This chapter considers objections to the proposal of the second part of the book which are not simply objections to the claim that our arithmetical concepts are empirically grounded. These include some objections that might be generated by a broadly Quinean outlook, a circularity worry (which are related here to the Wittgensteinian notion of ‘deep nonsense’), and a number of issues concerning the epistemic step from possession of concepts to belief in conceptually true propositions. The chapter also discusses in some detail the objection that, by definition, arithmetical knowledge cannot be a priori if it is empirical.
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