4. Accounting for possibility. As we will see in Chapter 15, Atomic Truthmaker Theory is quite compatible with Logical Atomism's account of possibility.
5. Causation. If we adopt Atomic Truthmaker Theory, and we suppose that it is truthmakers (and only truthmakers) that can serve as causes and effects, this will have significant effect upon our conception of causation. In particular, it will entail that all causation is fundamentally positive. This will create a difficulty, as we shall see in Chapter 27, in accounting for negative causation, such as prevention or causation by omission.
6. Accounting for fundamental truths. It is natural to think, as we saw above, that some truths are more fundamental than others. For example, conjunctions usually depend for their truth on the truth of their parts (or conjuncts). Atomic Truthmaker Theory provides a simple account of which truths are fundamental: each fundamental truth corresponds to the existence of a single possible truthmaker. In other words, if a truth is fundamental, then it is made true by just one thing in the actual world, and, moreover, it is made true by the existence of that same thing in every world in which it is true. Suppose, for example, that we have a fundamental truth of the form ‘b is F’. According to Atomic Truthmaker Theory, this is made true by a single, simple truthmaker: b's F-ness or the fact that b is F. Moreover, this truth can be made true only by the existence of this same truthmaker. There is no possibility in which ‘b is F’ is true but b's F-ness does not exist. We can call any proposition that could be made true only by one possible truthmaker a fundamental proposition.
Next, we have those truths that are negations of fundamental propositions. Suppose that b is not in fact F, but that ‘b is F’ would be a fundamental truth if it were true at all. In that case, the proposition ‘b is not F’ is true by virtue of the non-existence of the appropriate truthmaker for the more basic proposition that b is F.
Finally, all other truths derive their truth from the fundamental truths and from the true negations of fundamental propositions. For example, a disjunction of two more fundamental propositions p and q would be true by deriving its truth from that of p or of q or both. Such disjunctive truths would not be fundamental, since there is no one possible truthmaker that must exist in order for such propositions to be true: it is enough if one of a range of possible truthmakers exists. Similarly, if the predicate ‘F’ is definable as ‘G and H’, then the proposition that ‘b is F’ would, if true, derive its truth from the two more fundamental truths (viz., that b is G and H). We take up this idea of fundamentality in more detail in the next chapter.
2.5.2 Spectral Truthmaker Theory
We are now in a position to see a serious problem for an important motivation we had for believing in truthmakers. Recall the first argument for truthmakers, from the Correspondence Theory of Truth. That argument implicitly assumed that the things to which propositions correspond are facts.12 This is how we guaranteed that clause (i) of Def D2.1 (the definition of a truthmaker) was satisfied by the things to which propositions correspond. How could, we asked rhetorically, the fact that grass is green exist without the proposition that grass is green's being true? What this assumes is that facts (in this sense) are among the metaphysically fundamental bits of the world. But we have seen no reason to think this is true!
Suppose, for example, that it's just the grass that's among the metaphysically fundamental things. At rock bottom, metaphysically, you've just got the grass with its features. In that case, the fundamental things of the world might not satisfy clause (i) of the definition of a truthmaker. Grass might not have been green, so the sheer existence of the grass is not sufficient to make true the proposition that grass is green. There is another requirement: the grass must also be a certain way.
2.1A.1T Non-Classical Truthmaker Theory. Propositions are made true by the way things are in the world, but there are no classical truthmakers.
2.1A.1A No Truthmakers. Truths have no truthmakers, classical or otherwise.
If we give up the idea that is is just the existence or non-existence of certain things that make propositions true and false—an assumption we might call Binarity—but we want to hold on to as much of Truthmaker Theory as possible, we end up with something we call ‘Spectral Truthmaker Theory’. This name is meant to denote the fact that the fundamental parameters form a spectrum of possible values, not simply a binary choice between existence or non-existence. A theory of this kind has been proposed by Josh Parsons (1999). Parsons argues that the mere existence of a truthmaker is not sufficient to entail the truth of the corresponding proposition. Instead, we should think of a proposition's truthmaker as an entity of such a kind that its being intrinsically the way it is, is sufficient for the truth of the proposition. That is, it is both the existence and the actual intrinsic character of the fundamental thing that, taken together, ground the truth of the proposition.
2.1A.1T.1 Spectral Truthmaker Theory. Every fundamental atomic truth is made true by something's existing and being a certain way intrinsically.
It is the italicized phrase that distinguishes Spectral Truthmaker Theory from Classical Truthmaker Theory. A classical truthmaker makes a proposition true simply by existing. In contrast, a spectral truthmaker makes a proposition true both by existing and by having a certain intrinsic character. So, for example, a blade B of grass cannot be a classical truthmaker for the proposition that B is green, since B could exist without being green (it could be brown, for example). However, blade B could be a spectral truthmaker for this same proposition, since whether B is green or not is intrinsic to B.
