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Abstractionism: Essays in Philosophy of Mathematics(English)

Abstractionism: Essays in Philosophy of Mathematics(English)

          
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About the Book

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.

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


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Product Details
  • ISBN-13: 9780199645268
  • Publisher: Oxford University Press
  • Publisher Imprint: Oxford University Press
  • Height: 241 mm
  • No of Pages: 368
  • Series Title: English
  • Sub Title: Essays in Philosophy of Mathematics
  • Width: 158 mm
  • ISBN-10: 0199645264
  • Publisher Date: 08 Dec 2016
  • Binding: Hardback
  • Language: English
  • Returnable: Y
  • Spine Width: 25 mm
  • Weight: 664 gr


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