Studia Logica 107 (2):375-397 (2019)

Authors
Susanne Bobzien
Oxford University
Abstract
This paper shows that, for the Hertz–Gentzen Systems of 1933, extended by a classical rule T1 and using certain axioms, all derivations are analytic: every cut formula occurs as a subformula in the cut’s conclusion. Since the Stoic cut rules are instances of Gentzen’s Cut rule of 1933, from this we infer the decidability of the propositional logic of the Stoics. We infer the correctness for this logic of a “relevance criterion” and of two “balance criteria”, and hence that a particular derivable sequent has no derivation that is “normal” in the sense that the first premiss of each cut is cut-free. We also infer that Cut is not admissible in the Stoic system, based on the standard Stoic axioms, the T1 rule and the instances of Cut with just two antecedent formulae in the first premiss. OPEN ACCESS
Keywords Sequent Stoic Logic Decidability  Analyticity   Stoic Logic  Proof Theory  Decidability   Relevance  Gentzen
Categories (categorize this paper)
Reprint years 2018, 2019
ISBN(s)
DOI 10.1007/s11225-018-9797-5
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: 71,199
Through your library

References found in this work BETA

Relevant Logic : a Philosophical Examination of Inference.Stephen Read - 1988 - Revue Philosophique de la France Et de l'Etranger 179 (4):656-656.
Untersuchungen über das logische Schließen. II.Gerhard Gentzen - 1935 - Mathematische Zeitschrift 39:405–431.
Contraction-Free Sequent Calculi for Intuitionistic Logic.Roy Dyckhoff - 1992 - Journal of Symbolic Logic 57 (3):795-807.
Early Structural Reasoning. Gentzen 1932.Enrico Moriconi - 2015 - Review of Symbolic Logic 8 (4):662-679.

View all 6 references / Add more references

Citations of this work BETA

Stoic Sequent Logic and Proof Theory.Susanne Bobzien - 2019 - History and Philosophy of Logic 40 (3):234-265.
Sextus Empiricus' Fourth Conditional and Containment Logic.Yale Weiss - 2019 - History and Philosophy of Logic 40 (4):307-322.

Add more citations

Similar books and articles

Logic: The Stoics (Part Two).Susanne Bobzien - 1999 - In Keimpe Algra, Jonathan Barnes & et al (eds.), The Cambridge History of Hellenistic Philosophy. Cambridge University Press.
Stoic Logic.Susanne Bobzien - 2003 - In Brad Inwood (ed.), The Cambridge Companion to Stoic Philosophy. Cambridge University Press.
Stoic Syllogistic.Susanne Bobzien - 1996 - Oxford Studies in Ancient Philosophy 14:133-92.
Aristotelian Versus Stoic Logic.J. Banas - 2003 - Filozofia 58 (8):551-563.
Is Stoic Logic Classical?Marek Nasieniewski - 1998 - Logic and Logical Philosophy 6:55.
Propositional Logic in Ammonius.Susanne Bobzien - 2002 - In Helmut Linneweber-Lammerskitten & Georg Mohr (eds.), Interpretation und Argument. Koenigshausen & Neumann.
Proof Theory for Admissible Rules.Rosalie Iemhoff & George Metcalfe - 2009 - Annals of Pure and Applied Logic 159 (1-2):171-186.
Stoická logika verzus aristotelovská.František Gahér - 2000 - Organon F: Medzinárodný Časopis Pre Analytickú Filozofiu 4 (4):379-415.
Aspects of Analytic Deduction.Athanassios Tzouvaras - 1996 - Journal of Philosophical Logic 25 (6):581-596.
Tautology Elimination, Cut Elimination, and S5.Andrezj Indrzejczak - 2017 - Logic and Logical Philosophy 26 (4):461-471.
The Combinatorics of Stoic Conjunction.Susanne Bobzien - 2011 - Oxford Studies in Ancient Philosophy 40:157-188.

Analytics

Added to PP index
2018-04-20

Total views
75 ( #155,468 of 2,518,144 )

Recent downloads (6 months)
4 ( #167,290 of 2,518,144 )

How can I increase my downloads?

Downloads

My notes