Arbitrary Logicism

Abstract This paper focuses on a lesser known version of abstractionism — called Arbitrary Logicism — which combines a deflationist account of abstraction and recent proposals about arbitrary reference. It makes explicit the relation of this proposal to canonical versions of Fregean abstractionist programs. In particular, Arbitrary Logicism will be tested against the epistemological claims of the abstractionist tradition, within which it emerges as an interesting alternative to Neologism and a direct heir to Frege’s Logicism.