Logic without contraction as based on inclusion and unrestricted abstraction

Studia Logica 64 (3):365-403 (2000)
Abstract
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
Categories (categorize this paper)
Reprint years 2004
DOI 10.1023/A:1005293713265
Options
 Save to my reading list
Follow the author(s)
My bibliography
Export citation
Find it on Scholar
Edit this record
Mark as duplicate
Revision history
Request removal from index
Download options
Our Archive


Upload a copy of this paper     Check publisher's policy     Papers currently archived: 27,606
Through your library
References found in this work BETA

No references found.

Add more references

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.
Contraction and Revision.Shawn Standefer - 2016 - Australasian Journal of Logic 13 (3):58-77.
Naive Set Theory and Nontransitive Logic.David Ripley - 2015 - Review of Symbolic Logic 8 (3):553-571.

View all 10 citations / Add more citations

Similar books and articles

Monthly downloads

Added to index

2009-01-28

Total downloads

35 ( #146,840 of 2,168,588 )

Recent downloads (6 months)

2 ( #187,166 of 2,168,588 )

How can I increase my downloads?

My notes
Sign in to use this feature


Discussion
Order:
There  are no threads in this forum
Nothing in this forum yet.

Other forums