Studia Logica

, Volume 64, Issue 3, pp 365–403

Logic Without Contraction as Based on Inclusion and Unrestricted Abstraction

  • Uwe Petersen

DOI: 10.1023/A:1005293713265

Cite this article as:
Petersen, U. Studia Logica (2000) 64: 365. doi:10.1023/A:1005293713265


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.

contraction free logic unrestricted abstraction type free logic foundation of the notion of natural number 

Copyright information

© Kluwer Academic Publishers 2000

Authors and Affiliations

  • Uwe Petersen
    • 1
  1. 1.GrosshansdorfGermany