On ways of being true

There are many ways for truths to be true. How should we understand that idea? One is that there are different kinds of truth: the ways are different truth-like properties. Another understanding is that a truth can be made true in different ways, by different kinds of entities. The former understanding supports alethic pluralism. But the latter can be understood as a kind of monism: truth is the existential property of having some truthmaker or other. On this view, the differences reside in how a truth is made true, but not in its being true. I’ll discuss how these two understandings differ and what the potential advantages of the latter idea might be.


Introduction
All theories of truth face problems. At some point, you begin to suspect this isn't just because they're philosophical theories (and so of course they have problems). Certain theories seem inherently better suited to some areas of discourse than others. Truths about the shape, size, and hardness of this Niels Møller chair seem well-accounted for by a broadly correspondence-style approach. These truths are 'out there', more or less independently of us. But when we turn to its aesthetic qualities-whether a model 77 looks better than this model 71, for example-the truth seems far more about us, collectively, and the kinds of judgements we make about style. If such facts are not 'out there', then how is a correspondence-style theory to account for such truths?
It seems that no traditional, substantial theory of truth works well across all such domains of discourse. This has become known as the scope problem (Lynch, 2004b(Lynch, , 2009Sher, 1998). Enter pluralism about truth (Wright, 1992(Wright, , 1996(Wright, , 2001(Wright, , 2003: there is not just one property of truth, but many. Each works within its own domain, but correspond to biological facts, for example, whereas moral sentences are true in some other way (perhaps, when they are superassertible).
[Throughout, I will speak of truth properties, whereas others talk of truth predicates or concepts. This reflects my concern with what truth is, not with analysis of the concept we in fact have. The concept might be utterly basic, or exhausted by a handful of a priori principles. But even if so, 'the question of which property or properties of propositions, or sentences, realize the concept can still sensibly be raised for every discourse in which truth has application' (Wright, 2001, p. 752).] According to Edwards (2018), predicates basically come in two kinds: those that are responsive to objective reality 'out there', and those that ngenerate parts of reality. Physical, chemical, and biological predicates fall into the former category; social, moral, and aesthetic into the latter. In general, sentences characterised by responsive predicates are apt for correspondence-truth, whereas sentences characterised by generative predicates are apt for some other kind of truth, such as superassertibility.
There may be many different specific truth-properties, corresponding to different domains of discourse. But, for present purposes, we might focus on just two domains: a 'heavyweight' one 'congenial to broadly realist thinking' (Wright, 2001, p. 752), in which there are mind-independent states of affairs, and a 'lightweight' one, in which (according to the pluralist) there are not. We might take discourse about medium-sized material objects as our example heavyweight domain and discourse about comedy as our example lightweight domain. (The 'heavyweight'/'lightweight' terminology is from (Pedersen & Wright, 2018). These are relative terms: domains, and the associated truth properties, may be more or less heavyweight, with traditional correspondencetruth being as heavy as it gets.) To each domain, the pluralist associates a truth property. We might take the truth-property for a heavyweight domain, truth heavy , to be the property of corresponding to a suitable mind-independent state of affairs. A lightweight truth property, truth light , might consist in coherence, or superassertibility, or something else entirely. Just what properties truth heavy and truth light are, and what features they possess, will not matter here; I assume only that they are not coextensive.
For Wright, a property counts as a truth-property by obeying a number of platitudes, including the T-scheme (Wright, 1992, p. 34), where the point is put in terms of truthpredicates; see also his (2001, p. 760, 2003, pp. 271-272). Where those platitudes are gives as schemas (or as universal generalisations over propositions), we must understand them in a domain-restricted way. For suppose that both truth heavy and truth light obey the unrestricted T-scheme, for any proposition A : We could then infer: (1) A is true heavy iff A is true light and so the supposedly different truth-properties would collapse (extensionally, at least). So this cannot be the proposal. Instead, each specific truth-property should obey a version of the T-scheme restricted to that property's domain of discourse: (T h ) is to be restricted to 'heavyweight' propositions (including about material objects) whereas (T l ) is to be restricted to 'lightweight' propositions (including about humour). Moreover, each proposition must belong to some such domain, so that some restricted T-scheme holds of it. This principle provides the guarantee that, for any proposition A , (2) A iff, for some truth-property T , A is T .

