Stable Axioms in Physical Theories

  • H.-J. Schmidt


Stability of a form may defined intuitively by demanding that small perturbations of the form cause no changes or only “wellbehaved” changes of the form. In the words of R. Thom [1]: “Une G-forme A sera dite structurellement stable si toute form B assez voisine de A. est G-équivalente a A.”. (R. Thorn considers a pseudo-group G operating on forms.) In physics one often deals with stability of states, e.g. of orbits under small perturbations or of thermodynamical states under external fluctuations [2]. However, one may also examine stability of a physical theory (PT) as a whole. The “perturbations” here would correspond to confrontations with the real world or with rival theories, which threaten to “destroy the form”, i.e. to falsify the theory. Following G. Ludwig [3] and U. Moulines [4], the PT can be stabilized against both kinds of “perturbation” by passing from exact applications to approximate applications and from exact intertheoretical relations to approximate ones. (The technical details involving “imprecision-sets”, i.e. entourages of “physical uniformities” are explained in the respective contributions of this volume.)


Physical Theory Uniform Space Stable Species Stable Procedure Axiomatic Basis 
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Copyright information

© Plenum Press, New York 1981

Authors and Affiliations

  • H.-J. Schmidt
    • 1
  1. 1.Fachbereich PhysikUniversität OsnabrückOsnabrückFederal Republic of Germany

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