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.
Unable to display preview. Download preview PDF.
- Abelard, Peter: 1956, Dialectica, ed. L.M. De Rijk, Assen: Van Gorcum.Google Scholar
- Anderson, A. and Belnap, N.: 1975, Entailment, Vol. I, Princeton: Princeton University Press.Google Scholar
- 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
- Bochenski, I.M.: 1961, A History of Formal Logic, Notre Dame: University of Notre Dame Press.Google Scholar
- Findlay, J.N.: 1958, Hegel; a Reexamination, London: Allen & Unwin.Google Scholar
- Kneale, W. and Kneale, M.: 1962, The Development of Logic, Oxford: Oxford University Press.Google Scholar
- McCall, S.: 1975, 'Connexive Implication', Section 29.8 of Anderson and Belnap (1975).Google Scholar
- Priest, G.: 1998, 'To Be and not to Be – That is the Answer', Philosophiegeschichte und logische Analyse 1, 91–130.Google Scholar
- Ross, W.D. (ed.): 1928, The Works of Aristotle, Vol. I, Oxford: Clarendon Press.Google Scholar
- Routley, R., Meyer, R.K., Plumwood, V. and Brady, R.: 1982, Relevant Logics and their Rivals, Atascadero: Ridgeview.Google Scholar
- Routley, R. and Routley, V.: 1985, 'Negation and Contradiction', Rivista Columbiana de Matemáticas 19, 201–231.Google Scholar
- Smiley, T.J.: 1959, 'Entailment and Deducibility', Proceedings of the Aristotelian Society 59, 233–254.Google Scholar
- Strawson, P.: 1952, Introduction to Logical Theory, Oxford: Oxford University Press.Google Scholar
- 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