The problem of mixed truths
My overall aim is to show that we need not accept alethic pluralism, even if we accept much of the pluralist's analysis of how different domains of discourse give rise to truths. Nevertheless, we need a clear picture of the form pluralism should take. In this section, I will discuss a number of problems for pluralism, which I take to show that the moderate form of pluralism is preferable to the more radical version. Pluralism requires many of the principles governing truth (such as the T-scheme) to be restricted to a specific domain of discourse. The details of this idea are not always smooth. One issue concerns the relationship between truth and logical entailment, which (as usually understood) requires some property to be preserved from premises to conclusion. How then are we to understand an entailment when the premises and conclusion belong to different domains? In particular, if propositions A and B belong to different domains, how should we account for the inference from A to A ∨ B , or from A ∨ B and ¬B to A ?
The radical pluralist (on which no truth-property is applicable to every domain) must argue that each valid inference preserves some specific truth-property from premises to conclusion, although no truth-property is preserved in each valid inference. Moderate pluralists, by contrast, allow that there is some generic truth-property, which is possessed by a proposition whenever it possesses some specific truth-property. This generic truth-property is then well-poised to account for valid entailment. [ (Wright, 2013) discusses these options.] The radical view seems hard to maintain. Suppose that A and B belong to heavyweight and lightweight domains, respectively (for which true heavy and true light , respectively, are the only applicable truth-properties). Then the radical pluralist must see the inference from A to A ∨ B as preserving true heavy , and the inference from B to A ∨ B as preserving true light . Thus A ∨ B may be true in either way, either by being true heavy or by being true light . That in itself is not so surprising: in general we expect there to be (at least) two ways for a disjunction to be true.
The problem arises when we consider the domain to which A ∨ B belongs. If it is true heavy , it must belong to the heavyweight domain d h ; but equally, if it is true light , it must belong to the lightweight domain d l . And, crucially, domain-membership does not depend on whether the proposition in question is in fact true. Thus A ∨ B must belong to both domains, irrespective of its actual truth vale. It follows that A ∨ B is a proposition governed by both restricted T-schemas, (T h ) and (T l ). But given this, we may infer: Yet this is false. Suppose now that B is true but A is false. Then A ∨ B is true in virtue of B 's lightweight truth (by being superassertible, say), and not in virtue of corresponding to some mind-independent facts. For, by assumption, there is no fact that A (since A is false) and no mind-independent facts sufficient for B 's truth in the lightweight domain at all. So, in this case, A ∨ B is true light but not true heavy , contradicting (3).
A related problem concerns conjunctive propositions (Tappolet, 1997). Suppose again that A and B are from heavyweight and lightweight domains, respectively, and that are both true. Then presumably, A ∧ B possesses some distinct truthproperty, part-heavyweight and part-lightweight. Call this property T h+l . But since A ∧ B entails B , the radical view must hold that T h+l is preserved in the inference, and hence that B possesses T h+l , the part-heavyweight truth-property. But this is bizarre: we are supposing that B is from a lightweight domain, which might be as lightweight as they come. What business does a partly-heavyweight notion of truth have with such propositions? If heavyweight truth consists wholly in correspondence with mind-independent facts, then T h+l would consist partly in correspondence with mind-independent facts. But this cannot be so since, by assumption, there are no such facts in B 's domain.
These problems, of disjunctive and conjunctive propositions, are instances of the problem of mixed-domain propositions, a problem primarily for the radical pluralist. Cotnoir (2009) argues that these problems can be resolved without commitment to a generic truth-property. He takes ¬A to be true/false in whichever way A is false/true and that a disjunction A ∨ B is true in whichever ways A or B are individually. He also takes De Morgan equivalence to preserve domain, so that A ∧ B belongs to the same domains as ¬(¬A ∨¬B) (Cotnoir, 2009, p. 478). But then each of A ∨ B , ¬A ∨ ¬B , ¬(¬A ∨ ¬B) , and A ∧ B belong to all the domains to which either A or B belong, and so this view falls to the objection raised above for disjunctive propositions.
This problem runs deep for the alethic pluralist, for Cotnoir's domain preserving rules seem unavoidable. Even dropping the assumption (which I find plausible) that negation preserves domain will not avoid the issue. For surely double-negation must preserve domain: if negation takes a proposition from domain d to d * , a further negation must bring it back: d * * = d. So if A belongs to d, ¬A and hence ¬A∨¬B belong to d * . Then ¬(¬A ∨ ¬B ) and (by De Morgan) A ∧ B belong to d * * = d. The De Morgan principle seems unavoidable (indeed, it is highly plausible that ¬(¬A∨¬B ) and A ∧ B are the same proposition).
