This is an examination of the dialectical structure of deep disagreements about matters not open to empirical check. A dramatic case in point is the Law of Non-Contradiction . Dialetheists are notoriously of the view that, in some few cases, LNC has a true negation. The traditional position on LNC is that it is non-negotiable. The standard reason for thinking it non-negotiable is, being a first principle, there is nothing to negotiate. One of my purposes is to show that the (...) first-principle defence of LNC is inadequate. A second purpose is to argue that it flows from this inadequacy that LNC stands or falls on economic considerations, much in the spirit of Quine's pragmatism about logic generally. This is a tactical victory for dialetheists. It gives them room to make the case against LNC on cost-benefit grounds. As things presently stand, no such case can be considered decisive. But, given that costs and benefits shift with changing circumstances, it is possible that a winning case for the dialetheist may present itself in the future. Notwithstanding the rivalry between consistentists and dialetheists, they share a common opponent. This is trivialism, the doctrine that everything whatever is true. It is an ironic alliance, in as much as the dialetheist's case against the consistentist can be adapted to a defence of trivialism. How damaging this turns out to be depends on the adequacy of the reasons for the dialetheist's rejection of trivialism. My further purpose is to show that the damage is slighter than dialetheists commonly believe. (shrink)

Impossible worlds are regarded with understandable suspicion by most philosophers. Here we are concerned with a modal argument which might seem to show that acknowledging their existence, or more particularly, the existence of some hypothetical (we do not say “possible”) world in which everything was the case, would have drastic effects, forcing us to conclude that everything is indeed the case—and not just in the hypothesized world in question. The argument is inspired by a metaphysical (rather than modal-logical) argument of (...) Paul Kabay’s which would have us accept this unpalatable conclusion, though its details bear a closer resemblance to a line of thought developed by Jc Beall, in response to which Graham Priest has made some philosophical moves which are echoed in our diagnosis of what goes wrong with the present modal argument. Logical points of some interest independent of the main issue arise along the way. (shrink)

This paper criticises necessitarianism, the thesis that there is at least one necessary truth; and defends possibilism, the thesis that all propositions are contingent, or that anything is possible. The second section maintains that no good conventionalist account of necessity is available, while the third section criticises model theoretic necessitarianism. The fourth section sketches some recent technical work on nonclassical logic, with the aim of weakening necessitarian intuitions and strengthening possibilist intuitions. The fifth section considers several a prioristic attempts at (...) demonstrating that there is at least one necessary proposition and finds them inadequate. The final section emphasises the epistemic aspect of possibilism. (shrink)

The dogma that the propositional logic of metaphysical modality is S5 is rebutted. The author exposes fallacies in standard arguments supporting S5, arguing that propositional metaphysical modal logic is weaker even than both S4 and B, and is instead the minimal and weak metaphysical-modal logic T.

We address an issue recently discussed by Graham Priest: whether the very nature of truth (understood as in correspondence theories) rules out true contradictions, and hence whether a correspondence-theoretic notion of truth rules against dialetheism. We argue that, notwithstanding appearances to the contrary, objections from within the correspondence theory do not stand in the way of dialetheism. We close by highlighting, but not attempting to resolve, two further challenges for dialetheism which arise out of familiar philosophical theorizing about truth.