This much is agreed: “x makes it true thatp” is a construction that signifies, if it signifiesanything at all, a relation borne to a truthbearer by something else,a truthmaker. But it isn’t generally agreed what that somethingelse might be, or what truthbearers are, or what the character mightbe of the relationship that holds, if it does, between them, or evenwhether such a relationship ever does hold. Indeed sometimesthere’s barely enough agreement amongst the parties to thetruthmaker dispute for them to be disagreeing about a common subjectmatter. This makes navigating the literature about truthmakers atreacherous undertaking but a necessary one because of thesignificance the debate about truthmakers bears for contemporarymetaphysics.

We can distinguish between the following questions that differentapproaches to truthmakers have been framed to answer:

1. What is it to be a truthmaker?
2. Which range, or ranges, of truths are eligible to be made true (ifany are)?
3. What kinds of entities are truthmakers?
4. What is the motivation for adopting a theory of truthmakers?
5. What are truthbearers?

These questions cannot be addressed in isolation from one another. Ourthinking about what it is to be a truthmaker will have knock-oneffects for how we answer the second and third questions. Our beliefsabout which truths have truthmakers will likely shape our answer tothe first and third. And the question of what our motivations are forpositing truthmakers in the first place will no doubt exert acontrolling influence upon our responses to the other questions.

The notion of a truthmaker cannot ultimately be understood inisolation from the notion of what it makes true, a truthbearer. Thisis understandable: metaphysicians are typically interested in whatthere is rather than representations thereof. But truthbearers arethe elephant in the room during these discussions.We cannot avoidtalking about them because what we think about truthbearers will haveconsequences for what we think about truthmakers. So we cannotpostpone indefinitely answering the fifth question. We’ll startwith the issue of what it is to be a truthmaker.

• 1. What is a Truthmaker?
  • 1.1 Truthmaking as Entailment
  • 1.2 Truthmaking as Necessitation
  • 1.3 Axiomatic Truthmaking
  • 1.4 TruthMaking as Grounding
• 2. Which range of truths are eligible to be made true (if any are)?
  • 2.1 Maximalism
  • 2.2 Truthmakers for Negative Truths
  • 2.3 Truthmakers for General Truths
  • 2.4 Optimalism
  • 2.5 Truth Supervenes Upon Being
• 3. What Motivates the Doctrine of Truthmakers?
  • 3.1 To catch a cheater
  • 3.2 Truth Depends on Being
  • 3.3 Truth: Correspondence and Deflationism
• Bibliography
• Academic Tools
• Other Internet Resources
• Related Entries

1. What is a Truthmaker?

Truthmakers are often introduced in the following terms:

(Virtue-T)

a truthmaker is that in virtue of which something is true

The sense in which a truthmaker “makes” something true issaid to be different from the causal sense in which, e.g., a pottermakes a pot. It is often added that the primary notion of atruthmaker is that of aminimal one: a truthmaker for atruthbearerp none of whose proper parts or constituents aretruthmakers forp. (Whether every proposition has a minimaltruthmaker is a further matter.) We are also cautioned that eventhough people often speak as if there is a unique truthmaker for eachtruth, it is usually the case that one truth is made true by manythings (collectively or severally).

Now whether (Virtue-T) provides a satisfactory elucidation oftruthmaking depends on whether we have a clear understanding of“in virtue of”. Some arguein virtue of is anunavoidable primitive whilst others are wary. But even if it isprimitive, we need to understand how the notions oftruthmaking andin virtue of are related to otherconcepts we grasp in order to establish their significance for us. Soto show that these are notions of sound theoretical standing it mustbe shown that they can at least be elucidated if not analysed in termsof notions that enjoy a life independently of the circle of notions towhichin virtue of andtruthmaking belong.

1.1 Truthmaking as Entailment

One proposal for improving upon (Virtue-T) appeals to thenotion ofentailment (Fox 1987: 189; Bigelow 1988:125–7):

(Entailment-T)

a truthmaker is a thing the very existence of which entails thatsomething is true.

Sox is a truthmaker for a truthp iffxexists and another representation that saysx exists entailsthe representation thatp. It is an attraction of thisprinciple that the key notion it deploys, namely entailment, isubiquitous, unavoidable and enjoys a rich life outsidephilosophy—both in ordinary life and in scientific andmathematical practice.