Pluralists can avoid these issues by accepting a generic truth-property, true g , in addition to the specific truth-properties. That is, they should be moderate, not radical, pluralists. [Wright (1992) and Edwards (2009) want to avoid this result, whereas it doesn't worry (Cotnoir, 2009).] A sentence possesses true g only in virtue of possessing some other truth-property. This move does not make the specific truth-properties dispensable. Pluralists may hold that logically complex propositions possess only true g (or f alse g ), and never any domain-specific truth-property. Atomic propositions (only) are generically true iff they have some specific truth property, so that generic truth (and falsity) 'bubble up' to complex propositions from their constituents in the usual way.
How should pluralists understand the relationship between specific and generic truth? One model is the familiar determinate/determinable relationship that holds between, e.g., being red and being scarlet. But that doesn't seem to be the correct reading here. For one thing, a truth may be both a truth-by-correspondence and superassertible (the truth that I'm alive, for example), whereas properties like being scarlet should exclude other determinates of the same determinable. Edwards (2018) describes the relationship on the model of winning, for which there are a number of 'winning-determining properties'. You can win by potting the black, by checkmating, and so on, depending on which game you're playing. Yet these seem to me to be ways of winning in much the way that being scarlet is a way of being red. Characteristic of Edwards's view is that generic truth is not ontologically derivative upon the specific truth properties. It is not the disjunction of them, for example. The generic property is more basic than any of its domain-specific determinates (2018, p. 155). Yet the domain-specific properties must all entail generic truth and so this view saddles us with necessary connections between (supposedly) wholly distinct entities. What explains this?
Edwards gestures towards conceptual norms governing truth (2018, p. 125), but this can't help if we're asking about a metaphysical relationship between properties. These worries would be overcome if truth were a disjunctive (either corresponding to a fact or being superassertible or …) or existential (being such that some domainspecific property applies) property. For then, the connection would be at bottom a logical one, explicable in virtue of the disjunctive or existential nature of that property. The disjunctive approach will build into the nature of generic truth the specific truthproperties which may ground it (saying, in effect, that to be true is either to correspond to a fact, or to be superassertible, or …) whereas the existential approach will not. On this basis I find the existential approach preferable to the disjunctive one, although there is not much in it.
So this is the option I recommend for pluralists: there is a generic truth property, which is the existential property of being true in some specific way. Only in this way can a moderate pluralist avoid the mystery of unexplained necessary connections between specific and generic truth properties. There is nothing wrong, metaphysically, with disjunctive or existential properties, and the view does not imply that the concept of truth is similarly disjunctive. One may take the concept of truth to be basic, for concepts need not run in lock-step with the underlying metaphysical reality.
I said previously that accepting a notion of generic truth does not undermine pluralism's key commitments. For, according to the pluralist, any explanation of why a proposition is true g must go via the possession of some specific truth-property or properties. Nevertheless, there is a sense in which accepting the existential notion of generic truth begins to undermine the original motivation for pluralism. That motivation is the scope problem (Sect. 1), the contention that no traditional, monistic theory of truth will work across all domains of discourse. Truths about chairs require a realismflavoured treatment, whereas truths about humour require a more anti-realist analysis. The additional assumption that gets us from here to pluralism is that any substantial truth-property will fall into one of these categories, realist or anti-realist. Yet existential generic truth falls into neither category. It does not care how a proposition comes to be true, but only that the proposition is true in some way, in virtue of possessing some specific truth-property.
This does not show that pluralism is inconsistent, of course, for pluralists cannot have generic truth without a plurality of specific truth-properties. But it does suggest a possible move: could there be a substantial, monistic property of truth which, like existential generic truth, can operate in both realist and anti-realist contexts, but which does not piggyback on more basic truth-properties? In the remainder, I will argue that having a truthmaker is one such property.

