David Bourget (Western Ontario)
David Chalmers (ANU, NYU)
Rafael De Clercq
Jack Alan Reynolds
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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.
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Citations of this work BETA
Zach Weber (2010). Transfinite Numbers in Paraconsistent Set Theory. Review of Symbolic Logic 3 (1):71-92.
Zach Weber (2010). Extensionality and Restriction in Naive Set Theory. Studia Logica 94 (1):87 - 104.
Zach Weber (2011). Reply to Bjørdal. Review of Symbolic Logic 4 (1):109-113.
Peter Verdée (2013). Non-Monotonic Set Theory as a Pragmatic Foundation of Mathematics. Foundations of Science 18 (4):655-680.
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