Here is a white cube. Call it 'Carl.' 'Carl is white' is true. But Carl, though white, might not have been white. (He would not have been white had I painted him red.) So 'Carl is white' is contingently true. There is no necessity that Carl be white. By contrast, 'Carl is three-dimensional' is necessarily true. It is metaphysically necessary that he be three-dimensional. Of course, the necessity here is conditional: given that Carl exists, he cannot fail to be three-dimensional. But Carl might not have existed. So Carl is subject to a two-fold contingency, one of existence and one of property-possession. It is contingent that Carl exists at all -- he is not a necessary being -- and with respect to some of his properties it is contingent that he has them. He exists contingently and he is white contingently. Or, using 'essence' and 'accident,' we can say: Carl is a contingent being that is accidentally white but essentially three-dimensional. By contrast, the number 7 is a necessary being that accidentally enjoys the distinction of being Poindexter's favorite number, but is essentially prime.
Some truths need truth-makers. 'Carl is white' is one of them. Grant me that some truths need truth-makers. My question is this: Can a trope do the truth-making job in a case like this or do we need a concrete fact?
Carl is white. That is given. Some say that (at least some of) the properties of particulars are themselves particulars (unrepeatables). Suppose you think along those lines. You accept that things have properties -- Carl, after all, is white extralinguistically -- and therefore that there are properties, but you deny that properties are universals. Your nominalism is moderate, not extreme. Suppose you think of Carl's whiteness as a trope or as an Husserlian moment or as an Aristotelian accident. (Don't worry about the differences among these items.) That is, you take the phrase 'Carl's whiteness' to refer, not to the fact of Carl's being white, which is a complex having Carl himself as a constituent, but to a simple item: a bit of whiteness. This item depends for its existence on Carl: it cannot exist unless Carl exists, and, being particular, it cannot exist in or at any other thing such as Max the white billiard ball. Nor is it transferrable: the whiteness of Carl cannot migrate to Max.
The truth-maker of a truth is an existing thing in virtue of whose existence the truth is true. Why can't Carl's whiteness trope be the truth-maker of 'Carl is white'? That very trope cannot exist unless it exists 'in' Carl as characterizing Carl. So the mere existence of that simple item suffices to make true the sentence 'Carl is white.' Or so it seems to some distinguished philosophers.
If this is right, then there is no need that the truth-maker of a truth have a sentence-like or proposition-like structure. (For if a proposition-like truth-maker is not needed in a case like that of Carl the cube, then presumably there is no case in which it is needed.) A simple unrepeatable bit of whiteness has no internal structure whatsoever, hence no internal proposition-like structure. A concrete fact or state of affairs, however, does: Carl's being white, for example, has at a bare minimum a subject constituent and a property constituent with the former instantiating the second.
My thesis is not that all truth-makers are proposition-like, but that some are. Presumably, the truth-maker of 'Carl is Carl' and 'Carl exists' is just Carl. But it seems to me that the truth-maker of 'Carl is white' cannot be the particular whiteness of Carl. In cases like this a simple item will not do the job. Why not?
1. If it is legitimate to demand an ontological ground of the truth of a truth-bearer, whether it be a sentence or a proposition or a judgment or whatever, then it is legitimate to demand an ontological ground of the contingency of the truth of a truth-bearer. If we have a right to ask: what makes 'Carl is white' true, then we also have a right to ask: What makes 'Carl is white' contingently or accidentally true as opposed to essentially true? Truth and contingent truth are not the same. And it is contingent truth that needs explaining. If a truth-bearer is necessarily true, it may be such in virtue of its logical form, or because it is true ex vi terminorum; in either case it is not clear that the is any need for a truth-maker. Does 'Bachelors are male' need a truth-maker? Not as far as I can see. But 'Tom is a bachelor' does. Unlike David Armstrong, I am not a truth-maker maximalist. See Truthmaker Maximalism Questioned.
2. The trope Carl's whiteness can perhaps explain why the sentence 'Carl is white' is true, but it cannot explain why it is accidentally true as opposed to essentially true. For the existence of the trope is consistent both with Carl's being essentially white and Carl's being accidentally white. If F is a trope, and F exists, then F is necessarily tied to a concrete individual (this is the case whether one is a trope bundle theorist or a trope substratum theorist like C. B. Martin), and so the concrete indiviual exists and is characterized by F. But this is so whether the concrete individual is essentially F or accidentally F.
3. To explain the contingency of a contingent truth it is not enough that the truth-maker be contingent; there must also be contingency within the truth-maker. Or so it seems to me. The fact theory can accommodate this requirement. For in the fact of Carl's being white, the fact itself is contingent, but so also is the connection between Carl and whiteness. Carl and whiteness can exist without the fact existing. (This assumes that whiteness is a universal) The contingency of the connection of the constituents within the fact accounts for the contingency of the truth of 'Carl is white.' But no trope is contingently connected to any concrete individual of which it is the trope.
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