Fact pluralism and realism
It's sometimes said by philosophers that a theory of truth settles the question of realism: of whether the world exists independently of our knowledge, beliefs, or thoughts. And it's often said that a theory of truthmaking carries a commitment to realism. 'To demand truthmakers for particular truths is to accept a realist theory for these truths', says David Armstrong (2004, p. 5), for 'realism about the truth of a particular true proposition [is] the contention that its truth is determined by something that lies outside that proposition' (Armstrong, 2003, p. 12). He's not alone here. John Bigelow also feels that, without truthmaking, 'I find I have no adequate anchor to hold me from drifting onto the shoals of some sort of pragmatism or idealism' (Armstrong, 1988, p. 123). John Heil agrees that truthmaking is 'a central tenet of realism' (Heil, 2003, p. 61). If this association between truthmaking and realism is correct, then a theory of truth in terms of truthmaking will not avoid the scope problem.
(In saying this, I do not mean to endorse the scope problem as a genuine problem. Perhaps it is not; perhaps realism is tenable across the board. My aim here is not to settle this large issue, but rather to show that pluralism is not warranted even granting that there is something to the scope problem.) This association between truthmaking and realism is a mistake. As always, it depends on what one means by 'realism' and 'anti-realism'. As alethic pluralists set up the debate, the contrast is between those facts or states of affairs 'out there', independently of us, and those that are in some way up to us. The former counts as realist, the latter as anti-realist. On that use, Berkeley (1995) is a paradigm case of antirealism about material objects. They are, he says, no more than constructions from our perceptions. They're not 'out there' in the world, independently of our thinking about them, as we usually think they are. Does it follow that there are no facts about material objects, as Berkeley understands them? No! Mental events, including perceptions and constructions out of them, exist and they have properties of their own. So there are facts about Berkeley's material objects: mental facts, but facts nevertheless. Truths about material objects would be made true by facts about our perceptions. Berkeley's view, despite being idealist-as-you-like, should not be understood as denying the existence of facts about material objects.
Going in the opposite direction, one may hold a realist-as-you-like theory of some subject matter and yet deny that all truths need a truthmaker. It is probably the default view (although not one I share) that a true negative existential, 'there is no F', is true for lack of Fs, not because something else (an F-absence, or whatever) exists (Lewis, 2001). And that's so regardless of whether we're inclined to be realists about Fs. Questions over whether truths have or need truthmakers is orthogonal to the issue of realism. I agree with Jamin Asay: The realism/anti-realism debate does not consist in whether or not the truths of some domain have truthmakers, but rather what the nature or character is of those truthmakers. Simply having truthmakers is not sufficient for realism. (Asay, 2012, p. 378) I want to liberate talk of facts or states of affairs from realist associations. Jokes are things too: you can count them, compare them, and re-identify them over time. Whether something is a joke is largely up to us, but that doesn't detract from its existence. Jokes have properties, like being funny. Again, whether a joke is funny is largely up to us, but that isn't to say the property doesn't exist. Where there are things-having-properties, there are facts; and where there are facts, there are truths determined by them. What is characteristic of a discourse amenable to anti-realist analysis is not that there are no facts relevant to a statement's truth, but rather that the relevant facts are facts involving us.
Perhaps the concept of correspondence leads us astray in thinking about the relationship between facts and truth. When we think that two things correspond to one another, we imagine them as wholly distinct existences, 'out there', awaiting a judgement of correspondence. As pluralists are keen to remind us, it seems unlikely that there are facts of that kind about, say, humour. If there are facts about humour, there is likely a mutual determination between those facts and the judgements of truth we make concerning them. But the issue dissolves once we cut out the correspondence metaphor and put the idea simply in terms of the existence of facts. There is no reason why a true sentence can't be involved, mutually, in a fact, as cases like 'sentences exist' and 'some sentences are true' demonstrate.
So we can agree with the pluralist that facts about this chair's shape are different in their nature from facts about the chair's aesthetic value, or about humour. These facts are brought into the world in different ways. And, in this sense, the truths they relate to differ in their grounding. But acknowledging this does not require us to abandon a substantial monist notion of truth. We can instead think that truth requires just the existence of a relevant fact.
This view might be thought of as pluralism about facts, instead of pluralism about truth. But the senses of 'pluralism' involved are not exactly the same. Pluralism about truth is theoretically demanding. Pluralists have to partition discourses into discreet domains and come up with a theory of truth for each domain. Not so for the view I'm suggesting. There are different kinds of fact in roughly the way that there are different kinds of fruit: apples and oranges grow, look, and taste differently. But they aren't different kinds of thing, requiring wholly different scientific accounts. At a certain level of abstraction, what goes for apples goes for oranges. Similarly for facts and how they make truths true. We will give different accounts of a chair's hardness and of its beauty. But, abstracting from those specifics, the metaphysical account of those facts and the corresponding truths runs in parallel. So when I say pluralism about facts, I mean only that facts come in different flavours, involving us to a greater or lesser extent.
