New problems for Tennant's definition of harmony

Abstract

Steinberger proposes as a counterexample to Tennant's harmony criterion a degenerate quantifier that makes it possible to prove consequences such as A ( a ) ⊨ A ( b ) for every propositional function and pair of terms. Tennant suggests an answer that, according to Steinberger, is inadequate for the purpose. In this paper, it is shown that Steinberger's counterexample works only within a finitary framework, and that, moreover, it rests on a controversial interpretation of Tennant's criterion. Another deepened interpretation of the same criterion is suggested and defended. It is then proved that this new reading solves Steinberger's counterexample but leads to an unacceptable weakening of the logical system.