Unfortunately this account threatens to over-generate truthmakers fornecessary truths—at least if the notion of entailment it employsis classical. It’s a feature of this notion that anythingwhatsoever entails a necessary truthp. It follows as aspecial case of this that any claim that a given object exists mustentailp too. So it also follows—if(Entailment-T) is granted—that any object makes anynecessary truth true. But this runs counter to the belief that, e.g.,the leftovers in your refrigerator aren’t truthmakers for therepresentation that 2+2=4. Even worse, Restall has shown how toplausibly reason from (Entailment-T) to “truth-makermonism”: the doctrine that every truthmaker makes every truthtrue (whether necessary or contingent). Every claim of the formp ∨ ~p is a necessary truth. So every existingthings is a truthmaker for each instance of this form (seepreceding paragraph). Now letp be some arbitrary truth(grass is green) ands any truthmaker forp ∨~p (a particular ice floe in the Antarctic ocean). Now it isintuitively plausible that something makes a disjunction trueeither by making one disjunct trueor by making theother disjunct true (Mulligan, Simons, & Smith 1984: 316). This iswhat Restall calls “the disjunction thesis”. It followsfrom this thesis that eithers makesp true ors makes ~p true. Given thatp is true,neithers nor anything else makes it true that ~p.Sos (the ice floe) must make it true thatp (grassis green)! But sinces andp were chosen arbitrarilyit follows that all truthmakers are on a par, making true every truth(Restall 1996: 333–4).

The unacceptability of these results indicates that insofar as we havean intuitive grip upon the concept of a truthmaker it is constrainedby the requirement that a truthmaker for a truth must be relevant toor about what it represents as being the case. For example, the truthsof pure arithmetic are not about what’s at the back of yourrefrigerator; what’s there isn’t relevant to their beingtrue. So we’re constrained to judge that what’s therecannot be truthmakers for them. This suggests that operating at theback of our minds when we issue these snap judgements there must besomething like the principle:

(Relevance)

what makes something true must—in somesense—be what it is “about”.

Of course the notions of “about” and“relevance” are notoriously difficult to pin down (Goodman1961). And a speaker can know something is true without knowingeverything about what makes it true. Often it will require empiricalresearch to settle what makes a statement true. Moreover, what isdetermineda posteriori to be a truthmaker may exhibit acomplexity quite different from that of the statement it makes true(Mulligan, Simons, & Smith 1984: 299). Nevertheless, it is clearthat unless (Entailment-T) is constrained in some way it willgenerate truthmakers that are unwanted because their presenceconflicts with (Relevance).

One way to restore accord between them would be to abandon theDisjunction Thesis that together with (Entailment-T) led usdown the path to Truthmaker Monism. Indeed isn’t theDisjunction Thesis dubious anyway? Consider examples involving theopen future. Can’t we imagine a situation arising that makes ittrue that one or other of the horses competing in a race will win, butwhich neither makes it true that one of the horses in particular willwin nor makes it true that another will (Read 2000; Restall 2009)? Forfurther discussion of issues surrounding truthmaking entailment, theDisjunctive Thesis and the Conjunctive Thesis, i.e. the principle thata truthmaker for a conjunction is a truthmaker for its conjuncts, seeRodriguez-Pereyra 2006a, 2009, Jago 2009, Lopez de Sa 2009 andTalasiewicz (et al) (2012) and Briggs 2012.

But even if the Disjunction Thesis is given up still this leaves inplace the embarrassing consequence of defining what it is to be atruthmaker in terms of classical entailment,viz. thatany existing thing turns out to be a truthmaker forany necessary truth. Some more radical overhaul of(Entailment-T) is needed to avoid over-generation. Onepossibility is to redefine what is to be a truthmaker in terms of amore restrictive notion of “relevant entailment” (in thetradition of Anderson & Belnap) that requires what is entailed tobe relevant to what it is entailed by (Restall 1996, 2000; Armstrong2004: 10–12, Simons 2008: 13).

