Translator Disclaimer
2017 Ekman’s Paradox
Peter Schroeder-Heister, Luca Tranchini
Notre Dame J. Formal Logic 58(4): 567-581 (2017). DOI: 10.1215/00294527-2017-0017

Abstract

Prawitz observed that Russell’s paradox in naive set theory yields a derivation of absurdity whose reduction sequence loops. Building on this observation, and based on numerous examples, Tennant claimed that this looping feature, or more generally, the fact that derivations of absurdity do not normalize, is characteristic of the paradoxes. Striking results by Ekman show that looping reduction sequences are already obtained in minimal propositional logic, when certain reduction steps, which are prima facie plausible, are considered in addition to the standard ones. This shows that the notion of reduction is in need of clarification. Referring to the notion of identity of proofs in general proof theory, we argue that reduction steps should not merely remove redundancies, but must respect the identity of proofs. Consequentially, we propose to modify Tennant’s paradoxicality test by basing it on this refined notion of reduction.

Citation

Download Citation

Peter Schroeder-Heister. Luca Tranchini. "Ekman’s Paradox." Notre Dame J. Formal Logic 58 (4) 567 - 581, 2017. https://doi.org/10.1215/00294527-2017-0017

Information

Received: 26 February 2014; Accepted: 6 July 2015; Published: 2017
First available in Project Euclid: 18 July 2017

zbMATH: 06803188
MathSciNet: MR3707652
Digital Object Identifier: 10.1215/00294527-2017-0017

Subjects:
Primary: 03A05, 03F05
Secondary: 00A30

Rights: Copyright © 2017 University of Notre Dame

JOURNAL ARTICLE
15 PAGES

This article is only available to subscribers.
It is not available for individual sale.
+ SAVE TO MY LIBRARY

SHARE
Vol.58 • No. 4 • 2017
Back to Top