Studia Logica 64 (3):365-403 (2000)
On the one hand, the absence of contraction is a safeguard against the logical (property theoretic) paradoxes; but on the other hand, it also disables inductive and recursive definitions, in its most basic form the definition of the series of natural numbers, for instance. The reason for this is simply that the effectiveness of a recursion clause depends on its being available after application, something that is usually assured by contraction. This paper presents a way of overcoming this problem within the framework of a logic based on inclusion and unrestricted abstraction, without any form of extensionality.
|Keywords||Philosophy Logic Mathematical Logic and Foundations Computational Linguistics|
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Citations of this work BETA
Transfinite Numbers in Paraconsistent Set Theory.Zach Weber - 2010 - Review of Symbolic Logic 3 (1):71-92.
Contractions of Noncontractive Consequence Relations.Rohan French & David Ripley - 2015 - Review of Symbolic Logic 8 (3):506-528.
Naive Set Theory and Nontransitive Logic.David Ripley - 2015 - Review of Symbolic Logic 8 (3):553-571.
Non-Monotonic Set Theory as a Pragmatic Foundation of Mathematics.Peter Verdée - 2013 - Foundations of Science 18 (4):655-680.
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