Minimalism, Reference, and Paradoxes

Picollo, Lavinia (2016): Minimalism, Reference, and Paradoxes. In: Arazim, Pavel; Dancak, Michal (eds.) : The Logica Yearbook 2015. London: College Publications. pp. 163-178

Abstract

The aim of this paper is to provide a minimalist axiomatic theory of truth based on the notion of reference. To do this, we first give sound and arithmetically simple notions of reference, self-reference, and well-foundedness for the language of first-order arithmetic extended with a truth predicate; a task that has been so far elusive in the literature. Then, we use the new notions to restrict the T-schema to sentences that exhibit "safe" reference patterns, confirming the widely accepted but never worked out idea that paradoxes can be characterised in terms of their underlying reference patterns. This results in a strong, ω-consistent, and well-motivated system of disquotational truth, as required by minimalism.

• Item Type: Book Section
• EU Funded Grant Agreement Number: 675415
• EU Projects: Horizon 2020 > Marie Skłodowska Curie Actions > Marie Skłodowska-Curie Innovative Training Networks > 675415: Diaphora: Philosophical Problems, Resilience and Persistent Disagreement
• Form of publication: Preprint
• Keywords: minimalism; disquotation; reference; paradoxes; well-foundedness
• Faculties: Philosophy, Philosophy of Science and Religious Science > Munich Center for Mathematical Philosophy (MCMP); Philosophy, Philosophy of Science and Religious Science > Munich Center for Mathematical Philosophy (MCMP) > Logic; Philosophy, Philosophy of Science and Religious Science > Munich Center for Mathematical Philosophy (MCMP) > Diaphora: Logic and Paradox
• Subjects: 100 Philosophy and Psychology > 100 Philosophy; 100 Philosophy and Psychology > 160 Logic
• ISBN: 978-1-84890-213-8
• Place of Publication: London
• Language: English