Abstractionism: Essays in Philosophy of Mathematics by Philip A Ebert

Abstractionism: Essays in Philosophy of Mathematics

EditorPhilip A Ebert, Marcus Rossberg

Hardcover | January 7, 2017

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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 bookcontains three contributions that discuss Frege's application constraint within an abstractionist setting.

About The Author

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 Fel...
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Title:Abstractionism: Essays in Philosophy of MathematicsFormat:HardcoverDimensions:368 pages, 9.21 × 6.14 × 0 inPublished:January 7, 2017Publisher:Oxford University PressLanguage:English

The following ISBNs are associated with this title:

ISBN - 10:0199645264

ISBN - 13:9780199645268

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Table of Contents

I. Introduction1. Philip A. Ebert and Marcus Rossberg: Introduction to AbstractionismII. Semantics and Ontology of Abstraction2. William Stirton: Caesar and Circularity3. Richard G. Heck, Jr.: The Existence (and Non-existence) of Abstract Objects4. Matti Eklund: Hale and Wright on the Metaontology of Neo-Fregeanism5. Fraser MacBride: Neo-Fregean Ontology: Just Don't Ask Too Many Questions6. Friederike Moltmann: The Number of Planets, a Number-Referring Term?III. Epistemology of Abstraction7. Philip A. Ebert: A Framework for Implicit Definitions and the A Priori8. Crispin Wright: Abstraction and Epistemic Entitlement: On the Epistemological Status of Hume's Principle9. Nikolaj Jang Lee Linding Pedersen: Hume's Principle and Entitlement: On the Epistemology of the Neo-Fregean Programme10. Agustin Rayo: Neo-Fregeanism ReconsideredIV. Mathematics of Abstraction11. Roy T. Cook: Conservativeness, Cardinality, and Bad Company12. Oystein Linnebo: Impredicativity in the Neo-Fregean Programme13. Hannes Leitgeb: Abstraction Grounded: A Note on Abstraction and Truth14. Stewart Shapiro and Gabriel Uzquiano: Ineffability within the Limits of Abstraction AloneV. Application Constraint15. Paul McCallion: On Frege's Applications Constraint16. Peter Simons: Applications of Complex Numbers and Quaternions: Historical Remarks, with a Note on Clifford Algebra17. Bob Hale: Definitions of Numbers and Their Applications