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  Philosophers have taken a number of views about the true nature of propositions. Some claim they are fundamental abstract objects. Among those who take this view, some maintain that propositions have no internal structure and have primitive representational features, while others maintain that propositions have some sort of quasi-linguistic structure and represent what they do because of this structure. Others claim that propositions are certain sorts of fact in the world, like facts about which objects have which features or which objects are related to which other objects or facts about objects and features of objects in combination with facts about some language or other. Still others claim that propositions are just arbitrary classes of “possible worlds.” (We discuss possible worlds in Chapters 14–16.) There are pluses and minuses to each of these views of propositions, and unfortunately we do not have the space to discuss them in detail here. Happily, which view of propositions one takes will not have a substantial impact on how our discussion proceeds from this point forward; we simply want to flag these issues and suggest that the interested reader take up these interesting questions for him- or herself.

  To wrap things up, we can articulate a simple and basic theory of propositions. Propositions are:

  Abstract (immaterial, not located in space or time).

  Capable of being true or false.

  Capable of being believed, doubted, considered or assumed.

  Capable of being expressed by simple indicative statements.

  Things that stand in various logical or quasi-syntactic relations to other propositions: e.g., each proposition has a unique negation; two propositions have a conjunction, etc.

  Things that contain one or more concepts, either individual or general, where concepts are also abstract things that stand in some sort of intentional relation (a relation of representation or aboutness) to some particular thing, general property or class of things.

  This theory leaves much about the exact nature of propositions up for grabs, but articulates certain crucial features of propositions that any adequate theory must accommodate.

  2.1.2 Truthmakers

  What can we say about the world side of the correspondence story? The central question concerns what propositions must correspond to in order to be true. It seems fairly clear that we shouldn't say that a proposition must correspond to the whole of the world in order to be true. Consider the proposition that grass is green. It shouldn't take the whole world for that proposition to come out true!

  There was a tradition in metaphysics during the nineteenth century, however, that would claim that in an important sense every truth was necessarily connected to every truth. These British Idealists and Hegelians believed the world was a single, interconnected, inseparable whole. That is, these philosophers were holists. Holists maintain that the interconnection of the world is so pervasive that if one truly understands one part of reality, one thereby understands the whole of reality. Because of this interconnectedness, any sentence must correspond to the whole world in order to be true.

  The early part of the twentieth century saw a strong reaction against holism, led prominently by Bertrand Russell and Ludwig Wittgenstein. These philosophers argued that holism failed to conform to common sense and to our best scientific practices and that there must be a set of fundamental, logically independent facts, the “logical atoms.” Two facts a and b are logically independent if and only if all four of the following are possible: (i) a and b both exist, (ii) neither a nor b exists, (iii) a exists but b doesn't, and (iv) b exists but a doesn't. Logical atoms, according to logical atomists, were the proper parts of the world to which propositions must correspond in order to be true. Supposing, for example, that grass's being green is a logical atom, the proposition that grass is green is true because it corresponds to the logical atom of grass's being green. Further, and unlike holists, logical atomists would say that the fact that grass is green is utterly independent and distinct from the fact that the sky is blue, and thus that the proposition that the sky is blue need not correspond to the fact that grass is green in order to be true.

  Logical atomists like Russell and Wittgenstein, as well as other philosophers like G.E. Moore, further developed the Correspondence Theory of Truth by asserting that facts are what make propositions true. In so doing, they built on an idea first expressed by Aristotle in his Categories:

  [I]f there is a man, the statement whereby we say that there is a man is true, and reciprocally—since if the statement whereby we say that there is a man is true, there is a man. And whereas the true statement is in no way the cause of the actual thing's existence, the actual thing does seem in some way the cause of the statement's being true: it is because the actual thing exists or does not that the statement is called true or false.”

  (Aristotle, Categories 14b15–22; 1984: 22)3

  Because the fact that grass is green is what makes the proposition that grass is green true, the fact that grass is green is a truthmaker for the proposition that grass is green.

  Definition (Def) D2.1 Classical Truthmaker. A thing x is a (classical) truthmaker for proposition p if and only if (i) necessarily, if x exists, then p is true and (ii) necessarily, if x exists and p is true, then p is true at least in part in virtue of x's existence.

  The fact that grass is green seems to satisfy these constraints for being a truthmaker of the proposition that grass is green. It's necessarily the case that if the fact that grass is green exists, then the proposition that grass is green is true; thus (i) is satisfied. And it's necessarily true that the proposition that grass is green is true, at least in part, in virtue of the existence of the fact that grass is green; thus (ii) is satisfied. Similarly, the proposition that the University of Texas is the largest university in Texas is true whenever the fact that UT is the largest university in Texas exists, and it is true in virtue of the existence of that fact. (What, exactly, are facts? Good question. We take it up in Chapter 9.)

  This truthmaking story is plausible as a way of working out the Correspondence Theory of Truth. Though we aren't interested at this point in the tug-of-war between holism and atomism that initiated the philosophical discussion of truthmakers, we are interested in truthmakers themselves. The remainder of this chapter is devoted to whether we ought to go in for truthmaker theory, how we ought to formulate truthmaker theory if we do go in for it, and what truthmakers might be.

