On Paradoxes in Normal Form

&
Topoi 38 (3):605-617 (2019)
  Copy   BIBTEX

Abstract

A proof-theoretic test for paradoxicality was famously proposed by Tennant: a paradox must yield a closed derivation of absurdity with no normal form. Drawing on the remark that all derivations of a given proposition can be transformed into derivations in normal form of a logically equivalent proposition, we investigate the possibility of paradoxes in normal form. We compare paradoxes à la Tennant and paradoxes in normal form from the viewpoint of the computational interpretation of proofs and from the viewpoint of proof-theoretic semantics.

Categories

Keywords

Reprint years

DOI

10.1007/s11245-018-9543-7

Other Versions

No versions found

Links

PhilArchive

    This entry is not archived by us. If you are the author and have permission from the publisher, we recommend that you archive it. Many publishers automatically grant permission to authors to archive pre-prints. By uploading a copy of your work, you will enable us to better index it, making it easier to find.

    Upload a copy of this work     Papers currently archived: 104,060

External links

Setup an account with your affiliations in order to access resources via your University's proxy server

Through your library

My notes

Similar books and articles

A normal paradox.Lucas Rosenblatt - 2024 - Analysis 84 (3):534-546.
On Proof-Theoretic Approaches to the Paradoxes: Problems of Undergeneration and Overgeneration in the Prawitz-Tennant Analysis.Seungrak Choi - 2019 - Dissertation, Korea University
Which Paradox is Genuine in Accordance with the Proof-Theoretic Criterion for Paradoxicality?Seungrak Choi - 2023 - Korean Journal of Logic 3 (26):145-181.
A New Unified Account of Truth and Paradox.N. Tennant - 2015 - Mind 124 (494):571-605.
A normal form for logical derivations implying one for arithmetic derivations.G. Mints - 1993 - Annals of Pure and Applied Logic 62 (1):65-79.
Which ‘Intensional Paradoxes’ are Paradoxes?Neil Tennant - 2024 - Journal of Philosophical Logic 53 (4):933-957.
Harmony and Paradox: Intensional Aspects of Proof-Theoretic Semantics.Luca Tranchini - 2024 - Springer Verlag.
A proof of the normal form theorem for the closed terms of Girard's system F by means of computability.Silvio Valentini - 1993 - Mathematical Logic Quarterly 39 (1):539-544.
Ekman’s Paradox.Peter Schroeder-Heister & Luca Tranchini - 2017 - Notre Dame Journal of Formal Logic 58 (4):567-581.
Proof Terms for Classical Derivations.Restall Greg - manuscript

Analytics

Added to PP
2018-02-21

Downloads
77 (#289,583)

6 months
13 (#245,473)

Historical graph of downloads
How can I increase my downloads?

Author's Profile

Citations of this work

Which ‘Intensional Paradoxes’ are Paradoxes?Neil Tennant - 2024 - Journal of Philosophical Logic 53 (4):933-957.
Core Type Theory.Emma van Dijk, David Ripley & Julian Gutierrez - 2023 - Bulletin of the Section of Logic 52 (2):145-186.

Add more citations

References found in this work

Natural deduction: a proof-theoretical study.Dag Prawitz - 1965 - Mineola, N.Y.: Dover Publications.
Paradox without Self-Reference.Stephen Yablo - 1993 - Analysis 53 (4):251-252.
Structural Proof Theory.Sara Negri, Jan von Plato & Aarne Ranta - 2001 - New York: Cambridge University Press. Edited by Jan Von Plato.
Investigations into Logical Deduction.Gerhard Gentzen - 1964 - American Philosophical Quarterly 1 (4):288 - 306.

View all 21 references / Add more references