Contraction, Infinitary Quantifiers, and Omega Paradoxes

Journal of Philosophical Logic 47 (4):611-629 (2018)
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Abstract

Our main goal is to investigate whether the infinitary rules for the quantifiers endorsed by Elia Zardini in a recent paper are plausible. First, we will argue that they are problematic in several ways, especially due to their infinitary features. Secondly, we will show that even if these worries are somehow dealt with, there is another serious issue with them. They produce a truth-theoretic paradox that does not involve the structural rules of contraction.

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Author Profiles

Bruno Da Re
Universidad de Buenos Aires (UBA)
Lucas Rosenblatt
Universidad de Buenos Aires (UBA)

Citations of this work

Noncontractive Classical Logic.Lucas Rosenblatt - 2019 - Notre Dame Journal of Formal Logic 60 (4):559-585.
Systems for Non-Reflexive Consequence.Carlo Nicolai & Lorenzo Rossi - 2023 - Studia Logica 111 (6):947-977.
Structural Weakening and Paradoxes.Bruno Da Ré - 2021 - Notre Dame Journal of Formal Logic 62 (2):369-398.

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References found in this work

Basic proof theory.A. S. Troelstra - 1996 - New York: Cambridge University Press. Edited by Helmut Schwichtenberg.
Axiomatic Theories of Truth.Volker Halbach - 2010 - Cambridge, England: Cambridge University Press.
Truth without contra(di)ction.Elia Zardini - 2011 - Review of Symbolic Logic 4 (4):498-535.
Axiomatic theories of truth.Volker Halbach - 2008 - Stanford Encyclopedia of Philosophy.

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