Abstractionism: Essays in Philosophy of Mathematics
Philip A Ebert and Marcus Rossberg
Abstract
The collection contains an extensive introduction and 16 original papers on the philosophical and mathematical aspects of Abstractionism—a position in the philosophy of mathematics which is a development of Frege’s original Logicism. The collection is structured as follows: After an extensive editors’ introduction to the topic of abstractionism, part II contains five contributions that deal with semantics and metaontology of Abstractionism, as well as the so-called Caesar Problem. Part III collects four contributions that discuss abstractionist epistemology, focusing on the idea of implicit de ... More
The collection contains an extensive introduction and 16 original papers on the philosophical and mathematical aspects of Abstractionism—a position in the philosophy of mathematics which is a development of Frege’s original Logicism. The collection is structured as follows: After an extensive editors’ introduction to the topic of abstractionism, part II contains five contributions that deal with semantics and metaontology of Abstractionism, as well as the so-called Caesar Problem. Part III collects four contributions that discuss abstractionist epistemology, focusing on the idea of implicit definitions and non-evidential warrants (entitlements) to account for a priori mathematical knowledge. Four papers in part IV concern the mathematics of Abstractionism, in particular the issue of impredicativity, the Bad Company objection, and the question of abstractionist set theory. The last section contains three contributions that discuss Frege’s application constraint within an abstractionist setting.
Keywords:
Abstractionism,
abstraction principles,
metaontology,
semantics,
epistemology,
logic,
application
Bibliographic Information
| Print publication date: 2016 |
Print ISBN-13: 9780199645268 |
| Published to Oxford Scholarship Online: January 2017 |
DOI:10.1093/acprof:oso/9780199645268.001.0001 |
Authors
Affiliations are at time of print publication.
Philip A Ebert, editor
University of Stirling
Marcus Rossberg, editor
University of Connecticut
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