In particular, there's no 'mixed facts' worry with pluralism about facts, analogous to the 'mixed truths' problems of Sect. 3. A conjunctive fact (if there are such things) is just the existence of each conjunct fact (or the mereological sum of the two, if you like). Since there's no theoretical need to categorise facts for alethic purposes, we don't face the issue of what kind of fact a conjunctive fact is. The fact that the chair is both hard and beautiful is a fact with a part that's fixed purely by the world and a part that's fixed partly by us. Such facts, partly about the world and partly about us, are commonplace. The fact that you've got enough money for a coffee, for example, is partly about us, since it's partly about the existence of money. The key point is that a proposition doesn't care for its truth about categories of facts. All it wants is for certain facts to exist. It doesn't care what those facts are like, beyond their being the ones it wants.
In discussion, I'm often met with scepticism over facts about humour, fashion, and similar subjects. (The workshop for which this paper was written was one such occasion.) Go on then, tell us what these facts look like! And it's true, I am a little shifty on what facts of humour look like. But that's because I don't have a good account of humour to give. (And, I protest: I only signed up to give an account of truth.) Equally, I don't have good accounts of the origins of the cosmos, quantum gravity, or large cardinals. No one takes that as counting against talk of facts of cosmology, quantum physics, or set theory. You give me your best account of humour (or whatever), and I'll tell you what the facts look like, according to that theory.
Roughly speaking, a theory of humour will involve some combination of objective physical facts (sounds were made or marks were written) and facts about us: certain beliefs were held and certain responses were made, or perhaps would be made in certain circumstances. So long as there's facts about each component of the account, then there will be facts about humour. Let's flesh this out by looking at Crispin Wright's account of humour. Whilst I'm not myself convinced by this account, it has undeniably been influential amongst pluralists, so it will serve well as an illustrative example. He adopts a response dependent account, intended to capture the intuitive idea of a concept whose extension is constitutively sensitive to those of our verdicts which are delivered under what we conceive as the very best possible circumstances, rather than merely reflected by such verdicts. (Wright, 2003, p. 389) Such concepts-Euthyphronic in Wright's terminology-are specified by an appropriate biconditional of the form: (4) If conditions C are met of a subject S and utterance x, then: x is funny iff it seems to S that x is funny (1992, ch. 3 appendix; 2003, p. 388).
For the biconditional to be appropriate, it must satisfy various requirements. In particular, the conditions C must be specified in substantial, non-question-begging terms. The condition 'S is someone who finds all and only funny things funny', for example, will not do. Rather, C is intended to specify that 'normal' conditions obtain (or Wright's 'very best possible circumstances'): that S is not a maniac who will laugh at puppies being hurt, nor someone in the darkness of deep depression. Specifying such conditions is no easy task (hence my scepticism towards this kind of account), but that is the pluralist's worry, not mine. My point here is simply that if any such account can be given of humour, then we can use it to spell out what the facts of humour might look like. And since pluralists typically support some such account, they cannot thereby object to facts of humour. The fact that xis f unny will be a fact partly about conditions C being met (that is, about conditions being 'normal') and partly about S's mental state, that x seems funny to S. If physicalism holds, then all such facts will ultimately be grounded in physical facts.
In saying 'there are facts about humour', or about any subject matter, I do not mean to exclude indeterminacy amongst that subject matter. The claim is that there exist facts pertaining to the discourse in question, not that each question we may ask within that discourse has a determinate answer. Thinking of humour in Wright's terms, indeterminacy in whether some joke is funny may arise from indeterminacy in how it seems to our chosen subject S, but it may also arise from our selection of S. Perhaps our verdicts diverge, even in 'the very best possible circumstances'. Just how a response-dependent theory should handle such cases is not my concern here. My concern is, when a joke is funny, what makes it so? To what kind of fact can we appeal in this case? Wright's response-dependent account gives one possible answer: the facts are facts about how things seem to subjects in the best possible circumstances.
