On Expressive Power Over Arithmetic

  • Carlo Nicolai
Part of the Boston Studies in the Philosophy and History of Science book series (BSPS, volume 334)


The paper is concerned with the fine boundary between expressive power and reducibility of semantic and intensional notions in the context of arithmetical theories. I will consider three notions of reduction of a theory characterizing a semantic or a modal notion to the underlying arithmetical base theory – relative interpretability, speed up, conservativeness – and highlight a series of cases where moving between equally satisfactory base theories and keeping the semantic or modal principles fixed yields incompatible results. I then consider the impact of the non-uniform behaviour of these reducibility relations on the philosophical significance we usually attribute to them.



This research has been supported by the European Commission, grant no. 658285 FOREMOTIONS. I would like to thank Martin Fischer, Albert Visser, and an anonymous referee for useful comments and insights.


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© Springer International Publishing AG, part of Springer Nature 2018

Authors and Affiliations

  • Carlo Nicolai
    • 1
  1. 1.King’s College LondonStrandLondonUK

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