quantum Theory of Black Body Radiation. Philosophy of Science 54 327–350.CrossRefGoogle Scholar
  29. Norton, J. (1993), A Paradox in Newtonian Gravitation Theory. PSA 1992 Vol. 2, East Lansing: Philosophy of Science Association, pp. 412–420.Google Scholar
  30. Pais, A. (1991), Niels Bohr’s Times Oxford: Oxford University Press.Google Scholar
  31. Popper, K. (1940), What is Dialectic? Mind 49, 403–426.CrossRefGoogle Scholar
  32. Popper, K. (1972), The Logic of Scientific Discovery Hutchinson and Co. (1959).Google Scholar
  33. Post, H. R. (1971), Correspondence, Invariance and Heuristics. Studies in History and Philosophy of Science 2 213–255.CrossRefGoogle Scholar
  34. Priest, G. (1987), In Contradiction. Martinus Nijhoff.CrossRefGoogle Scholar
  35. Priest, G. and R. Routley (1984), Introduction: Paraconsistent Logics. Studia Logica 43 3–16.CrossRefGoogle Scholar
  36. Reichenbach, H. (1949), The Theory of Probability University of California Press.Google Scholar
  37. Smith, J. (1988a), Scientific reasoning or Damage Control: Alternative Proposals for Reasoning with Inconsistent Representations of the World. PSA 1988 Vol. 1, East Lansing: Philosophy of Science Association, pp. 241–248.Google Scholar
  38. Smith, J. (1988b), Inconsistency and Scientific Reasoning. Studies in History and Philosophy of Science 19 429–445.CrossRefGoogle Scholar
  39. Thompson, P. (1989), Explanation in the Semantic Conception of Theory Structure. PSA 1988 Vol. 2, East Lansing: Philosophy of Science Association, pp. 286–296.Google Scholar

Copyright information

© Springer Science+Business Media Dordrecht 2002

Authors and Affiliations

  1. 1.Department of PhilosophyUniversity of São PauloBrasil
  2. 2.Division of History and Philosophy of ScienceUniversity of LeedsUK

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