, Volume 18, Issue 2, pp 141–148 | Cite as

Negation as Cancellation, and Connexive Logic

  • Graham Priest


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.


Classical Logic Logical Truth Double Negation Relevant Logic Paraconsistent Logic 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. Abelard, Peter: 1956, Dialectica, ed. L.M. De Rijk, Assen: Van Gorcum.Google Scholar
  2. Anderson, A. and Belnap, N.: 1975, Entailment, Vol. I, Princeton: Princeton University Press.Google Scholar
  3. Angell, R.B.: 1962, 'A Propositional Logic with Subjunctive Conditionals', Journal of Symbolic Logic 27, 327–343.CrossRefGoogle Scholar
  4. Berkeley, George: 1951, The Works of George Berkeley, Vol. IV, ed. A.A. Luce and T.E. Jessop, London: Thomas Nelson and Sons.Google Scholar
  5. Bochenski, I.M.: 1961, A History of Formal Logic, Notre Dame: University of Notre Dame Press.Google Scholar
  6. Findlay, J.N.: 1958, Hegel; a Reexamination, London: Allen & Unwin.Google Scholar
  7. Kneale, W. and Kneale, M.: 1962, The Development of Logic, Oxford: Oxford University Press.Google Scholar
  8. Lear, J.: 1988, Aristotle: the Desire to Understand, Cambridge: Cambridge University Press.CrossRefGoogle Scholar
  9. McCall, S.: 1966, 'Connexive Implication', Journal of Symbolic Logic 31, 415–433.CrossRefGoogle Scholar
  10. McCall, S.: 1967, 'Connexive Logic and the Syllogism', Mind 76, 346–356.CrossRefGoogle Scholar
  11. McCall, S.: 1975, 'Connexive Implication', Section 29.8 of Anderson and Belnap (1975).Google Scholar
  12. Mortensen, C.: 1984, 'Aristotle's Thesis in Consistent and Inconsistent Logics, Studia Logica 43, 107–116.CrossRefGoogle Scholar
  13. Nelson, E.J.: 1930, 'Intensional Relations', Mind 39, 440–453.CrossRefGoogle Scholar
  14. Priest, G.: 1998, 'To Be and not to Be – That is the Answer', Philosophiegeschichte und logische Analyse 1, 91–130.Google Scholar
  15. Rescher, N. and Manor, R.: 1970–1971, 'On Inference from Inconsistent Premises', Theory and Decision 1, 179–217.CrossRefGoogle Scholar
  16. Ross, W.D. (ed.): 1928, The Works of Aristotle, Vol. I, Oxford: Clarendon Press.Google Scholar
  17. Routley, R.: 1978, 'Semantics for Connexive Logics, I' Studia Logica 37, 393–412.CrossRefGoogle Scholar
  18. Routley, R., Meyer, R.K., Plumwood, V. and Brady, R.: 1982, Relevant Logics and their Rivals, Atascadero: Ridgeview.Google Scholar
  19. Routley, R. and Routley, V.: 1985, 'Negation and Contradiction', Rivista Columbiana de Matemáticas 19, 201–231.Google Scholar
  20. Smiley, T.J.: 1959, 'Entailment and Deducibility', Proceedings of the Aristotelian Society 59, 233–254.Google Scholar
  21. Strawson, P.: 1952, Introduction to Logical Theory, Oxford: Oxford University Press.Google Scholar
  22. Sylvan, R.: 1989, Bystanders' Guide to Sociative Logics, Research Series in Logic and Metaphysics, No. 4, Department of Philosophy, Research School of Social Sciences, Australian National University, Canberra.Google Scholar

Copyright information

© Kluwer Academic Publishers 1999

Authors and Affiliations

  • Graham Priest
    • 1
  1. 1.Department of PhilosophyUniversity of QueenslandUSA

Personalised recommendations