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  Truthmakers offer a way to understand the difference between pairs of theories that describe the world similarly and pairs of theories that describe the world differently. Two theories are ontologically distinct when they describe the world differently, and two theories are merely ideologically distinct when they describe the world similarly using different terminology. Using truthmakers, we can give a clear analysis of these notions. Two theories are ontologically distinct if and only if there is a set of possible truthmakers that would make one theory true and the other false. Two theories are merely ideologically distinct if and only if any set of possible truthmakers that would make one theory true also would make the other true.

  Suppose one theory uses the concept bachelor as one of its fundamental notions, and the other contains only the complex concept unmarried male adult. The first theory might entail that there are bachelors, while the second theory could not have any such implication (although it might imply that there are unmarried male adults). If every truthmaker for the proposition that there are unmarried male adults were also a truthmaker for the proposition that there are bachelors, then the two theories would differ only ideologically, not ontologically.

  To take another example, suppose that one theory includes the implication that there are crowds, while a second refers only to people and their spatial relationships. Is this difference ontological or merely ideological? The correct answer to the question would depend on whether a truthmaker for the proposition that there is a crowd in the plaza must include some single entity corresponding to the crowd or could the truthmaker merely consist of a large number of individual people in close proximity in the plaza.

  Is there any way to tell whether two theories differ ontologically without appealing to truthmakers? We might think that we could do this by simply asking whether it is possible for one of the theories to be false while the other is true. If we can construct a possible scenario in which one theory would be true while the other would be false, then we would know that the two theories were ontologically distinct, while if we could not construct such a scenario, we might reasonably conclude that the difference is merely ideological or verbal. This is the modal method of testing for ontological difference. It seems that we can employ the modal method without making any reference to truthmakers.

  Suppose that theory A says that Austin is a part of Texas and that Texas is a part of the United States. Theory B says only that Austin is a part of the United States; theory B says nothing about the state in which Austin is located. We can easily show that there is an ontological difference between the two. Theory A has more information about the world than theory B because we can imagine a possible situation in which everyone would agree that theory B is true while theory A is false, like a situation in which Austin is made part of Oklahoma.

  However, the modal method will not always give the right answer. For example, it won't work if we are considering two ontologically distinct theories about mathematical entities like numbers. Numbers do not and cannot change, so it makes no sense to talk about different possible scenarios involving them. The numbers 3 and 2 exist in every scenario, and 3 is greater than 2 in every scenario. Nonetheless, philosophers have proposed what seem to be clearly ontologically different theories about the numbers. For example, one might propose that numbers are really sets: the number zero is the empty set, and the number 1 is the set containing just the empty set, and so on. Another philosopher might disagree, arguing that numbers are not sets but are a quite disjoint class of mathematical objects. This is clearly an ontological difference, since the two theories disagree about what the numbers are. But there are no possible, alternative scenarios involving the numbers that we could use to show that the two theories carry different information about the world. If the number zero is identical to the empty set, then it would be so in every possible situation, and if it isn't identical to that set, it would be non-identical to it in every situation. So, each theory is (by the lights of its proponents) true in every possible situation. Thus, the modal method fails.

  In contrast, truthmakers can be used to show that the two theories of the numbers are ontologically different. What is the truthmaker for the proposition that zero exists? The first theory entails that the truthmaker is the empty set, while the proponent of the second theory will deny this.

  Another case in which the modal method will fail involves theories about supervenient facts. G.E. Moore (1903a) proposed that moral goodness is a special, non-natural quality. To say that a person or an action has this quality is to assert the existence of a moral fact, and such moral facts are distinct from all natural or non-moral facts (like facts about psychology or physiology). Nonetheless, Moore believed that moral qualities like goodness supervene on non-moral qualities, in such a way that it is impossible for two situations to differ morally without some non-moral difference. Now consider two possible theories, M and N. M is a theory about all of the moral and non-moral facts in the world. N contains exactly the same non-moral facts as M, but it contains absolutely nothing about moral facts. It seems clear that there is an ontological difference between the two theories. According to M, the ontology of the world is richer than it is according to N. However, given Moore's claim that moral facts supervene on non-moral facts, there is no possible situation in which N is true but M is not, and obviously there is no possible situation in which M is true and N is not (since M contains N). Thus, the modal method fails.

  In contrast, Truthmaker Theory can be used to demonstrate the ontological difference between M and N. For M to be true, there must be some moral truthmakers, containing moral qualities, while no such moral truthmakers are needed to make N true.

  It is difficult to mark the difference between ontologically distinct theories and theories that differ only ideologically without appealing to truthmakers. This gives us some reason to think that there are truthmakers, since it is clear that we can tell whether theories are ontologically distinct or are merely ideologically distinct.