We can illustrate the advantage of Spectral Truthmaker Theory over Classical Truthmaker Theory by considering the phenomenon of determinates and determinables. Determinable properties are properties that come in different kinds, and those different kinds are a determinable's determinates. For example, the property of being a certain temperature is a determinable property, with determinates like the properties of being 10° Celcius, of being 30° Celcius, and so on. Similarly, the property of being red is a determinable property, with determinates like the properties of being scarlet, of being burgundy, and so on. If an entity has a determinable property (e.g., temperature), then it must have exactly one corresponding determinate (a specific value of the temperature variable, like 10° C). It cannot have two determinate temperatures or none at all. On Classical Truthmaker Theory, the independence of temperature from other parameters or determinables is explained by the existence of a separate truthmaker for a thing's temperature, an accident or trope of temperature. However, Classical Truthmaker Theory predicts that each specific temperature is independent of every other. If body B has a truthmaker for its having a temperature of 10°, it should be possible for it to have simultaneously a truthmaker for the determinate temperature of 15°. The impossibility of having two determinate temperatures at the same time is, relative to Classical Truthmaker Theory, a brute or unexplained necessity.
In contrast, Spectral Truthmaker Theory does not over-generate interdependencies, since it doesn't posit distinct and separate truthmakers for each determinate property. Instead, it entails the existence of just one possible truthmaker for each parameter of each entity, with the specific or determinate property corresponding to some internal state of that truthmaker (not simply to its existence). This gives us no reason to expect it to be possible for one thing to have two determinate temperatures at once, since there is no reason to think that the internal state of one truthmaker could correspond to two different temperatures.
The main disadvantage for Spectral Truthmaker Theory, as compared with Classical Truthmaker Theory, is that it does not provide a unified definition of the correspondence relation. Consequently, it isn't clear that correspondence is a real relation on Spectral Truthmaker Theory, a relation corresponding to a real similarity between distinct cases of truth. Consider the propositions that blade B is green and that the Moon is round. The spectral truthmaker of the first proposition is the blade B, and the spectral truthmaker
of the second is the Moon. What it is for the first proposition to be true is for its truthmaker to be green, and what it is for the second to be true is for its truthmaker to be round. Thus, truth for the first proposition is something entirely different from truth for the second proposition. This would seem to support a deflationist view of truth.
If we accept Spectral Truthmaker Theory, we can ask how many truthmakers we need, given a set of fundamental truths. Could there be just one Big Truthmaker that is responsible for making true all of the truths of the world? This possibility runs contrary to the underlying spirit of all truthmaker theory, which is to ground truths in relevant parts of reality. At the very least, it seems that if there are two different, equally fundamental properties being predicated in two truths, those truths ought to have distinct truthmakers:
Principle of Truth (PTruth) 1 One Truthmaker per Fundamental Property. If p is the true predication of a fundamental property P to x1 through xn, and q is the true predication of a different fundamental property Q to the same things x1 through xn, then p and q have distinct truthmakers.
(One Truthmaker per Fundamental Property will become important in later chapters.)
2.5.3 Truth Supervenes on Being
There is another, more radical way of replacing individual truthmaking with plural or joint truthmaking. This view drops the truthmaking relation entirely and makes use instead of the idea of weak supervenience introduced above. Truth Supervenes on Being (TSB) is such a view. TSB claims that there is a special class of ultimately real or fundamental entities E and a special class of perfectly natural or fundamental properties and relations N, and that the fundamental propositions are those atomic predications involving only fundamental entities and natural relations.
2.1A.1A.1T Truth Supervenes on Being (TSB). The property of being true weakly supervenes on the property of being a truth about what things exist (and don't exist) and about exactly which natural properties they have and which natural relations they stand in.
2.1A.1A.1A Truth does not supervene on being.
The main difference between Spectral Truthmaker Theory and TSB is that Spectral Truthmaker Theory is committed to One Truthmaker per Fundamental Property while TSB is not. Suppose that the various shapes and colors are natural properties and that we have a ball that is spherical and red. For Spectral Truthmaker Theory, there must be two entities, which we can call the ball's ‘shape’ and its ‘color’, one of which is a spectral truthmaker for the ball's being circular and the second of which is a spectral truthmaker for the ball's being red. TSB has no such commitment. The ball's being red and its being circular must both supervene on how things are, but there is no implication that the things involved include such finely individuated things as the ball's shape and its color. TSB theorists can simply suppose that the things involved include only the ball itself, which, by being a certain way, ensures that both propositions are true.
We've seen what TSB permits. What sort of things does it forbid? TSB prohibits any fundamental truth that does not involve actually existing things. Consider, for example, Bucephalus, the horse owned by Alexander the Great. Bucephalus no longer exists, having long since died. If we suppose that the only things that exist are things that exist now, that is, assuming Presentism, then we would have to say that nothing is Alexander's horse. Consider now (19):
(19) Bucephalus was fierce.
