Synthese 199 (Suppl 3):741-765 (2016)

Authors
Francesco Paoli
Universita di Cagliari
Abstract
Dave Ripley has recently argued against the plausibility of multiset consequence relations and of contraction-free approaches to paradox. For Ripley, who endorses a nontransitive theory, the best arguments that buttress transitivity also push for contraction—whence it is wiser for the substructural logician to go nontransitive from the start. One of Ripley’s allegations is especially insidious, since it assumes the form of a trivialisation result: it is shown that if a multiset consequence relation can be associated to a closure operator in the expected way, then it necessarily contracts. We counter Ripley’s objection by presenting an approach to multiset consequence that escapes this trap. This approach is multiple-conclusioned in a heterodox way, for multiple succedents are given a conjunctive, rather than a disjunctive reading. Finally, we address a further objection by French and Ripley to the effect that the informational interpretation of sequents in linear logic does not motivate cut.
Keywords No keywords specified (fix it)
Categories (categorize this paper)
Reprint years 2021
ISBN(s)
DOI 10.1007/s11229-016-1209-7
Options
Edit this record
Mark as duplicate
Export citation
Find it on Scholar
Request removal from index
Revision history

Download options

PhilArchive copy


Upload a copy of this paper     Check publisher's policy     Papers currently archived: 69,066
External links

Setup an account with your affiliations in order to access resources via your University's proxy server
Configure custom proxy (use this if your affiliation does not provide a proxy)
Through your library

References found in this work BETA

The Logical Basis of Metaphysics.Michael Dummett - 1991 - Harvard University Press.
Change in View.Gilbert Harman - 1986 - Behaviorism 16 (1):93-96.
The Taming of the True.Neil Tennant - 1997 - Oxford, England: Oxford University Press.
Paradoxes and Failures of Cut.David Ripley - 2013 - Australasian Journal of Philosophy 91 (1):139 - 164.

View all 36 references / Add more references

Citations of this work BETA

Noncontractive Classical Logic.Lucas Rosenblatt - 2019 - Notre Dame Journal of Formal Logic 60 (4):559-585.

View all 9 citations / Add more citations

Similar books and articles

Contraction and Closure.David Ripley - 2015 - Thought: A Journal of Philosophy 4 (2):131-138.
A Single-Sorted Theory of Multisets.Hoang-Vu Dang - 2014 - Notre Dame Journal of Formal Logic 55 (3):299-332.
Contractions of Noncontractive Consequence Relations.Rohan French & David Ripley - 2015 - Review of Symbolic Logic 8 (3):506-528.
Vagueness, Truth and Permissive Consequence.Pablo Cobreros, Paul Egré, David Ripley & Robert van Rooij - 2015 - In Kentaro Fujimoto, José Martínez Fernández, Henri Galinon & Theodora Achourioti (eds.), Unifying the Philosophy of Truth. Springer Verlag. pp. 409-430.
Logical Consequence and the Paradoxes.Edwin Mares & Francesco Paoli - 2014 - Journal of Philosophical Logic 43 (2-3):439-469.
Graded Consequence Relations and Fuzzy Closure Operator.Giangiacomo Gerla - 1996 - Journal of Applied Non-Classical Logics 6 (4):369-379.
Comparing Substructural Theories of Truth.David Ripley - 2015 - Ergo: An Open Access Journal of Philosophy 2.
Approximate Reasoning Based on Similarity.M. Ying, L. Biacino & G. Gerla - 2000 - Mathematical Logic Quarterly 46 (1):77-86.
Multiset Theory.Wayne D. Blizard - 1988 - Notre Dame Journal of Formal Logic 30 (1):36-66.

Analytics

Added to PP index
2016-09-10

Total views
63 ( #179,462 of 2,498,779 )

Recent downloads (6 months)
8 ( #89,793 of 2,498,779 )

How can I increase my downloads?

Downloads

My notes