Abstractionism Essays in Philosophy of Mathematics

Philip A Ebert, University of Stirling,Marcus Rossberg, University of Connecticut

Philip A. Ebert received his PhD in Philosophy from the University of St Andrews in 2006 and was a Post Doctoral Fellow at the Arche Centre from 2005-2007. He is currently a Senior Lecturer at the University of Stirling.


Marcus Rossberg received his PhD in Philosophy from the University of St Andrews in 2006 and was a Post Doctoral Fellow at the Arche Centre from 2005-2008. He is currently an Associate Professor at the University of Connecticut.

I. Introduction
1. Introduction to Abstractionism, Philip A. Ebert and Marcus Rossberg
II. Semantics and Ontology of Abstraction
2. Caesar and Circularity, William Stirton
3. The Existence (and Non-existence) of Abstract Objects, Richard G. Heck, Jr.
4. Hale and Wright on the Metaontology of Neo-Fregeanism, Matti Eklund
5. Neo-Fregean Ontology: Just Don't Ask Too Many Questions, Fraser MacBride
6. The Number of Planets, a Number-Referring Term?, Friederike Moltmann
III. Epistemology of Abstraction
7. A Framework for Implicit Definitions and the A Priori, Philip A. Ebert
8. Abstraction and Epistemic Entitlement: On the Epistemological Status of Hume's Principle, Crispin Wright
9. Hume's Principle and Entitlement: On the Epistemology of the Neo-Fregean Programme, Nikolaj Jang Lee Linding Pedersen
10. Neo-Fregeanism Reconsidered, Agustin Rayo
IV. Mathematics of Abstraction
11. Conservativeness, Cardinality, and Bad Company, Roy T. Cook
12. Impredicativity in the Neo-Fregean Programme, Oystein Linnebo
13. Abstraction Grounded: A Note on Abstraction and Truth, Hannes Leitgeb
14. Ineffability within the Limits of Abstraction Alone, Stewart Shapiro and Gabriel Uzquiano
V. Application Constraint
15. On Frege's Applications Constraint, Paul McCallion
16. Applications of Complex Numbers and Quaternions: Historical Remarks, with a Note on Clifford Algebra, Peter Simons
17. Definitions of Numbers and Their Applications, Bob Hale