TWO-SORTED FREGE ARITHMETIC IS NOT CONSERVATIVE

Abstract Neo-Fregean logicists claim that Hume’s Principle ( HP ) may be taken as an implicit definition of cardinal number, true simply by fiat. A long-standing problem for neo-Fregean logicism is not deductively conservative over pure axiomatic second-order logic. This seems to preclude from being In this paper, we study Richard Kimberly Heck’s Two-Sorted Frege Arithmetic 2FA ), a variation on which has been thought We show it isn’t. fact, n -th order logic, all $n \geq 2$ . It follows in the usual one-sorted setting, Field-conservative second- or higher-order