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Higher-Order Logic and Disquotational Truth

Picollo, L; Schindler, T; (2022) Higher-Order Logic and Disquotational Truth. Journal of Philosophical Logic 10.1007/s10992-022-09654-8. (In press). Green open access

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Abstract

Truth predicates are widely believed to be capable of serving a certain logical or quasi-logical function. There is little consensus, however, on the exact nature of this function. We offer a series of formal results in support of the thesis that disquotational truth is a device to simulate higher-order resources in a first-order setting. More specifically, we show that any theory formulated in a higher-order language can be naturally and conservatively interpreted in a first-order theory with a disquotational truth or truth-of predicate. In the first part of the paper we focus on the relation between truth and full impredicative sentential quantification. The second part is devoted to the relation between truth-of and full impredicative predicate quantification.

Type: Article
Title: Higher-Order Logic and Disquotational Truth
Open access status: An open access version is available from UCL Discovery
DOI: 10.1007/s10992-022-09654-8
Publisher version: https://doi.org/10.1007/s10992-022-09654-8
Language: English
Additional information: This article is licensed under a Creative Commons Attribution 4.0 International License, which permits use, sharing, adaptation, distribution and reproduction in any medium or format, as long as you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons licence, and indicate if changes were made. The images or other third party material in this article are included in the article's Creative Commons licence, unless indicated otherwise in a credit line to the material. If material is not included in the article's Creative Commons licence and your intended use is not permitted by statutory regulation or exceeds the permitted use, you will need to obtain permission directly from the copyright holder. To view a copy of this licence, visit http://creativecommons.org/licenses/by/4.0/.
Keywords: Truth, Disquotation, Sentential quantification, Higher-order quantification, Theoretical equivalence
UCL classification: 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
UCL > Provost and Vice Provost Offices > UCL SLASH
UCL
URI: https://discovery.ucl.ac.uk/id/eprint/10149267
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