We are part of the world. To say that some fact is 'up to us'-by being about our mental states, reactions, or how things seem to us-is not to deny that it is determined by the world. It is determined by those aspects of microphysical reality that also determine our thoughts and behaviour. Anti-realist domains correspond to facts whose grounding story passes through us at some point. By this, I don't mean to say that all facts about us-about my height, or about what words I wrote yesterday, for exampleare in any way 'anti-realist'. Rather, the claim is that, at some point, 'objective' physical facts about what we say, believe, and do, combine and give rise to an important subcategory of socially constructed facts.
Neither am I claiming that we can reduce a concept like being funny to objective physical concepts. I do not even require a type-type determination between the physical and the funny. It is likely that very different physical setups will give rise to funniness. The conceptual analysis of humour stops with facts partly about us (about how things seem to us, for example). We can't analyse the concept without mentioning us and our potential reactions. But that line is compatible with facts of humour being determined, metaphysically, by diverse, substantial physical facts.

Truth as truthmaking
Now let's return to the discussion of truth. To be true, I'll argue, is to be made true by some entity. There exists a relation, truthmaking, and whenever it holds between some existing entity and a proposition, that proposition is true. Suppose further that the converse holds (for which I'll argue in Sect. 6). Then we would have identified a property which, of necessity, is coextensive with being true: the property of having a truthmaker. We can think of this property in terms of existential quantification into the first argument-place of the truthmaking relation: the property λx∃y(y truthmakes x). I claim numerical identity between these properties: (TaTM) Being true is numerically identical to having a truthmaker. This is the truth as truthmaking principle. Correspondingly for falsity: (FaFM) Being false is numerically identical to having a falsitymaker.
A falsitymaker for A is whatever truthmakes ¬A . So a full understanding of truthmaking thereby provides an account of falsitymaking and thereby of falsity.
The existential quantifier involved in being true is fully general: it doesn't care what kind of entity the truthmaker is. Wherever there's a quantifier, there can be restricted uses, as in 'there's no Vegemite in the cupboard', or 'there's no Vegemite in the shop'. These express different contents, to be sure, but not different kinds of existence. Vegemite exists in precisely the same way, whether in the cupboard, the shop, or elsewhere. Similarly, we might restrict the quantifier in 'is made true by some entity' to the domain of mind-independent states of affairs involving medium-sized dry goods. In that sense, we get a domain-specific truth property. But propositions with this property aren't true in a different way to truths in different domains, just as the Vegemite in the cupboard doesn't exist in a different way to the Vegemite in the shop. Rather, Vegemite exists; some in the cupboard, and some in the shop. Similarly, truths in different domains are true, simpliciter, some in one domain, some in the other.
This suggests that talking of 'domains of discourse' is a red herring when discussing truth. There are different kinds of entity out there: some spatiotemporal, some not; some causal, some not; some whose existence and qualitative profile is independent of us, some not. These distinctions concern the natures of those entities, not the property of truth that attaches to the true propositions about them. This thought echos the line Mark Sainsbury took in his review of Truth and Objectivity: even if it is one thing for 'this tree is an oak' to be true, another thing for 'burning live cats is cruel' to be true, and yet another for 'Buster Keaton is funnier than Charlie Chaplin' to be true, this should not lead us to suppose that 'true' is ambiguous; for we get a better explanation of the differences by alluding to the differences between trees, cruelty, and humor. (Sainsbury, 1996, p. 900) My argument for (TaTM) is an inference to best explanation. To be explained are certain features of truth, involving platitudes which regulate our use of the predicate 'is true' (Wright, 1992(Wright, , 2001. The best explanation of these features, I claim, is that being true is identical to having a truthmaker. The foremost such platitude is that A is true iff A, which is easily explained by (TaTM): A is true iff A has a truthmaker iff the state of affairs that A exists iff A.
Another platitude is that a truth A is true because A (1992, pp. 25-26, 2001, p. 747). Even Paul Horwich, clearly no friend of truthmaking, says It is indeed undeniable that whenever a proposition or an utterance is true, it is true because something in the world is a certain way-something typically external to the proposition or utterance. … Snow is white is true because snow is white. (Horwich, 1998, pp. 104-105) One prominent and highly plausible theory of 'because' is that it expresses some kind of metaphysically explanatory relation, or else expresses an operator whose content consists in metaphysical explanations (Schnieder, 2010(Schnieder, , 2011(Schnieder, , 2015. The puzzle here is that an explanation relates explanans to explanandum, on the model of a binary relation, whereas truth is a one-place property. We can easily explain this using (TaTM), for then, underlying the monadic existential property having a truthmaker is the binary relation-truthmakes-. An entity x stands in its first argument place when the proposition in the second argument place is true in virtue of x's existence. This 'in virtue of' is used canonically to express metaphysical explanations. We may replace 'is true in virtue of x's existence' with 'is true because x exists'. And there we have our explanation for the platitude, having assumed (TaTM).