Nevertheless since truthmaking concerns the bestowal of truth,entailment its preservation, there mustat some level be animportant connection to be made out between truthmaking andentailment; the effort expended to make out such a connection will beeffort spent to the advantage of metaphysicians and logicians alike.But even granted this is so there are reasons to be doubtful that anyoverhaul of (Entailment-T), however radical, will capturewhat it is to be a truthmaker. One vital motivation for believing intruthmakers is this. Positing truthmakers enables us to make senseof the fact that the truth of something depends on how things standwith an independently given reality. Truthmakers are posited toprovide the point of semantic contact whereby true representationstouch upon an independent reality, upon somethingnon-representational. Since entailment is a relation betweenrepresentations it follows that the notion of a truthmaker cannot befully explicated in terms of the relation ofentailment—regardless of whether representations are bestunderstood as sentences or propositions or some other candidatetruthbearer (Heil 2000: 233–4; 2003: 62–5; Merricks 2007:12–13). Ultimately (Entailment-T), or a relevance logicversion if it, will leave us wanting an account of what makes arepresentation of the existence of a truthmaker—whatever itentails—itself beholden to an independent reality.

1.2 Truthmaking as Necessitation

Appreciating that truthmaking cannot be entailment, Armstrong made abold maneuver. He posited a primitive relation of metaphysicalnecessitation (1997: 151, 2004: 96)). The relation in question lightsupon a portion of reality at one end and upon a truth at the other.Armstrong then defined what is to be a truthmaker in terms of thismetaphysical bridging relation which relates portions of the world totruthbearers.

(Necessitation-T)

a truthmaker is a thing that necessitates something’s beingtrue.

In the simplest case that means that the truth making relation is onethat “holds between any truthmaker,T, which issomething in the world, and the proposition” thatTexists (2004: 6). This conception of truth making avoids the“category” mistake that results from attempting to definetruthmaking in terms of entailment. It also makes some advance upon(Virtue-T) and its primitive use of “in virtueof” because at least (Necessitation-T) relates thenotion of truth making to other modal notions, like that of necessity,upon which we have some independent handle.

But what is there to be said in favour of conceiving of truthmakersin terms of “necessitation”? Armstrong offers thefollowing argument. Suppose thatT is a candidate truthmakerfor a truthp even thoughT fails to necessitatep. Then it is possible forT to exist even whenp is false. Armstrong now reflects “we will surelythink that the alleged truthmaker was insufficient by itself andrequires to be supplemented in some way” (1997: 116). Supposethis supplementary condition is the existence of another entity,U. Then “T+U would appear to be thetrue and necessitating truthmaker forp” (2004: 7).Armstrong concludes that a truthmaker for a truth must necessitatethe truth in question.

This argument takes us nowhere except around in a circle.(Necessitation-T) embodies the doctrine that it is bothnecessary and sufficient for being a truthmaker that a thingnecessitates the truth it makes true. Armstrong’s argument forthis doctrine relies upon the dual assumptions: (1) anything thatfails to necessitatep (witnessT) cannot be atruthmaker forp,whereas (2) anything that succeeds innecessitatingp (witnessT+U) must be. But(1) just is the claim that it is necessary, and (2) just the claimthat it is sufficient for being a truthmaker that a thingnecessitates the truth it makes true. Since it relies upon (1) and(2), and (1) and (2) are just equivalent to(Necessitation-T), it follows that Armstrong’s argumentis incapable of providing independent support for the conception hefavours of what it is to be a truthmaker.

Even though this argument is circular, does (Necessitation-T)at least have the favourable feature that adopting it enables us toavoid the other difficulty that beset (Entailment-T),viz. over-generation? Not if there are things thatnecessitate a truth whilst still failing to be sufficiently relevantto be plausible truthmakers for it. If the necessitation relation isso distributed that it holds between any contingently existing portionof reality, e.g., an ice-floe, and any necessary truth, e.g., 2+2=4,then we shall be no further forward than we were before. So Armstrongneeds to tell us more about the cross-categorial relation in questionto assure us that such cases cannot arise.

Smith suggests another problem case for(Necessitarian-T).

Suppose that God wills that John kiss Mary now. God’s willingact thereby necessitates the truth of “John is kissingMary”. (For Malebranche, all necessitation is of this sort.) ButGod’s act is not a truth-maker for this judgement. (Smith 1999:6)

If such cases are possible then (Necessitation-T) fails toprovide a sufficient condition for being a truthmaker.

