Date of Completion

12-2-2019

Embargo Period

12-2-2019

Keywords

logic, logical consequence, nominalism, fictionalism, abstract objects

Major Advisor

Keith Simmons

Associate Advisor

William Lycan

Associate Advisor

Thomas Bontly

Field of Study

Philosophy

Degree

Doctor of Philosophy

Open Access

Campus Access

Abstract

Nominalists, as the term is sometimes used, are those who do not believe in abstract objects. Hartry Field in his 1980 book Science without Numbers offered a fictionalist (and thereby nominalistically acceptable) treatment of mathematics. An objection was raised against Field called “the objection from logical consequence”. The objection states, put simply, that Field illicitly helps himself to abstract objects in his account of logical consequence the same things he purported to rid himself of in his fictionalist treatment of mathematics. But the problem is in the same spirit as a more general worry raised by the historically well-established view, which some philosophers share, that logic by itself should not commit us to the existence of anything. This is believed by some to be in sharp contrast to many logic texts which presuppose the existence of infinite sets of formulae, proofs, models, etc. Marcus Rossberg and Daniel Cohnitz attempt to offer, in response to the specific objection from logical consequence, a completely nominalistic account of logical consequence. Their account purports to be literally true. Field too offered a revised account of consequence in response to the objection, but one which was itself fictional in the sense that everything it says is literally false. However, Rossberg and Cohnitz account is itself subject to several fatal objections. My project in this dissertation is to offer an improved account of consequence acceptable to the nominalist which avoids the objections to Rossberg and Cohnitz’ account and is also, unlike Field’s, really and genuinely true.

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