Part 1: Introducing the Idea
In this post I introduce the idea of reference-making, which I take to be more-or-less undefined, and use it to account for the idea of truth-making for subject-predicate sentences. I take a truth-maker to be a reference-maker for a sentence. In Part 2 I’ll give a quasi-formal account of how it can be applied to truth-functional compounds and quantified sentences, and in Part 3 I’ll discuss some of its philosophical implications.
Let us say that the reference-maker for a noun or a noun-phrase is just what is ordinarily called its referent, the thing that it “corresponds to” or ‘”picks out” in the world. Nothing interesting so far. For predicates, however, the idea is different: Just as sentences can have many truth-makers–“Planets exist” being made true by each planet–on this view a predicate can have many reference-makers, without thereby becoming ambiguous (as nouns/noun-phrases would become if they had many reference-makers). This is a key difference between predicates and nouns/noun-phrases. We will therefore say that predicates have reference, but not that they have referents. We could say that every reference-maker for F is a referent of F, but that would be misleading in that it would suggest that F was ambiguous. (This is a terminological point introduced to prevent confusion. Nothing beyond that hangs on our choice of terms.) A reference-maker for a predicate is something that it is true of, or that satisfies it. Any red thing is a reference-maker for the predicate ‘red’ or ‘is red’. In this ‘red’ and ‘is red’ differ from ‘redness’, whose reference maker, if any, is redness; i.e., the property of being red.
Since I take the relation of predicates to reality to be, in general, one-many, I think it would be a mistake to take the “referent” or the semantic value of a predicate to be its extension, the set of things of which it is true. On my view, any reference-maker for a predicate can be said to be a semantic value of the predicate. Still, most predicates of a given language will have but one meaning.
What of relational predicates? Their reference-makers can indeed be taken to be sets, namely ordered n-tuples. Still, we will not identify “the” semantic value of a predicate with its extension (nor with the property, if any, that it expresses): A reference-maker for an n-ary predicate is any ordered n-tuple of which that predicate is true, not the set of all such n-tuples–unless that set is one of the things of which the predicate is true; but still it would only be only one reference maker among many.
We can now say what a truth-maker, which is a reference maker for a sentence, is for subject-predicate sentences. An object x (‘object’ being broadly construed as anything that exists) is a truth-maker for a subject-predicate sentence p iff x is a reference-maker for p’s subject term and is also a reference-maker for p’s predicate term. Similarly, for relational sentences: An ordered n-tuple o is a truth-maker for an n-ary relational sentence p iff the objects ordered in o are each reference makers for one of p’s subject terms, and o is a reference-maker for p’s predicate term. In Part 2, I’ll extend this account to define truth-makers for truth-functional compounds and quantified sentences.