Smith endeavours to avoid such failures of sufficiency by appealing toa notion ofprojection, where the projection of atruthbearer is, roughly speaking, the subject matter of thetruthbearer, what it is ‘about’. Then a truthmaker for atruth bearerp can be defined as something that necessitatesp and falls within the projection ofp (Smith 1999).For this solution to be effective we need to be given criteria for thenotion of projection which ensure that it doesn’t also lead toan overgeneration of truthmakers. But it’s questionable whetherthis can be done without drawing on further notions that aren’tobviously clearer than truthmaking itself. (See Gregory 2001, Smith2002 and Schnieder 2006b and Schipper 2020 for a related account oftruthmaking in terms of ‘aboutness’).

Asay responds to failures of sufficiency by biting the bullet. Asayholds (2023: 8; 2020: 51) that an entitye’snecessitating the truth of a sentences is necessary andsufficient fore to be a truthmaker ofs. Hisresponse to apparent counterexamples, e.g., an ice floe’s makingit true that 2+2=4, is to bite the bullet: these are genuine case oftruthmaking (2020: 234). He argues that any impression to the contraryoverlooks (1) the fact that ‘“truthmaking” is a termof art, employed for a certain theoretical purpose withinmetaphysics’ viz. ‘developing a proper harmonybetween’ truth and reality (2023: 8). And (2) that mathematicsconsists of ‘trivial truths’ – in fact, Asay claims,mathematical truths are analytic--and that numbers and functions areonly ‘trivial objects’ whose significance for ontology isexhausted by their being truthmakers for ‘trivial truth’(2020: 234). Asay’s responses invite the followingrejoinders.

First: Asay’s attempt to dispel the counterexamples by claimingthat “truthmaking” is a term of art, employed for acertain theoretical purpose within metaphysics’ is undermined byhis own practice. He introduces the notion of truthmaking in a veryinformal fashion (2023: 2–3): he runs a thought experiment inwhich you exercise god-like powers of creating things while onebureaucracy keeps record of the increasing ontology and another keepsrecord of which sentences are made true. The theoretical purpose oftruthmaking cannot be arcane if it can be illustrated by such a simpleif fanciful hypothetical example. (Note too that, by followingAsay’s lead, we could block any counterexample to any cherishedphilosophical theory that used some term t simply by declaring thatour theory used t as a term of art to further some theoreticalpurpose.) Second: the claim that mathematics is, in general, analyticor trivial is a deeply controversial doctrine. So insofar as a theoryof truthmakers relies upon the view that mathematics is analytic thatraises a question about the tenability of that theory oftruthmakers.

Returning to (Necessitarian-T) there is a further objectionthat bears on the question of truthbearers. Armstrong conceives thenecessitation relation it uses as internal: “An internalrelation is one where the existence of the terms entails the existenceof the relation”; otherwise a relation is external (Armstrong1997: 87). Armstrong argues that the relation of truthmaking has tobe internal (in this sense) because if it weren’t then we wouldhave to allow that, absurdly, “anything may be a truth-maker forany truth” (1997: 198). But then nothing butpropositions—conceived in the self-interpreting sense—canbe truthbearers that are internally related to their truthmakers.Any other candidate for this representational role—a tokenbelief state or utterance—could have been endowed with adifferent representational significance than the one it possesses. Sothe other eligible candidates, by contrast to propositions,aren’t internally related to what makes them true.

Armstrong’s commitment to the truthmaking relation’sbeing internal clashes with his naturalism (David 2005: 156–9).According to Armstrong,

Truth attaches in the first place to propositions, those propositionswhich have a truth-maker. But no Naturalist can be happy with a realmof propositions. (1997: 131)

So Armstrong counsels that we don’t take propositions with“ontological seriousness”:

What exists are classes of intentionally equivalent tokens. Thefundamental correspondence, therefore, is not betweenentities called truths and their truth-makers, but between the tokenbeliefs and thoughts, on the one hand, and truth-makers on the other.(1997: 131)

But naturalistically kosher token beliefs and thoughts aren’tinternally related to what makes them true. So Armstrong’snaturalism commits him to denying that the truthmaking relation isinternal after all. Heil has also inveighed in a naturalistic spiritagainst incurring a commitment to propositions that are designed tohave their own “built-in intentionality” whilst continuingto maintain that truthmaking is an internal relation (2006:240–3). Since we have no idea of what a naturalisticrepresentation would look like that was internally related to whatmade it true, this appears to be an impossible combination of views.Our inability to conjure up a credible class of truthbearers that areinternally related to their truthmakers provides us with a verystrong incentive for supposing that the truthmaking relation isexternal. The long and short of it: if we are wary, as manynaturalists are, of the doctrine that truthbearers are propositions,then we should also be wary of thinking that the truthmaking relationis internal. This spells trouble for (Necessitarian-T) andany other account of truth making which invoke internal relations topropositions.

