Topoi

, Volume 18, Issue 2, pp 141–148

Negation as Cancellation, and Connexive Logic

Authors

  • Graham Priest
    • Department of PhilosophyUniversity of Queensland
Article

DOI: 10.1023/A:1006294205280

Cite this article as:
Priest, G. Topoi (1999) 18: 141. doi:10.1023/A:1006294205280

Abstract

Of the various accounts of negation that have been offered by logicians in the history of Western logic, that of negation as cancellation is a very distinctive one, quite different from the explosive accounts of modern "classical" and intuitionist logics, and from the accounts offered in standard relevant and paraconsistent logics. Despite its ancient origin, however, a precise understanding of the notion is still wanting. The first half of this paper offers one. Both conceptually and historically, the account of negation as cancellation is intimately connected with connexivist principles such as ¬(α → ¬α). Despite this, standard connexivist logics incorporate quite different accounts of negation. The second half of the paper shows how the cancellation account of negation of the first part gives rise to a semantics for a simple connexivist logic.

Copyright information

© Kluwer Academic Publishers 1999