Implicit commitments of „implicit commitments”: the ω-rule and second-order internal categoricity

Our next meeting takes place on 13.05.2024 at 4.45 pm (CEST). Our speaker is Tim Button (UCL). He will deliver the talk entitled Implicit commitments of “implicit commitments”: the ω-rule and second-order internal categoricity

Abstract. I accept Peano Arithmetic. In doing so, I think I am probably implicitly committed to Con_{PA}; to the Local Reflection principle; to stronger reflection principles still… 

But my aim in this talk is not to probe the frontiers of these implicit commitments. Instead, I want to consider the implicit commitments of (common) arguments for the claim that we have such implicit commitments. I argue that these arguments are implicitly committed to both 

(1) the soundness of the ω-rule, and 

(2) the acceptability of second-order induction with an (impredicative comprehension schema)

These commit us (respectively) to both the intra-subjective and inter-subjective determinacy of the natural numbers.