As an alternative to account of truthmaking in terms of necessitation,Mulligan and Lowe have suggested that truthmaker of a proposition issomething such that it is part of the essence of that proposition thatit is true if that thing exists. (Mulligan 2003: 547, 2006: 39, 2007;Lowe 2006: 203–10, 2009: 209–15. ). Lowe suggests thathelps rules out spurious case of truth making--because it isn’tpart of the essence of the proposition that John is kissing Mary thatit is true if there exists an act of God’s willing it, or partof the essence of the proposition that 2+2=4 that it is true if thereis a particular ice floe in the Antarctic, or part of the essence ofthe proposition that 2+2=4 that it is true if π exists (2006:202–3). But, on the downside, it may be questioned whether ourgrip upon the notion of the essence of a proposition is any firmerthan the notion of truthmaker for it and since relation of aproposition to its truthmakers is internal, the essentialist approachinherits the difficulties of (Necessitatian-T).

1.3 Axiomatic Truthmaking

All this might be taken to show that the project of definingtruthmaking in more basic terms is misconceived, much as the projectof defining knowledge in more basic terms has come to seemmisconceived because e.g., of the Gettier cases. Of coursethere’s no gain to be had from, doing nothing more thandeclaring the notion of a truthmaker to be primitive. If it’sprimitive then we also need to know how the notion may be fruitfullyapplied in association with other concepts we alreadydeploy—entailment, existence, truth, etc. —to describe theinterplay of truthbearers and the world. As Simons remarks,

The signs are that truth-making is not analysable in terms of anythingmore primitive, but we need to be able to say more than just that. Sowe ought to consider it as specified by principles of truth-making.(2000: 20)

In other words, the notion needs to be introduced non-reductively butstill informatively and this is to be achieved by appealing to itssystematic liaisons with other concepts.

This is the approach of Mulligan, Simons and Smith’s 1984:312–8. The principal schemata they employed to convey anarticulate grasp of whattruthmaking means in non-reductiveterms included:

(i)

(Factive) IfA makes it true thatp, thenp

(ii)

(Existence) IfA exists, thenA makes it truethatA exists

(iii)

(Entailment) IfA makes it true thatp, and thatp entails thatq, thenA makes it true thatq

Each of these schemata specifies a definite linkage between theapplication of the notion oftruthmaking and some othercondition.Truthmaking is introduced as the notion thatsustains all of these linkages. Putting the schemata together what itis to be a truthmaker is then definable intra-theoretically asfollows,

(Axiomatic-T)

A truthmaker is somethingx such that (i) ifxmakes it true thatp thenp, (ii) ifxexists thenx makes it true thatx exists…and so on for each of the axiom schemata of our favoured theory oftruthmakers.

It is important to appreciate that adopting this approach totruthmaking doesn’t have the benefits of theft over honesttoil. For one thing it doesn’t obviate the threat of superfluoustruthmakers for necessary truths. (Entailment) is theprinciple that truthmaking tracks entailment: ifA makesp true then it makes all the consequences ofp truetoo. It’s a principle that recommends itself irrespective ofwhether truthmaking can be defined. This is because it dovetailssmoothly with the idea that one truthmaker can make many truths true.For example, suppose that a particulara has some absolutelydeterminate mass. It is entailed by this description that variousdeterminable descriptions are also truly predicable ofa.Some of these truths say more than others, nonetheless they all havethe same truthmaker. Why so? Because they are entailed bya’s having the mass it does (Armstrong 1997: 130; 2004:10–11). To answer so is to appeal to (Entailment). Butif the entailment that truthmaking tracks is classical then we areback to flouting (Relevance). Ifq is necessary thenany contingentp classically entailsq. So ifsomething at the back of your refrigerator makes it true thatp then by (Entailment) it makesq true too.To avoid flouting (Relevance) in this way(Entailment) had better be a principle that linkstruthmaking to a more restrictive, non-classical notion of entailment(Mulligan, Simons, & Smith 1984: 316).