Yet another platitude (this time a generalisation about truth, rather than a schema) is that truths depend on the ways the world is. The ways the world is are the states of affairs that exist, and truthmaking is a dependency relation in which a proposition's truth depends on the existence of some entity (typically, a state of affairs). So, given (TaTM), each truth will depend on the existence of some entity (typically, a state of affairs).
The final platitude I'll consider here is that the truths correspond to the facts. You might think that's too theoretically loaded to count as a platitude governing ordinary uses of 'is true'. But both Horwich and Wright take it to be one: [Horwich's theory] does not deny that truths do correspond-in some sense-to the facts; it acknowledges that statements owe their truth to the nature of reality. (Horwich, 1998, p. 104) The Correspondence Platitude-for a proposition to be true is for it to correspond to reality, accurately reflect how matters stand, "tell it like it is," etc. (Wright, 2001, p. 760) Given (TaTM), for each truth there exists a corresponding state of affairs. We might use 'the fact that A' to mean 'the state of affairs that A', or more neutrally to mean just that A is the case. Either way, we can reason as follows: A is true iff there exists a state of affairs that A iff A iff it's a fact that A. Generalising, the truths correspond to the facts.
Perhaps there are more truth-involving platitudes we could consider. Michael Lynch mentions these: 'truth is a worthy goal of inquiry' and 'truth is worth caring about for its own sake' (Lynch, 2004a, p. 19). Both are true, but I don't know whether to treat them as principles governing our use of 'is true'. If they are, then both principles are analytic and so anyone who denies them doesn't know what 'is true' means. If that were so, would Lynch need an entire book to defend them? I'm also unsure whether Lynch's platitudes essentially concern truth. I'm tempted to treat the use of 'truth' in 'truth is a worthy goal of inquiry' as a means of generalisation, comparable with 'everything Stephen Fry says is true'. For, strictly speaking, truth itself can't be the goal of an inquiry. An inquiry into whether A does not aim to bring about A's truth. Rather, the aim is knowledge that A is true (or at least, justified true beliefs concerning whether A). But that aim can be expressed without using 'truth': the goal of an enquiry into whether A is to gain knowledge whether A (or to believe A just in case A). We can generalise by universally quantifying over propositions. Or, more succinctly, we can say that the aim is to believe only what's true. All that we require to secure this use of 'truth' is that it satisfy the T-scheme, and we've already seen that (TaTM) underpins the T-scheme. So (TaTM) easily and straightforwardly explains the central platitudes governing truth. I doubt any competing identity hypothesis does so as smoothly. So, inferring to the best explanation secures (TaTM). Being true is numerically identical to having a truthmaker. That's the argument.
One might think that correspondence is a genuine rival to (TaTM), by identifying being true with having a corresponding state of affairs. But correspondence is a symmetrical relation: if x corresponds to y, then y corresponds to x. So this identity claim cannot hope to explain the asymmetrical platitudes, that A is true because A, and that truths depend on the ways the world is (but not vice versa). Moreover, we cannot in general infer from 'x corresponds to y' to 'x depends on y'. The sounds from the CD player and the grooves in the vinyl correspond but neither depends on the other. We could always build more into our notion of correspondence, insisting that it's asymmetric and many-many, not one-one. That doesn't sound like correspondence to me. In fact, it sounds an awful lot like truthmaking. If you want to insist on calling this relation 'correspondence', that's fine with me, but don't think that gives you a competitor to (TaTM).

Objections
Two immediate objections to (TaTM) loom large: first, that it is circular, and second, that it is not even extensionally correct, since there are truths without truthmakers.
The circularity objection is that, to understand 'truthmaker', we must first understand 'truth', and so we can't define 'truth' in terms of 'truthmaker'. It's indeed highly likely that an understanding of the term 'truthmaker' requires a previous grasp on truth, but (TaTM) is not offered as a conceptual analysis. It is a metaphysical account: there is a relation R between entities and propositions, on which a property, being true, depends. The nature of the dependence is existential, as set out by (TaTM). One could take R to be metaphysically primitive. That provides a coherent metaphysical account, even if we need to grasp the concept of truth in order to understand what relation R is.
