Abstractionism : Essays in Philosophy of Mathematics

Abstractionism is a recent and much debated position in the philosophy of mathematics. This collection of 16 original articles by leading scholars covers a variety of topics concerning both the philosophy and mathematics of Abstractionism and includes an extensive introduction to the field by the editors.

Abstractionism, which is a development of Frege''s original Logicism, is a recent and much debated position in the philosophy of mathematics. This volume contains 16 original papers by leading scholars on the philosophical and mathematical aspects of Abstractionism. After an extensive editors'' introduction to the topic of abstractionism, five contributions deal with the semantics and meta-ontology of Abstractionism, as well as the so-called Caesar Problem. Four papers then discuss abstractionist epistemology, focusing on the idea of implicit definitions and non-evidential warrants (entitlements) to account for a priori mathematical knowledge. This is followed by four chapters concerning the mathematics of Abstractionism, in particular the issue of impredicativity, the Bad Company objection, and the question of abstractionist set theory. Finally, the last section of the book contains three contributions that discuss Frege''s application constraint within an abstractionist setting.