On the Existence and Identity of Fregean Abstracta
In this talk a ramified plural theory for Fregean objects will be presented that is based on Boolos’ intuition that Fregean abstraction principles rely on explicit existential assumptions. As Anderson & Zalta point out, all these explicit existential assumptions may be captured by a single existential axiom, stating the existence of Fregean abstracta. Nevertheless, such a principle, when accompanied by full second-order logic, leads to inconsistency. In this talk, an axiomatisation along the lines of Anderson & Zalta's will be provided, but the interaction of the axioms of the theory is so regimented that the resulting system is both consistent and strong enough to deliver a general abstraction principle as a theorem. On the basis of this latter, some important local Fregean abstraction principles (e.g. BLV and HP) and PA2 via Frege’s definitions are derived within the system. The derivation of different abstraction principles governing different kinds of Fregean abstracta poses a philosophical question, namely whether abstracta governed by different principles are indeed different abstracta. This is a specific formulation of the so-called Julius Caesar Problem. On the basis of Cook & Ebert's critical survey of the solutions to this formulation of the Caesar problem presently on the market and their respective weaknesses, Boccuni will provide her own reply to this issue.
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