Nevertheless, I am not content to leave the story there. Whilst we cannot do without primitives in our theorising, we should not use the claim 'it's a primitive!' as our getout-of-jail-free card. A metaphysics with truthmaking as a primitive is coherent but perhaps not so attractive. Fortunately, we can do better.
Many find it plausible to identify propositions with truth conditions, and these with sets of possible worlds. I do not fully agree. Sets of possible worlds divide contents too coarsely: equivalent propositions are identified and contradictions are banned (or else treated as the empty set). Yet when we discuss logic, maths, or metaphysics, we discuss matters necessarily true or necessarily false. It cannot be that all we are debating is whether 1 + 1 = 2 or 1 + 1 = 3. Propositions care not just about whether they are true or false (as sets-of-possible-worlds truth conditions do), but also about how they are true or false. Equivalent contents differ, not in their truth, but in the ways they come to be true or false. So I find it plausible to identify propositions with truthmaking conditions. If truth-conditions are given by sets of possible worlds, then truthmaker conditions are given by sets of possible (and perhaps even impossible) truthmakers . (Think of non-actual truthmakers in whichever way you think of nonactual worlds. The nod to potentially impossible truthmakers is to allow for various closure conditions on the space of truthmakers. The details are not important here.) On this view, as on the possible worlds account, propositions are sets of entities, and much of the theoretical machinery of the latter approach carries over. On the possible worlds view, a proposition p is true at a world w just in case w ∈ p and true (simpliciter) iff it has the actual world as a member. Similarly, on the truthmaker condition account, a proposition p is made true by a possible state s just in case s ∈ p.
(The sense of 'made true' used here is possibilist and non-factive: s would make p true, were s to obtain. This sense is analogous to 'truth at a world'.) A proposition p is true at a world w when s ∈ p for some state which is part of (or obtains at) world w; and p is actually true when s ∈ p for some actually obtaining state of affairs. In this way, if we can make good sense of propositions as truthmaker conditions (as I think we can), then we have the theoretical resources to define the truthmaking relation purely in terms of set-membership.
The second objection is that truthmaker maximalism, the view that all truths have a truthmaker, is false. Many hold this view on the grounds that true negative existentials, modal or counterfactual truths, or some other difficult class of truths, lack truthmakers. Showing that truthmakers do exist in each case, on a case-by-case basis, is painstaking work. Thankfully, a shorter response is available. An entity is logically possible when there is no contradiction in assuming it exists. And despite the many arguments against truthmaker maximalism-from Lewis (1992), Liggins (2008), Melia (2005), Molnar (2000), Schnieder (2006), and others-none claim logically inconsistency (in the weak sense just given). So let us suppose (P) For each true proposition p, a truthmaker for p is logically possible.
And let us also suppose, as part of the logic of truthmaking, that having a truthmaker is (i) factive and (ii) distributes over conjunction (so that conjuncts have truthmakers when their conjunction does), and that (iii) p has a truthmaker if the proposition that pistrue has a truthmaker.
Given these very weak assumptions we can, somewhat surprisingly, prove maximalism. [Here I draw on .] Assume for reductio that some proposition p is true but lacks a truthmaker. By (P), it is logically possible for that conjunction itself to have a truthmaker. That supposed possibility is a situation in which there is a truthmaker for the proposition that ( p is true and p lacks a truthmaker). That situation contains a truthmaker for the proposition that p is true and hence (by (iii)) contains a truthmaker for p. But by factivity, p lacks a truthmaker in that situation: contradiction. By reductio, every truth has a truthmaker.

Conclusion
Pluralists identify an important phenomenon: there are differences between truths in different domains of discourse. Pluralists understand this difference as a difference in their truth. But, I argued, we may instead understand the difference in terms of the different kinds of states of affairs that make those truths true. This understanding allows us to retain a monist conception of truth, in terms of the existence of a truthmaker (Sect. 5), and hence to avoid the various problems surrounding 'mixed' truths (Sect. 3). Understanding truth in terms of truthmaking does not involve a commitment to realism, for one may understand the truthmakers in a particular domain along anti-realist lines (Sect. 4).

Declarations
Conflict of interest There are no conflicts of interest.
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