The Universal Theory Building Toolkit Is Substructural

In Ivo Düntsch & Edwin Mares (eds.), Alasdair Urquhart on Nonclassical and Algebraic Logic and Complexity of Proofs. Springer Verlag. pp. 261-285 (2021)
  Copy   BIBTEX

Abstract

Consider the set of inferences that are acceptable to use in all our theory building endeavors. Call this set of inferences the universal theory building toolkit, or just ’the toolkit’ for short. It is clear that the toolkit is tightly connected to logic in a variety of ways. Beall, for example, has argued that logic just is the toolkit. This paper avoids making a stand on that issue and instead investigates reasons for thinking that, logic or not, the toolkit is substructural. It is presented as a dialogue for the simple reason that it summarizes a range of dialogues on this subject that the author has had with various folks over the past few years. The method I use to investigate the toolkit is inspired in both philosophical and technical details by Alasdair Urquhart’s work on semantics for relevance logics from the early 1970s.

Links

PhilArchive

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

Substructural Logics: A Primer.Francesco Paoli - 2002 - Dordrecht, Netherland: Springer.
An Algebraic Approach to the Disjunction Property of Substructural Logics.Daisuke Souma - 2007 - Notre Dame Journal of Formal Logic 48 (4):489-495.
Models for Substructural Arithmetics.Greg Restall - 2011 - Australasian Journal of Logic 8:82-99.
LP, K3, and FDE as Substructural Logics.Lionel Shapiro - 2017 - In Pavel Arazim & Tomáš Lavička (eds.), The Logica Yearbook 2016. London: College Publications.
The finite model property for semilinear substructural logics.San-Min Wang - 2013 - Mathematical Logic Quarterly 59 (4-5):268-273.
Substructural epistemic logics.Igor Sedlár - 2015 - Journal of Applied Non-Classical Logics 25 (3):256-285.
Synthesized substructural logics.Norihiro Kamide - 2007 - Mathematical Logic Quarterly 53 (3):219-225.
An Outline of a Substructural Model of BTA Belief.Igor Sedlar - 2013 - Organon F: Medzinárodný Časopis Pre Analytickú Filozofiu 20 (2):160-170.
Comparing Substructural Theories of Truth.David Ripley - 2015 - Ergo: An Open Access Journal of Philosophy 2.
Synthesized substructural logics.Norihori Kamide - 2007 - Mathematical Logic Quarterly 53 (3):219-225.
Conuclear Images of substructural logics.Giulia Frosoni - 2016 - Mathematical Logic Quarterly 62 (3):204-214.
Glivenko theorems revisited.Hiroakira Ono - 2010 - Annals of Pure and Applied Logic 161 (2):246-250.

Analytics

Added to PP
2021-12-17

Downloads
278 (#70,313)

6 months
71 (#61,512)

Historical graph of downloads
How can I increase my downloads?

Author's Profile

Shay Logan
Kansas State University

Citations of this work

No citations found.

Add more citations

References found in this work

No references found.

Add more references