Denyer's $ Not Backed By Sterling Arguments

Abstract

A number of people have suggested that an inconsistency-tolerating position is immune from criticism, since objectors are left weaponless.1 This, however, seriously underestimates the weapons of criticism; in particular, it betrays an overly formalistic conception thereof. A particularly powerful and legitimate form of criticism is that form ad hominem which convicts the position in question of being guilty of the very failings of which it accuses others.2 In 'Dialetheism and Trivialisation'3 Nick Denyer demonstrates a shrewd appreciation of this fact. He criticizes dialetheic solutions to the semantic paradoxes (which are inconsistencytolerating) by giving an ingenious argument to show that, given dialetheic logic, the T-scheme leads to triviality if there is a certain binary connective, $, of apparently legitimate credentials. The only way out of this, he argues, opens the dialetheist to just such criticism. The argument fails to work, however. Denyer's triviality argument breaks down for two reasons. The first is that the 'iff' used at a crucial stage of the argument fails to have the properties Denyer takes it to have. The second is that Denyer's $ fails to have the properties he takes it to have. Moreover, in each case, the reasons for these failures have an intellectual integrity which protects them from the ad hominem argument. I take up the two reasons in the order stated.