Ditter, Andreas;
(2023)
Fine on the Possibility of Vagueness.
In: Faroldi, Federico LG and Van De Putte, Frederik, (eds.)
Kit Fine on Truthmakers, Relevance, and Non-classical Logic.
(pp. 715-734).
Springer, Cham: Cham, Switzerland.
![]() |
Text
FOPV UCL Profile.pdf - Accepted Version Access restricted to UCL open access staff until 27 September 2024. Download (392kB) |
Abstract
In his paper ‘The possibility of vagueness’ (Fine in Synthese 194(10):3699–3725, 2017), Kit Fine proposes a new logic of vagueness, CL, that promises to provide both a solution to the sorites paradox and a way to avoid the impossibility result from Fine (Philos Perspect 22(1):111–136, 2008). The present paper presents a challenge to his new theory of vagueness. I argue that the possibility theorem stated in Fine (Synthese 194(10):3699–3725, 2017), as well as his solution to the sorites paradox, fail in certain reasonable extensions of the language of CL. More specifically, I show that if we extend the language with any negation operator that obeys reductio ad absurdum, we can prove a new impossibility result that makes the kind of indeterminacy that Fine takes to be a hallmark of vagueness impossible. I show that such negation operators can be conservatively added to CL and examine some of the philosophical consequences of this result. Moreover, I demonstrate that we can define a particular negation operator that behaves exactly like intuitionistic negation in a natural and unobjectionable propositionally quantified extension of CL. Since intuitionistic negation obeys reductio, the new impossibility result holds in this propositionally quantified extension of CL. In addition, the sorites paradox resurfaces for the new negation.
Type: | Book chapter |
---|---|
Title: | Fine on the Possibility of Vagueness |
ISBN: | 3031294157 |
ISBN-13: | 978-3-031-29414-3 |
DOI: | 10.1007/978-3-031-29415-0_31 |
Publisher version: | https://doi.org/10.1007/978-3-031-29415-0_31 |
Language: | English |
Additional information: | This version is the author-accepted manuscript. For information on re-use, please refer to the publisher’s terms and conditions. |
UCL classification: | UCL UCL > Provost and Vice Provost Offices > UCL SLASH UCL > Provost and Vice Provost Offices > UCL SLASH > Faculty of Arts and Humanities UCL > Provost and Vice Provost Offices > UCL SLASH > Faculty of Arts and Humanities > Dept of Philosophy |
URI: | https://discovery.ucl.ac.uk/id/eprint/10189459 |
Archive Staff Only
![]() |
View Item |