On the notion of validity for the bilateral classical logic


This paper considers Rumfitt’s bilateral classical logic (BCL), which is proposed to counter Dummett’s challenge to classical logic. First, agreeing with several authors, we argue that Rumfitt’s notion of harmony, used to justify logical rules by a purely proof theoretical manner, is not sufficient to justify coordination rules in BCL purely proof-theoretically. For the central part of this paper, we propose a notion of proof-theoretical validity similar to Prawitz for BCL and proves that BCL is sound and complete respect to this notion of validity. The major difficulty in defining validity for BCL is that validity of positive +A appears to depend on negative −A, and vice versa. Thus, the straightforward inductive definition does not work because of this circular dependance. However, Knaster-Tarski’s fixed point theorem can resolve this circularity. Finally, we discuss the philosophical relevance of our work, in particular, the impact of the use of fixed point theorem and the issue of decidability.



External links

  • This entry has no external links. Add one.
Setup an account with your affiliations in order to access resources via your University's proxy server

Through your library

  • Only published works are available at libraries.

Similar books and articles

Some Comments on Ian Rumfitt’s Bilateralism.Nils Kürbis - 2016 - Journal of Philosophical Logic 45 (6):623-644.
Bilateralism in Proof-Theoretic Semantics.Nissim Francez - 2013 - Journal of Philosophical Logic (2-3):1-21.
Inference Rules and the Meaning of the Logical Constants.Hermógenes Oliveira - 2019 - Dissertation, Eberhard Karls Universität Tübingen
A proof–theoretic study of the correspondence of hybrid logic and classical logic.H. Kushida & M. Okada - 2006 - Journal of Logic, Language and Information 16 (1):35-61.
An Expressivist Bilateral Meaning-is-Use Analysis of Classical Propositional Logic.John Cantwell - 2015 - Journal of Logic, Language and Information 24 (1):27-51.
Relevance for the Classical Logician.Ethan Brauer - 2020 - Review of Symbolic Logic 13 (2):436-457.
A constructive game semantics for the language of linear logic.Giorgi Japaridze - 1997 - Annals of Pure and Applied Logic 85 (2):87-156.
Revisiting Dummett's Proof-Theoretic Justification Procedures.Hermógenes Oliveira - 2017 - In Pavel Arazim & Tomáš Lávička (eds.), The Logica Yearbook 2016. London: College Publications. pp. 141-155.


Added to PP

212 (#90,816)

6 months
58 (#72,254)

Historical graph of downloads
How can I increase my downloads?

Author's Profile

Citations of this work

No citations found.

Add more citations

References found in this work

No references found.

Add more references