  Any view that believes there are things satisfying Def 2.1, that is, any view that believes in (classical) truthmakers, is a ‘Classical Truthmaker Theory’.

  2.1T Classical Truthmaker Theory. There are classical truthmakers for all truths or for some very large sub-classes of truths.

  2.1A No Classical Truthmakers. There are few, if any, truths with classical truthmakers.

  There are a number of varieties of Classical Truthmaker Theory, and we consider them below (Sections 2.4 and 2.5). Before we do that, we consider why we should believe in Classical Truthmaker Theory in the first place (Section 2.2), as well as a fundamental challenge to the very foundation of truthmaker theory: the deflationary theory of truth (Section 2.3).

  If at the end of Section 2.3, you find Classical Truthmaker Theory convincing, or if you find the whole idea of truthmakers mysterious and unhelpful, then you need not consider the variations in Sections 2.4 and 2.5. If, in contrast, you find the basic motivation for truthmakers to be compelling but are unsatisfied with the Classical picture, then Sections 2.4 and 2.5 offer some useful alternatives. There is Atomic Truthmaker Theory, in which the truthmaker principle is applied only to the simplest truths, those that lack negation or any other logical connective. We also consider two more radical departures from Classical Truthmaker Theory: Spectral Truthmaker Theory and Truth Supervenes on Being. Spectral Truthmaker Theory is based on the observation that reality does not seem to be uniformly binary in character—namely, that truthmakers simply exist or do not—as Classical Truthmaker Theory supposes. Truth Supervenes on Being tries to capture some of the leading motivations for
truthmaker theory while dispensing with truthmakers altogether.

  2.2 Five Arguments for Classical Truthmaker Theory

  Why should we believe that there are truthmakers? Here are five arguments for truthmakers.

  1. The Correspondence Theory of Truth leads naturally to truthmakers. This is something we've already seen, but the point can be turned into an argument for truthmaker theory. First point, one that's already been made: the Correspondence Theory of Truth is initially highly plausible. It seems to make sense of our usual ways of thinking about most, if not all, truths. It also explains why it is that we investigate the world in order to ascertain whether a claim is true or not. We seem to take our knowledge of the meaning of a sentence whose truth is in question and compare it to what we find in the world; if there is a match, we think the sentence is true, and if not, then it's false. This is precisely what we would expect if the Correspondence Theory were correct. So suppose the Correspondence Theory of Truth is in fact correct.4

  Second point: The chunk of the world to which a proposition must correspond in order to be true satisfies clause (i) of the definition of a truthmaker. The proposition that grass is green simply cannot fail to be true if grass is in fact green!5

  Third point: There seems to be an asymmetric dependence of the truth of a proposition on the chunk of the world to which that proposition must correspond. In other words, it is because grass is green that the proposition that grass is green is true. It is difficult to argue for this, but it is even more difficult to deny! Compare: it is because the proposition that grass is green is true that grass is green in fact. That seems wrong. But then, the proposition that grass is green is true in virtue of the existence of the fact that grass is green. Thus, the chunk of the world to which a proposition must correspond in order to be true satisfies clause (ii) of the definition of a truthmaker.

  Let's approach this question from another tack. The Correspondence Theory proposes that truth consists in a certain kind of relation, call it ‘truthful correspondence’, between a proposition and some real thing or things. What kind of relation is truthful correspondence?

  One question we can ask is this: is truthful correspondence an internal relation? G.E. Moore articulated a distinction between internal and non-internal relations according to which an internal relation is a relation R which is such that, whether it holds of two entities, x and y, depends only on the intrinsic characters of x and y, considered individually.

  Def D2.2 Internal Relation. R is an internal relation if and only if, necessarily, for every x and y, whether R holds between x and y depends only on the intrinsic properties of x and of y.

  Relations are non-internal if and only if they are not internal. Of course, to understand this definition, one must understand what it takes for a property to be intrinsic. An object's intrinsic character is determined by its intrinsic properties, where a property is intrinsic to an object if that object has the property because of the way it is or its parts are, rather than in relation to something that is not itself or its parts.6

  Def D2.3 Intrinsicality. x is intrinsically F if and only if nothing that is not x or a part of x is part of the ground of x's being F.

  The class of internal relations includes the relation of being the same size as, that of being twice as tall as, being smarter than, contains more parts than, etc. Consider the relation of being smaller than. To tell if one thing is smaller than another, all we need to know are the sizes of each of the two things, and size is an intrinsic property of a thing. Relations that are not internal include those of being at least a meter apart from, being to the north of, is moving away from, etc. If a relation is not internal, we have to know something beyond the intrinsic characters of the two things to know if the relation holds.

  Truthful correspondence seems to be an internal relation. If we know everything there is to know about the intrinsic character of a proposition (including its content), and if we know everything there is to know about the intrinsic character of the part of the world that the proposition is about (its worldly correlate), we should able to tell whether the proposition is true or false. Moreover, the intrinsic character of the proposition is eternal and essential to it: propositions don't vary intrinsically from one time or one situation to another. So, the truth of the proposition must depend on the character of its worldly correlate. This is exactly the asymmetric dependency of the truth on the world that Aristotle mentions in the Categories, and it is why we find it natural to speak of ‘truthmakers’.