So adopting the Axiomatic approach won’t save us the labour offiguring out which non-classical connective it is that contributes tocapturing what it is to be a truthmaker. Nor will appealing to(Axiomatic-T) save us the hard work of figuring out whattruthmakers and truthbearers must be like in order to collectivelyrealise the structure described by the axiom schemata for truthmakerswe favour. But, on the other hand, there is nothing about theseschemata that demands truthbearer and truthmaker be internallyrelated.

The Axiomatic approach to truthmaking has proved less attention thanother more metaphysically-loaded conceptions, in terms ofnecessitation, essence or grounding. But an attraction of theAxiomatic approach is its metaphysical neutrality. .

1.4 TruthMaking as Grounding

Can truthmaking be defined in terms ofgrounding or what issometimes described as non-causalmetaphysical dependence?The notion of truthmaking is typically introduced, as we have seen,in terms of the ideology of “in virtue of”. As we havealso seen, many philosophers then ask: but what independent contentcan be given to this notion? In response to this challenge, a theoryof grounding may be conceived as a general theory of “in virtueof” in terms of which truthmaking may then be explained. Afurther consideration which motivates those already committed togrounding is the general methodological principle that favourstheoretical unification. Their idea is that by conceiving oftruthmaking as a kind of grounding, we are able to understandtruthmaking better, i.e. not as an isolated phenomenon but as aninstance of a more general pattern, thereby illuminating not only thenature of truthmaking but grounding too.

How truthmaking is to be defined in terms of grounding depends uponhow non-causal dependence is logically conceived, either as apredicate (‘grounds’) or a non-causal operator(‘because’). Consider the following alternatives:

(Grounding-Predicate-T)

A truthmaker is an entityx which makes a propositiony true iff the fact thatx exists grounds the factthaty is true.

(Grounding-Operator-T)

A truthmaker is an entityx which makes a propositiony true iffy is true becausex exists.

(For the former, see Rodriguez-Pereyra 2005, Schaffer 2009, Jago 2018:184–202, for the latter, Correia 2005, 2014, Schnieder 2006a,Mulligan 2007, Caputo 2007).

One attraction of conceiving truthmaking as based on grounding arisesfrom taking grounding to be “hyperintensional”. Groundingis intended to be a notion that’s fine-grained enough todistinguish those entities, e.g., the cardinal numbers, that ground anecessary truth, such as 2+2=4, from those that don’t, e.g. acontingent existent such as the aforementioned ice floe. Becausegrounding is so fine-grained, the hope is that neitherGrounding-Predicate-T orGrounding-Operator-T willgive rise to the over-generation that besetEntailment-T andNecessitation-T but without having to appeal to anunderdeveloped notion of “about” or“relevance”.

Of course, in light of sec, 1.2 and 1.3 above, we can foresee adownside to this. BothGrounding-Predicate-T andGrounding-Operator-T quantify over propositions that standhyperintensionally to their truthmakers. It follows that bothGrounding-Predicate-T andGrounding-Operator-T sharea commitment withNecessitarian-T, viz. an ontology ofabstract propositions which have their meanings essentially. Supposegrounding is,eo ipso, an internal or necessitating relation.Then if the truth of a propositionP is grounded in theexistence of somethingG then in every world in which bothG andP exists,P is true. Now thispresupposes thatP bears the same meaning in every world inwhich bothP andG exists—because wedon’t wantG to makeP true ifPmeant something different from what it first did. But if propositionsare conceived, say, as sentence tokens, then there can be no guaranteethat the presupposition will be met—since sentence tokens may bedifferently interpreted in different worlds. Of course the guaranteecan be made if propositions are conceived as abstract things whichhave their meanings essentially. But this is a theoretical cost of theproposal. So the grounding theorists must either bear the cost orprovide an alternative account of what propositions are such that theyare hyper-intensionally related to their truthmakers. But, again, thismay be a commitment many grounding theorists have already made or bewilling to accept if it gives them a good account of truthmaking.

So far we have considered efforts to define truthmaking in terms ofgrounding. But there are other approaches in the literature which seekto endorse one notion at the expense of the other. One way acceptsgrounding as a welcome theoretical innovation but argues that we arebetter off without truthmaking, at least in the forms which havebecome familiar to us. A second way continues to endorse truthmakingwhilst rejecting grounding. (Other available positions include: thattruth making is a special kind of grounding which involves a uniqueform of dependence (Griffith 2013), that truth making isn’tgrounding but that grounding is key to truthmaking (Saenz 2018) andthat grounding obviates the need to appeal to truthmaking (Liggins2012)).

