David Bourget (Western Ontario)
David Chalmers (ANU, NYU)
Rafael De Clercq
Jack Alan Reynolds
Learn more about PhilPapers
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||No keywords specified (fix it)|
|Categories||categorize this paper)|
Setup an account with your affiliations in order to access resources via your University's proxy server
Configure custom proxy (use this if your affiliation does not provide a proxy)
|Through your library|
References found in this work BETA
No references found.
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.
Peter Verdée (2013). Non-Monotonic Set Theory as a Pragmatic Foundation of Mathematics. Foundations of Science 18 (4):655-680.
Zach Weber (2011). Reply to Bjørdal. Review of Symbolic Logic 4 (1):109-113.
Similar books and articles
John Bacon (1982). First-Order Logic Based on Inclusion and Abstraction. Journal of Symbolic Logic 47 (4):793-808.
W. V. Quine (1937). Logic Based on Inclusion and Abstraction. Journal of Symbolic Logic 2 (4):145-152.
Sven Ove Hansson (2010). Multiple and Iterated Contraction Reduced to Single-Step Single-Sentence Contraction. Synthese 173 (2):153 - 177.
Andreja Prijatelj (1995). Connectification Forn-Contraction. Studia Logica 54 (2):149 - 171.
Greg Restall (1993). How to Bereally Contraction Free. Studia Logica 52 (3):381 - 391.
Richard B. White (1993). A Consistent Theory of Attributes in a Logic Without Contraction. Studia Logica 52 (1):113 - 142.
Sven Ove Hansson (2008). Specified Meet Contraction. Erkenntnis 69 (1):31 - 54.
Raghav Ramachandran, Abhaya C. Nayak & Mehmet A. Orgun (2012). Three Approaches to Iterated Belief Contraction. Journal of Philosophical Logic 41 (1):115-142.
Added to index2009-01-28
Total downloads16 ( #98,837 of 1,096,676 )
Recent downloads (6 months)5 ( #53,220 of 1,096,676 )
How can I increase my downloads?