Abstractionism
Essays in Philosophy of Mathematics
Edited by Philip A Ebert and Marcus Rossberg
Table of Contents
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, Agustín Rayo
IV. Mathematics of Abstraction
11:Conservativeness, Cardinality, and Bad Company, Roy T. Cook
12:Impredicativity in the Neo-Fregean Programme, Øystein 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