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All There Is: On the Semantics of Quantification over Absolutely Everything

Abstract
This thesis concerns the problem of providing a semantics for quantification over absolutely all there is. Chapter 2 argues against the common view that Frege understood his quantifiers in Begriffsschrift to range over all objects and discusses Michael Dummett's analysis of the inconsistent system of Grundgesetze, which generalises into his famous argument against absolute quantification from indefinite extensibility. Chapter 3 explores the possibility to adapt Tarski's first definition of truth to hold for sentences with absolute quantification. Taking the concept of logical consequence into account results in an argument for adopting a set-theory with an ill-founded membership relation as a metatheory. Chapter 4 reviews and deflates an influential argument due to Timothy Williamson against the coherence of absolute quantification. Chapter 5 discusses three important contemporary semantic theories for absolute quantification that tackle Williamson's argument in different ways. Chapter 6 challenges the widespread view that it is impossible to give a model-theoretic semantics for absolute quantification simply by providing such a semantics in NFUp. This semantic framework provides models with the universal class as domain. I show, furthermore, that the first-order logical consequence relation stays the same in this setting, by proving the completeness theorem for first-order logic in NFUp.
Degree
Doctor of Philosophy
University
Göteborgs universitet. Humanistiska fakulteten
University of Gothenburg. Faculty of Arts
Institution
Department of Philosophy, Linguistics and Theory of Science ; Institutionen för filosofi, lingvistik och vetenskapsteori
Disputation
Fredagen den 26 januari 2018, kl. 13:00, T302, Olof Wijksgatan 6, Göteborg
Date of defence
2018-01-26
URI
http://hdl.handle.net/2077/54485
Collections
  • Acta Philosophica Gothoburgensia
  • Doctoral Theses / Doktorsavhandlingar Institutionen för filosofi, lingvistik och vetenskapsteori
  • Doctoral Theses from University of Gothenburg / Doktorsavhandlingar från Göteborgs universitet
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Thesis (589.3Kb)
Abstract (42.73Kb)
Date
2017-12-22
Author
Filin Karlsson, Martin
Keywords
absolute generality
quantification
NFU
model-theoretic semantics
Publication type
Doctoral thesis
ISBN
978-91-7346-949-4 (tryckt)
978-91-7346-950-0 (Pdf)
ISSN
0283-2380
Series/Report no.
Acta Philosophica Gothoburgensia
31
Language
eng
Metadata
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