Dialectical Considerations on the Logic of Contradiction: Part I
By John Woods
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 (LNC). 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.
Key Words: antinomy, Aristotle, contradiction, costs and benefits, consistentism, Curry Paradox, detonation, dialetheism, Frege, Law of Non-Contradiction, Liar Paradox, Locke, proof, Russell, near-trivialism, paraconsistency, Philosophy's Most Difficult Problem, set theory, semantics, Solving Paradox, Tarski, truth
Appeared in the Logic Journal of IGPL 2005 13(2):231-260