The first approach, taken by Fine, involves keeping grounding butrejecting truthmaking because grounding does a better job (Fine 2012;43–6). Here truthmaking is conceived as a relation between aworldly entity and a representation where the existence of the entityguarantees the truth of the representation. But, Fine argues, it ismore theoretically fruitful to take grounding as the central notionfor metaphysics. This is partly because, Fine maintains, grounding isa less restrictive notion than truthmaking, because grounding doesnot require that the ultimate source of what is true should lie inwhat exists, rather we can remain open about what form groundingtakes. Moreover, whilst there may be genuine questions about what theground is for the truth of the representation thatp theremay be further questions about what makes it the case thatpand these questions will typically have nothing to do withrepresentation as such. Because truthmaking is typically understoodin modal terms, i.e. necessitation is conceived to be sufficient fortruthmaking, Fine is also sceptical that there is any way of avoidingthe over-generation of truthmakers we have already discussed (see 1.1and 1.2 above). Finally, Fine thinks that we should be able toconceive of the world hierarchically, whereby (e.g.) the normative isgrounded in the natural, the natural in the physical and the physicalin the micro-physical. But this is difficult to do if we think interms of truthmaking, because if (e.g.) we conceive of a normativerepresentation being made true by the existence of something natural,that natural thing is just the wrong sort of thing to be made true bysomething at the physical level because it is not arepresentation.

Fine’s critique of truthmaking presupposes that we can onlyavail ourselves of truthmaking if we conceive of truthmaking inmonolithic terms, as providing a unique method for metaphysics. Butwhilst, for example, Armstrong may have had a tendency to think insuch terms, this doesn’t appear to be mandated by the nature oftruthmaking itself. One might, as Asay (2017) argues, insteadconceive of grounding and truthmaking as complementary projects,whereby a theory of truthmaking doesn’t purport to doeverything a theory of grounding does and so reciprocal illuminationremains a live possibility.

The second approach, outlined above, refusing grounding but favouringtruthmaking, is advanced by Heil (2016). Heil is generally suspiciousof grounding because grounding is often characterized in different andincompatible ways, so he is sceptical that there is a univocal conceptof grounding to be had. But, more specifically, Heil has longmaintained that hierarchical conceptions of reality spell troublebecause of the difficulties explaining the causal and nomologicalrelationship between the layers (Heil 2003: 31–9). He arguesthat this was the problem identified for supervenience and realizationin the ‘90s and it’s a problem inherited by thehierarchical conception of reality to which grounding gives rise. SoHeil does a modus tollens where Fine does a modus ponens. Whilst Fineconceives of the hierarchical styles of explanation grounding providesas one of the principal virtues of grounding, Heil considers this isone of the deepest drawbacks of grounding. So Heil recommends seekingtruthmakers as the proper methodology for metaphysics because itenables us to give a non-hierarchical description of reality wherebyfundamental physics gives us the truthmakers for truths that havetruthmakers.

Suppose, however, that the notion of truthmaking were to admit of asatisfactory analysis or elucidation in terms of grounding. It’sstill further question whether this shows truthmaking to be arespectable notion. Because if grounding isn’t, truthmakingisn’t either and whether grounding is intelligible or aneligible candidate to serve a foundational role in metaphysics iscontroversial (Daly 2012, 2023, Wilson 2014, Miller and Norton 2017,MacBride and Janssen-Lauret 2022). It might be replied that eventhough grounding is controversial, if it it did help yield asatisfactory account of truthmaking that would have advanced ourunderstanding of truthmaking and would be a point in grounding’sfavour. But if grounding is dubious and controversial that underminesthe prospects of it providing a satisfactory account of truthmaking(or, indeed, of anything else). 

2. Which range of truths are eligible to be made true (if any are)?

Agreeing about what it is to be a truthmaker, isn’teoipso to agree about the range of truths that are eligible to bemade true. There is potential for disagreement here because differentranges of truths appear to require different kinds of truthmakers andsome may not appear to require any truthmakers at all. So, forexample, an unwillingness to countenance one or other kind oftruthmaker, may force a reconsideration of which truths reallyrequire truthmakers or even a reconsideration of what it is to be atruthmaker. We can get a sense of the complex interplay of forces atwork here by starting out from the most simple and general principleabout truthmaking, i.e. maximalism, and then seeing what pressuresthere are to make us step back from it.