  Therefore, the Correspondence Theory is a theory about what truth consists in. For a proposition to be true is for that proposition to be in the truthful correspondence relation to some part of the world, its worldly correlate. So, we should be able to say something like this:

  (1) For p to be true is for p to stand in the truthful correspondence relation to the worldly correlate of p.

  Since the truthful correspondence relation is an internal relation, for some proposition p to stand in this relation to something is just for that thing to have the right kind of intrinsic character. For each proposition p, we should be able to say the following, where X stands for this intrinsic character or property:

  (2) For p to be true is for the worldly correlate of p to be X.

  If truth is a real property in the world, then truthful correspondence must also be a real relation. By ‘real relation’, we mean a relation that corresponds to some real, intrinsic similarity between different cases. A real relation has some unifying theme that ties together all of its instances. An unreal or merely nominal relation occurs in a highly variegated, gerrymandered set of instances. So, being spatially next to seems to be a real relation. Any two cases of one thing's being in contact with another are very similar to each other. On the other hand, being next to something in an arbitrary list, like a laundry or grocery list, is merely nominal.

  For truthful correspondence to be such a real relation, the character X should be the same character for every proposition p. For it to be true that the Moon is cubical is for something to be X, and for blood to be red is for something to be X—the same X in both cases. Classical Truthmaker Theory provides just such an account. The worldly correlate of a proposition is some possible fact or state of affairs, and the X factor is existence or actuality. Thus, the worldly correlate of the proposition that blood is red is the possible fact of blood's being red, and for that proposition to be true is for that fact to exist. Similarly, the correlate of the proposition that the Moon is cubical is the possible fact of the Moon's being cubical, and for that proposition to be true is for that fact to exist. Since that fact does not exist (the Moon isn't cubical), the proposition is not true.

  Is there any other X that could work as well as existence? Propositions can be about anything, and they can predicate any sort of property. This is why X cannot be a feature that is specific or limited to a particular topic or set of questions. For example, X couldn't be redness. Redness might work as an account of the truth of the proposition that blood is red. We could suppose that the correlate of the proposition is simply blood, and that for that proposition to be true is just for blood to be red. But then what could we do with the proposition that grass is green? There isn't anything z in the world such that for it to be true that grass is green is for z to be red. Nothing's being red can make it true that grass is green. For similar reasons, the X factor can't be any specific shape, size, or material composition. A feature like existence can work because it is generic and universal. Every proposition can be correlated with some possible fact, and it makes sense to suppose that what it is for that proposition to be true is for the possible fact to exist.

  Are there any other alternatives to existence as the X factor? Are there other features that are equally generic and universal in scope? We might consider the relation of exemplification or instantiation (which we will discuss in more detail in Chapter 7). This is the relation that holds between a thing and a property when that thing has the property. So, we might
suppose that the proposition that the Moon is round has two things as its correlate, the Moon and the property of roundness, and we might then hypothesize that what it is for the proposition that the Moon is round to be true is for one of the correlates (the Moon) to instantiate the other (the property of roundness). However, this account will only work for simple or atomic propositions. It doesn't tell us what to do with logically complex propositions, like negations or disjunctions. In addition, it requires us to assume that all atomic propositions have a subject-predicate or individual-property structure, and this might be disputed. Classical Truthmaker Theory doesn't have to make any such assumptions about the internal structure of propositions.

  If the Correspondence Theory of Truth is correct, and if it holds for all propositions, and if the correspondence relation is a real relation that unifies all the cases of truth, then Classical Truthmaker Theory seems inescapable. However, many defenders of truthmaker theory argue that the theory has nothing to do with truth! (For example, see Horwich 1998 and Lewis 2001.) As the following four points will make clear, there are arguments for something like truthmaker theory that do not depend on the Correspondence Theory of Truth. In addition, there is a sixth argument for a specific type of Classical Truthmaker Theory, namely, Atomic Truthmaker Theory. Atomic Truthmaker Theory can provide a grounding for the distinction between fundamental and non-fundamental truths.

  2. Without truthmakers we would be unable to discern whether theories differ with respect to what they say about the world. Theories describe at least part of the world. We can understand the claim that theories describe the world by noting that a theory is true if and only if the world is a certain way, that is, if and only if certain things exist, have certain intrinsic features, and stand in certain relations to other things. Clearly, different theories can describe the world differently. But equally, different theories can describe the world similarly by using different sets of fundamental terminology. Theories can be formulated, not just in two different languages, but by means of two different sets of propositions, with two different sets of fundamental concepts. For example, geometry can be formulated in terms of fundamental points, but equivalently by taking spheres or other solids as fundamental. This is a sort of cognitive or notional difference between the theories, as the two theories describe the world in equivalent ways. Though this may seem insubstantial, we can describe cases that don't seem quite so trivial.