Inconsistency in Science: A Partial Perspective

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


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).


Quantum Theory Classical Logic Epistemic Attitude Paraconsistent Logic Doxastic Attitude 
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© 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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