  3. Truthmaker Theory is needed to rule out metaphysical “cheaters.” Some philosophers have argued that without truthmakers we have no way to combat theories which help themselves to putative truths without wanting to say anything metaphysically serious about the bits of the world to which those truths correspond.

  (See Armstrong (1968: 85), and Sider (2001). For discussion, see Merricks (2007).) Metaphysical “cheaters” are people who appeal to such theories, theories that appear to capture some truth or class of truths without a serious metaphysical undergirding.

  Here is an example of putative metaphysical cheating from the metaphysics of time (see Chapters 19–21 for more): Presentism (20.2T.4) is (roughly) the view that there are no objects that do not exist at the present moment. Eternalism (20.2A.1T), on the other hand, is (again, roughly) the view that there is nothing ontologically special about the present moment; all moments in time are equally real, and objects that exist only in the past or future really do exist. Presentists and Eternalists agree, for example, that dinosaurs don't exist now, but they disagree about whether dinosaurs exist. Eternalists think they do. Presentists think they don't.

  A notorious problem for Presentists is making sense of the truth of ordinary, uncontroversially true sentences like ‘Dinosaurs existed in the past’. This sentence seems to require the existence of some things—namely, the dinosaurs—that exist only in the past. But if there are these things, the dinosaurs, then dinosaurs exist (even if not in the present)! Some Presentists, in the face of this sort of problem, make something like this speech:

  The best way to understand the sentence in question is to say that there are irreducible tense operators in English. To say, “Dinosaurs existed in the past” is just to say, “PAST(Dinosaurs exist),” where PAST(p) is true if and only if it was the case that p. But the thing about the PAST operator is that one is not ontologically committed to the existence of things that fall under its scope. It's like a belief operator in this way. If one allows that a person c
an believe that the Fountain of Youth exists, it doesn't thereby follow that one must believe there is this thing, the Fountain of Youth! Likewise, PAST (Dinosaurs exist) doesn't commit one to the existence of dinosaurs.

  Suppose, however, that we're committed to the Correspondence Theory of Truth. Presentists have told us nothing about how it is that the sentence, ‘Dinosaurs existed in the past’, corresponds to reality. And it's hard to see how they could, given that there is no dinosaur and no past to correspond to if Presentism is true. Some argue, on this basis, that unless Presentists supply a truthmaker for this claim, a really existent thing that grounds the truth of the claim, then they are simply cheating. Truthmaker Theory gives us a way to catch metaphysical cheaters by demanding that theorists specify the truthmakers for claims they are committed to the truth of.

  4. Truthmaker Theory can provide an explanation of possible truth. Ludwig Wittgen- stein, in his Tractatus Logico-Philosophicus (Wittgenstein 1921/1974), employed truthmakers (in the form of states of affairs) as a way of explaining what it is for propositions to be possibly true. Suppose that each of the truthmakers is utterly separate and independent from the others. If so, it would seem natural to think that the existence or non-existence of each truthmaker has nothing to do with the existence or non-existence of the others. We could assign the values ‘Exists’ or ‘Does not exist’ to each possible truthmaker without reference to the assignment of these same values to the others. Consequently, every permutation of such values would represent a real possibility. This Tractarian account of possibility is sometimes called ‘Combinatorialism’ (15.3T), since each combination of logical atoms constitutes a real possibility (see Section 15.2.1.1).

  5. Truthmakers as causes and effects. Some truths causally explain other truths. For example, that there were sectional differences in the United States over slavery is a cause of the truth that the Civil War occurred in the 1860s. Causation seems to be non-circular: facts don't causally explain themselves. One account of causation takes it to be a relation of a certain kind between truthmakers. When the truthmaker of the proposition that p causes the truthmaker of the proposition that q, then the truth of p is a causal explanation of the truth that q. We'll look at this account of causation in Chapter 27, on the relata of causation.

  2.3 The Challenge of Deflationism

  One of the fundamental motivations for truthmaker theory of any form is, as we have seen, the Correspondence Theory of Truth. But it is not clear that we really need the Correspondence Theory of Truth. Many philosophers defend a minimal or deflationary conception of truth, in which the predicate “is true” is explicated entirely in terms of Tarski's truth-schema (see Principle of Truth 2), first developed by the Polish logician, Alfred Tarski (1901–1983):

  (3) ‘Snow is white’ is true if and only if snow is white.

  (4) ‘Grass is green’ is true if and only if grass is green.

  According to such deflationary accounts (see Ramsey 1927, Grover 1992, Horwich 1998), to say that some sentence S is true is simply to assert S itself indirectly, or by proxy. For example, we might say that everything Einstein said about relativity was true. To do so is not to ascribe some sort of property to Einstein's statements or to claim that these statements correspond somehow to reality or the facts. It is simply to endorse those statements, to commit oneself as if one had asserted those very things.

