Bilateralism does not provide a proof theoretic treatment of classical logic

Journal of Applied Logic 25:S108-S122 (2017)
  Copy   BIBTEX

Abstract

In this short paper I note that a key metatheorem does not hold for the bilateralist inferential framework: harmony does not entail consistency. I conclude that the requirement of harmony will not suffice for a bilateralist to maintain a proof theoretic account of classical logic. I conclude that a proof theoretic account of meaning based on the bilateralist framework has no natural way of distinguishing legitimate definitional inference rules from illegitimate ones (such as those for tonk). Finally, as an appendix to the main argument, I propose an alternative non-bilateral formal solution to the problem of providing a proof-theoretic account of classical logic.

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: 106,894

External links

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

Through your library

Analytics

Added to PP
2017-12-04

Downloads
76 (#300,674)

6 months
13 (#267,047)

Historical graph of downloads
How can I increase my downloads?

Citations of this work

Logical Multilateralism.Heinrich Wansing & Sara Ayhan - 2023 - Journal of Philosophical Logic 52 (6):1603-1636.
Introduction: Bilateralism and Proof-Theoretic Semantics (Part I).Sara Ayhan - 2023 - Bulletin of the Section of Logic 52 (2):101-108.
Bilateral Inversion Principles.Nils Kürbis - 2022 - Electronic Proceedings in Theoretical Computer Science 358:202–215.

View all 10 citations / Add more citations

References found in this work

The Runabout Inference-Ticket.A. N. Prior - 1960 - Analysis 21 (2):38-39.
The runabout inference ticket.Arthur Prior - 1967 - In Peter Frederick Strawson, Philosophical logic. London,: Oxford University Press. pp. 38-9.
Yes and no.I. Rumfitt - 2000 - Mind 109 (436):781-823.
Rejection.Timothy Smiley - 1996 - Analysis 56 (1):1–9.
Harmony and autonomy in classical logic.Stephen Read - 2000 - Journal of Philosophical Logic 29 (2):123-154.

View all 11 references / Add more references