How to be really contraction free

Studia Logica 52 (3):381 - 391 (1993)
Abstract
A logic is said to becontraction free if the rule fromA (A B) toA B is not truth preserving. It is well known that a logic has to be contraction free for it to support a non-trivial naïve theory of sets or of truth. What is not so well known is that if there isanother contracting implication expressible in the language, the logic still cannot support such a naïve theory. A logic is said to berobustly contraction free if there is no such operator expressible in its language. We show that a large class of finitely valued logics are each not robustly contraction free, and demonstrate that some other contraction free logics fail to be robustly contraction free. Finally, the sublogics of (with the standard connectives) are shown to be robustly contraction free.
Keywords proof theory   Curry
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DOI 10.1007/BF01057653
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References found in this work BETA
Where Gamma Fails.Robert K. Meyer, Steve Giambrone & Ross T. Brady - 1984 - Studia Logica 43 (3):247 - 256.
Logical Paradoxes for Many-Valued Systems.Moh Shaw-Kwei - 1954 - Journal of Symbolic Logic 19 (1):37-40.

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Citations of this work BETA
Paradoxes and Failures of Cut.David Ripley - 2013 - Australasian Journal of Philosophy 91 (1):139 - 164.
On Artifacts and Truth-Preservation.Shawn Standefer - 2015 - Australasian Journal of Logic 12 (3):135-158.
Curry's Paradox and Omega Inconsistency.Andrew Bacon - 2013 - Studia Logica 101 (1):1-9.
Absolute Contradiction, Dialetheism, and Revenge.Francesco Berto - 2014 - Review of Symbolic Logic 7 (2):193-207.
Conditionals and Curry.Daniel Nolan - 2016 - Philosophical Studies 173 (10):2629-2647.

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