A free logic with simple and complex predicates.
Ermanno Bencivenga, Karel Lambert · Notre Dame Journal of Formal Logic · 1986
Consider a fragment of colloquial discourse sans modal or epistemic operators or psychological verbs.Examples of statements in this fragment are (1) Vulcan rotates around its axis, 1 and(2) Vulcan is self-identical.Some free logicians regard all such simple statements as asserting of the objects to which the constituent singular terms purport to refer that they are things which. (Here and elsewhere the blanks are to be filled in by appropriate verbs or verb phrases.)So, for instance, (1) and ( 2) respectively assert of Vulcan that it is a thing which rotates around its axis and, among other possibilities, that it is a thing which is the same as Vulcan.This kind of linguistic intuition underlies the conviction of many free logicians that all simple statements of the fragment of colloquial discourse in question imply the existence of the purported referents of their constituent singular terms, and hence that if the purported referents fail to exist, the host statement is false.Free logics of this sort are called negative free logics. 2 Other free logicians regard simple statements of the fragment of colloquial discourse in question merely as asserting that the objects to which the constituent singular terms purport to refer So, for instance, the sentences (1) and ( 2) respectively assert that Vulcan rotates around its axis and, among other possibilities, is the same as Vulcan.Accordingly, even if all the singular terms are irreferential -as in (2) -the truth-value of the host statement need not be false, and, indeed, is true in the case of (2).( 1) is either true or truth-valueless.This kind of linguistic intuition underlies the conviction of many free logi-