Weak disharmony: Some lessons for proof-theoretic semantics

Review of Symbolic Logic (3):1-20 (2016)
  Copy   BIBTEX

Abstract

A logical constant is weakly disharmonious if its elimination rules are weaker than its introduction rules. Substructural weak disharmony is the weak disharmony generated by structural restrictions on the eliminations. I argue that substructural weak disharmony is not a defect of the constants which exhibit it. To the extent that it is problematic, it calls into question the structural properties of the derivability relation. This prompts us to rethink the issue of controlling the structural properties of a logic by means of harmony. I argue that such a control is possible and desirable. Moreover, it is best achieved by global tests of harmony.

Links

PhilArchive



    Upload a copy of this work     Papers currently archived: 91,349

External links

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

Through your library

Similar books and articles

Bilateralism in Proof-Theoretic Semantics.Nissim Francez - 2013 - Journal of Philosophical Logic (2-3):1-21.
A Note on Harmony.Nissim Francez & Roy Dyckhoff - 2012 - Journal of Philosophical Logic 41 (3):613-628.
The strength of extensionality I—weak weak set theories with infinity.Kentaro Sato - 2009 - Annals of Pure and Applied Logic 157 (2-3):234-268.
Harmony in Multiple-Conclusion Natural-Deduction.Nissim Francez - 2014 - Logica Universalis 8 (2):215-259.
Against Harmony.Ian Rumfitt - forthcoming - In Bob Hale, Crispin Wright & Alexander Miller (eds.), The Blackwell Companion to the Philosophy of Language. Blackwell.
Some problems for proof-theoretic semantics.William R. Stirton - 2008 - Philosophical Quarterly 58 (231):278–298.
On the Equivalence Conjecture for Proof-Theoretic Harmony.Florian Steinberger - 2013 - Notre Dame Journal of Formal Logic 54 (1):79-86.
Meeting strength in substructural logics.Yde Venema - 1995 - Studia Logica 54 (1):3 - 32.

Analytics

Added to PP
2016-08-09

Downloads
53 (#293,652)

6 months
20 (#126,042)

Historical graph of downloads
How can I increase my downloads?

Author's Profile

Bogdan Dicher
University of Witwatersrand

Citations of this work

.Luca Incurvati & Julian J. Schlöder - 2023 - New York: Oxford University Press USA.
Sentence connectives in formal logic.Lloyd Humberstone - forthcoming - Stanford Encyclopedia of Philosophy.
Proof-theoretic pluralism.Filippo Ferrari & Eugenio Orlandelli - 2019 - Synthese 198 (Suppl 20):4879-4903.
On harmony and permuting conversions.Nissim Francez - 2017 - Journal of Applied Logic 21:14-23.

View all 10 citations / Add more citations

References found in this work

Paradoxes and Failures of Cut.David Ripley - 2013 - Australasian Journal of Philosophy 91 (1):139 - 164.
The Runabout Inference-Ticket.A. N. Prior - 1960 - Analysis 21 (2):38-39.
The Logical Basis of Metaphysics.Michael Dummett, Hilary Putnam & James Conant - 1994 - Philosophical Quarterly 44 (177):519-527.
Tonk, Plonk and Plink.Nuel Belnap - 1962 - Analysis 22 (6):130-134.
The runabout inference ticket.Arthur Prior - 1967 - In P. F. Strawson (ed.), Philosophical logic. London,: Oxford University Press. pp. 38-9.

View all 35 references / Add more references