The Truth Predicate vs the Truth Connective. On Taking Connectives Seriously

In his rich “The Truth Predicate vs. the Truth Connective. On taking connectives seriously.” Kevin Mulligan [14] starts an inquiry into the logical form of truth ascriptions and challenges the prevailing view which takes truth ascriptions to be of subject predicate form, that is a truth predicate applied to a name of a proposition or sentence. Rather than appealing to a truth predicate, Mulligan argues, we should account for the logical form of truth ascriptions using the “truth connective”. To this end Mulligan, in his genuine and original style, brings forward and merges arguments stemming from syntax theory, semantics, metaphysics and Bolzano to substantiate his dictum that it is not the truth predicate but the truth connective “which wears the trousers” (cf. Mulligan [14], p. 567). In this piece we shall first discuss Mulligan’s proposal from the perspective of linguistics and, especially, syntax theory. Even though theory of syntax provides little evidence for Mulligan’s view, we shall argue that this does not disqualify the thesis that it is a truth connective (or operator as we shall frequently say) which figures in the logical form of truth ascriptions. This view can be supported by distinguishing between the grammatical and the logical form of a sentence. Moreover, as Mulligan notes there is a similarity between truth and modal ascriptions, where in most formal treatments their logical form is very different, that is, truth is commonly treated as a predicate but the modalities are conceived as operators. We think that these notions should be treated in an uniform way, either both as predicates or both as operators. The prevailing philosophical view is that if truth and the modalities are treated as predicates, paradox will arise, though nothing of the like will arise when we opt for an operator treatment. We shall argue that the question of whether paradox will arise is somewhat orthogonal to whether we treat truth and the modalities as operators or as predicates. Rather it is the expressive power of the framework which is at stake, when it comes to the paradoxes.