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The Reason's Proper StudyEssays towards a Neo-Fregean Philosophy of Mathematics$
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Bob Hale and Crispin Wright

Print publication date: 2001

Print ISBN-13: 9780198236399

Published to Oxford Scholarship Online: November 2003

DOI: 10.1093/0198236395.001.0001

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Field and Fregean Platonism

Field and Fregean Platonism

Chapter:
(p.153) 6 Field and Fregean Platonism
Source:
The Reason's Proper Study
Author(s):

Crispin Wright (Contributor Webpage)

Publisher:
Oxford University Press
DOI:10.1093/0198236395.003.0007

This paper starts by offering a brief reconstruction of the Neo‐Fregean approach as suggested in Frege's Conception of Numbers as Objects and distinguishes various challenges against the method of Abstraction. It then focuses on one line of criticism––Rejectionism––which is endorsed by Field in his Review of the previously mentioned book. The thought is to grant that the method of abstraction provides singular terms, however questions its ability to produce true statements. Furthermore, Field draws an analogy between the stipulation of Hume's Principle, which commits one to the existence of numbers and the ontological argument, which commits one to the existence of God. It is then shown that this analogy is amiss and that there is no real point of affinity with the Fregean platonist's ontological strategy and the ontological arguments. A further objection concerning the tacit ontological commitments on the right hand side of Abstraction Principle is discussed. The paper concludes considering ‘the onus of proof’ – issue for Nominalism‐Platonism debates.

Keywords:   abstract objects, abstraction, Hartry Field, Frege, Hume's Principle, Nominalism, ontological argument, Platonism, reference, Rejectionism

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