On Expressive Power Over Arithmetic
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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