If Bucephalus does not exist, TSB theorists must deny that (19) is a fundamental truth. They must say one of two things about (19). Either it is in fact true that Bucephalus exists (even though it is not now alive)—a denial of Presentism—or the truth of (19) must consist in facts about other existing things, such as memories, records, or other traces of Bucephalus. The truth of (19) cannot simply float free of all the facts about existing things and their natural properties and relations. Since the second option is implausible (it is hard to believe that a fact like (19) is really made true by facts about remains and records), TSB is often taken to be incompatible with Presentism (an issue we will take up again when we consider theories of time in Chapters 19–21).
Here's another illustration of what TSB forbids, taken from Gilbert Ryle's theory of behavioral dispositions (Ryle 1949). According to Ryle, behavioral dispositions correspond to conditionals such as (20):
(20) If Roy is frustrated, he will curse loudly.
According to Ryle, conditionals like (20) can be true, even though there is nothing further to be said about why they are true or what makes them true. That is, there might be nothing about Roy's mind, body, or brain that could be expressed categorically (without making use of conditional statements) that is sufficient to guarantee the truth of (20): nothing about Roy's current memories, moods, feelings, thoughts, or neurochemistry. Assuming that conditional dispositions do not count as natural properties, then Ryle's theory entails that (20) can be true even though its truth does not supervene on any natural properties of Roy or any other things in Roy's environment. This violates the constraints of TSB.
The bite of TSB depends on the content of the idea of natural properties and relations. If just any relation is natural, then TSB ceases to be a substantive doctrine. Suppose, for example, that there were some truth p that intuitively doesn't supervene or depend upon being. If we were to count the property denoted by ‘being an x such that p’ as natural, then any proposition p whatsoever could easily satisfy the constraints of TSB: in every world in which p is true, if at least one thing exists in that world, then that thing has this property of being something such that p is true (or, in other words, being something that coexists with the truth of p). In the case of (20), suppose we thought that the property of being such that Bucephalus once was fierce was a natural property of presently existing things, like the Moon or the Eiffel Tower. On that assumption, TSB and Presentism would be compatible, after all. The same result would ensue if we treated as natural such properties as ‘are some atoms that once composed a fierce horse known as “Bucephalus”’. If that relation among atoms is natural, then the truth of (20) supervenes on this relation's holding between some currently existing atoms. So, a serious defender of TSB should not count such bizarre properties as natural.
Let's go back one more time to the six arguments for truthmaker theory and see which of them provides some support for TSB (as we did above for Atomic Truthmaker Theory).
1. Catching metaphysical cheaters. Catching metaphysical cheaters is the principal motivation for TSB. As we've seen, some supposed “cheaters” violate TSB. However, as we saw in the discussion of Atomic Truthmaker Theory, it is unclear that either the Atomic Truthmaker Theorist or TSB theorists can consistently apply the TSB standard, given that both allow negative truths to be ungrounded by any existent thing.
2. The Correspondence Theory of Truth. TSB Theorists can claim, with some plausibility, that TSB captures something of our common sense intuition that truths “correspond” to reality. TSB theorists cash out this correspondence in terms of difference-making: in order for a true proposition to be false, or a false proposition to be true, different things would have to exist, or existing things would have to stand in different natural relations to one another. A true proposition is one that corresponds with how things in general are.
3. Distinguishing ontological and ideological differences between theories. On TSB, two theories will be merely ideologically different when there is no difference between the theories with respect to what exists and what natural properties those things have and what natural relations they stand in. Thus, TSB can be used to distinguish ontological and ideological differences between theories.
4. Accounting for possibility.
5. Accounting for the relata of causation.
6. Accounting for fundamental truths. We'll lump the final three arguments together, since TSB theorists cannot appeal to any of them. Without truthmakers, they have no basis for a combinatorial theory of possibility. Without truthmakers, they have no special account to provide for the relata
of causation nor can they account for the difference between fundamental and derived truths.
Thus, TSB theorists must rely on one motivation, a sense that the TSB constraint is needed to take seriously the intuition that truths “correspond” to reality.
2.6 Conclusion and Preview
Recall that there were five initial arguments for truthmaker theory: (1) the appeal to the idea of correspondence, (2) distinguishing between ideological and ontological differences, (3) catching metaphysical “cheaters,” (4) accounting for metaphysical possibility, and (5) providing the relata for the causal relation. Along the way, we added a problem for Maximalism that motivated Atomic Truthmaker Theory, namely, identifying the fundamental truths. We've considered four versions of truthmaker theory: Truthmaker Maximalism, Atomic Truthmaker Theory, Spectral Truthmaker Theory, and Truth Supervenes on Being. Table 2.1 summarizes our results.
Table 2.1 Comparing Truthmaker Theories
Advantages Truthmaker Maximalism Atomic Truthmaker Theory Spectral Truthmaker Theory Truth Supervenes on Being
1. Correspondence Theory of Truth Yes Yes, but only for atomic truths Yes, for atomic sentences, given instantiation Yes, but only in terms of difference- making
2. Distinguishing theories Yes Yes Yes Yes
The Atlas of Reality Page 8