Comparing Theories: The Dynamics of Changing Vocabulary

Part of the Outstanding Contributions to Logic book series (OCTR, volume 5)


There are several first-order logic (FOL) axiomatizations of special relativity theory in the literature, all looking different but claiming to axiomatize the same physical theory. In this chapter, we elaborate a comparison between these FOL theories for special relativity. We do this in the framework of mathematical logic. For this comparison, we use a version of definability theory in which new entities can also be defined besides new relations over already available entities. In particular, we build an interpretation (in Alfred Tarski’s sense) of the reference-frame oriented theory \({\textsc {SpecRel}}\) developed in the Budapest Logic Group into the observationally oriented Signalling theory of James Ax published in Foundations of Physics. This interpretation provides \({\textsc {SpecRel}}\) with an operational/experimental semantics. Then we make precise, “quantitative” comparisons between these two theories via using the notion of definitional equivalence. This is an application of mathematical logic to the philosophy of science and physics in the spirit of Johan van Benthem’s work.


Special relativity Space-time geometry Definability theory Observational physics Mathematical logic 


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© Springer International Publishing Switzerland 2014

Authors and Affiliations

  1. 1.Alfréd Rényi Institute of MathematicsHungarian Academy of SciencesBudapestHungary
  2. 2.Alfréd Rényi Institute of MathematicsHungarian Academy of SciencesBudapestHungary

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