Solving the Caesar Problem—with Metaphysics

According to neo-Fregean Platonism, abstraction principles—such as the principle that the direction of line a is identical to the direction of line b iff a and b are parallel—may in some cases be regarded as introducing new singular terms (e.g., “the direction of line a”) and as fixing the truth-conditions of genuine identity statements featuring them. If neo-Fregeanism is to vindicate Frege’s idea that a plausible philosophy of arithmetic can and should treat the natural numbers as a species of object, it must address the so-called “Caesar Problem”: the problem of explaining in general terms which objects given in other terms they are to be distinguished from. This chapter pilots a novel solution to the Caesar Problem via the notion of a real definition: a definition whose purpose is not to explain a meaning, but to characterize the essential nature of the thing introduced.