  Importantly, deflationists are anti-realists only about one thing: the existence of a real property of truth. Deflationists can be as realist as one might like about other things, like the past, unobservable physical entities, consciousness, moral facts, and so on. Equally, deflationists can be anti-realist about any of those things. A commitment to deflationism involves only a commitment to the unreality of a metaphysically special property of truth and of metaphysically fundamental facts involving the truth of propositions. Typically, deflationists embrace classical logic, including the Law of Excluded Middle (for all p, either p or not-p). Thus, deflationists can accept that reality outruns our understanding or knowledge of it. They simply deny that we should flesh out our “robust sense of reality” in terms of a special property of truth.

  The specter of deflationism is clearly a serious worry for advocates of Truthmaker Theory, given that the Correspondence Theory of Truth is such a crucial motivation for believing in truthmakers. Is there reason to conclude that deflationism is false?

  The form of deflationism that is relevant to truthmaker theory is a metaphysical thesis: the thesis that there is no real property of truth (or of falsity). For deflationists, true propositions have nothing in common with one another.7 They are as dissimilar to one another as the various parts of reality are. The truth that snow is white is as dissimilar to the truth that black holes are massive as the whiteness of snow is dissimilar to the massiveness of black holes. Deflationists deny that true propositions bear any resemblance to one another just by being true. Each truth is true in its own unique and incomparable way. The only thing that true propositions have in common is that they all bear the name “true” by virtue of the relevant pair of instances of the Tarski schema. Consequently, deflationists must deny that there is any property of truth (or relation of truthmaking) in any metaphysically robust sense. To use David Lewis's (1983) term, deflationists deny that truth is a natural property. The thinness of deflationist truth disqualifies truth from playing certain kinds of explanatory roles. Truth as such cannot figure (for deflationists) in any causal or metaphysical explanation, nor can it appear in a causal law or other law of nature.

  There have been five major objections to deflationism in this metaphysical sense.

  1. The methodology of science requires truth as a natural property. In science and other forms of inquiry, we are always trying to find methods, practices, and authorities that are reliable sources of information. For example, we have come to accept that many of the methods of established science are reliable in the sense that they have a high probability of generating true results (or, at the very least, a probability of doing so that is greater than mere chance). We take our past experience with such methods as providing good grounds for expecting future applications of the method to be similarly reliable in generating truths. We take our experience with science to provide us with “projectible” generalizations, to use the term introduced by Nelson Goodman (1954).

  A projectible generalization must, as Goodman pointed out, make use of projectible predicates. We can make inferences about the future using predicates like “green” but not bizarrely gerrymandered predicates like Goodman's “grue” (a thing is “grue” if it has or will have been first observed before 2100 AD and is green, or will not be observed until 2100 AD and is blue). Lewis (1983) has argued that projectible predicates are those that signify natural properties. Since deflationists deny that truth is natural, they must deny that we can make projectible generalizations about truth, including generalizations about the relative reliability of various sources and methods.

  2. The pursuit of truth is constitutive of belief and inquiry. Many philosophers have recognized that the pursuit of the truth is a norm for certain kinds of cognition and uses of language (Williams 1973, Dummett 1980). We are supposed to aim at truth when we make assertions, form beliefs or decide upon methods of inquiry. Deflationism is consistent with recognizing the normative character of truth, since it isn't obvious that a norm must make use only of natural properties. However, it seems that the pursuit of truth is a special kind of norm: a constitutive or essential norm. It is of the very essence of assertion and belief that they aim at truth. Acts of belief that have nothing to do with pursuit of truth seem to be a metaphysical impossibility. It seems that the property of truth is partly constitutive of our powers to believe and to assert things. In other words, the property of pursuing the truth is a part or constituent of the power of believing, and the property of truth is a constituent of the pursuit of the truth.

  Deflationists may reply that social practices can be constituted by n
orms that make use of non-natural properties, like truth. There is no limit to how complex socially constructed norms can be. Consider, for example, fantastically complicated games like cricket or baseball. Why couldn't belief and assertion also be constituted by such complex norms, norms that apply each instance of the Tarski schema to our practices?

  Truthmaker Theorists can reply that belief and assertion are themselves fundamental and natural functions, not wholly created by arbitrary conventions. Conventions can vary widely from one social context to another, but we would expect to find belief and assertion in a wide range of actual and counterfactual situations, even situations involving non-human species. It seems reasonable to suppose that such natural functions are constituted by natural norms, norms involving simple, real properties, not grue-like constructions.