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Analyticity, balance and non-admissibility of Cut in Stoic logic

Abstract:

This paper shows that, for the Hertz–Gentzen Systems of 1933 (without Thinning), extended by a classical rule T1 (from the Stoics) and using certain axioms (also from the Stoics), 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 o...

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Publication status:
Published
Peer review status:
Peer reviewed

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Publisher copy:
10.1007/s11225-018-9797-5

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Institution:
University of Oxford
Division:
Humanities Division
Department:
Philosophy
Oxford college:
All Souls College
Role:
Author
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Role:
Author
ORCID:
0000-0002-5677-9792
Publisher:
Springer Verlag Publisher's website
Journal:
Studia Logica Journal website
Volume:
107
Article number:
375
Publication date:
2018-04-20
DOI:
EISSN:
1572-8730
ISSN:
0039-3215
Source identifiers:
847359
Language:
English
Keywords:
Pubs id:
pubs:847359
UUID:
uuid:38cf6349-ab97-4e35-b854-95a91bf51442
Local pid:
pubs:847359
Deposit date:
2019-02-09

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