2.1 Maximalism

Truthmakermaximalism is the doctrine that no truth lacks atruthmaker, hence,

(Maximalism)

For every truth, there must be something in the world that makesit true.

Maximalism lies at one end of the spectrum of positions potentiallyavailable to occupy. At the other end, liestruthmakernihilism, the view that no truth needs to be made true becausethere is no such role as making something true for anything toperform.Truthmaker optimalism is the intermediate positionthat only some truths stand in need of truthmakers: not so few thattruth fails to be anchored in reality but not so many that we straincredulity about the kinds of things there are.

What is there to be said in defence of maximalism? Even though hefavours it, Armstrong finds himself obliged to admit that “I donot have any direct argument” for recommending the position(2004: 7). Instead he expresses the hope that ‘philosophers ofrealist inclinations’ will find the view ‘immediatelyattractive’. So instead let us follow Armstrong and treatmaximalism as a “hypothesis to be tested”.

Maximalism needs to be distinguished from the even stronger claim,

(Correspondence)

For each truth there is exactly one thing that makes it true andfor each truthmaker there is exactly one truth made true by it.

There’s clear blue water between these claims because if wecombine maximalism with (Entailment)—that whatevermakes a truthp true makes whatp entails true too.Sop and all of its consequences are not only all made true(as maximalism demands) but they also share a truthmaker (asCorrespondence denies). This takes us halfway to appreciatingthat so far from being an inevitably profligate doctrine—as itsname suggests—maximalism is compatible with denying that somelogically complex claims have their own bespoke truthmakers. (Theinspiration for thinking this way comes from the logical atomism ofRussell (1918–19) that admitted some logically complex facts butnot others—it is to be contrasted with Wittgenstein’sversion of the doctrine (1921) which admitted only atomic facts.)

Suppose, for the sake of expounding the view, that some truthbearersare atomic. Also suppose thatP andQ are atomic andt makesP true. Then, byEntailment,t makesP ∨Q true too. Similarly, ifs makesP true ands* makesQ truethen, byEntailment,s ands* together makeP &Q true. Since the task of makingP∨Q andP &Q true has already beendischarged by the truthmakers for the atomic truth bearers, there isno need to posit additional truthmakers for making these disjunctiveand conjunctive truths true. Similar reasoning suggests that there isno need to posit bespoke truthmakers for existential generalisationsor truths of identity either (Mulligan, Simons, & Smith 1984: 313;Simons 1992: 161–3; Armstrong 2004: 54–5). But maximalismis not thereby compromised: even though disjunctive and conjunctivetruths lack specific truthmakers of their own, they’re stillmade true by the truthmakers of the basic or atomic claims from whichthey’re compounded by the logical operations of disjunction andconjunction.

But positing truthmakers for atomic truths doesn’t obviate theneed—supposing maximalism—to posit additional truthmakersfor negative and universal truths. This becomes apparent in the caseof negative truths when we compare the truthtables for conjunctionand disjunction with the truthtable for negation. The former tell usthat the truth of a disjunctive formula is determined by the truth ofone or other of its disjuncts, whilst the truth of a conjunctiveformula is determined by the truth of both its conjuncts. But thetruthtable for negation doesn’t tell us how the truth of~P is determined by the truth of some other atomic formulaQ from which ~P follows; it only tells us that~P is true iffP isfalse. The strategy foravoiding bespoke truthmakers for logically complex truths can’tget a grip in this case: there’s noQ such thatsupplying a truthmaker for it obviates the necessity of positing anadditional truthmaker for ~P (Russell 1918–19:209–11; Hochberg 1969: 325–7).

The problem is even starker for universal truths: there’s notruthtable for them because there is no set of atomic formulae whosetruth determines that a universally quantified formula is true too.Why so? Because whatever true atomic formulae we light upon(Fa,Fb…Fn), it doesn’tfollow from them that ∀xFx is true. To extract thegeneral conclusion one would need to add to the premises thata,b…n areall the thingsthere are; that there’s no extra thing waiting in the wings toappear on stage that isn’tF. But this extra premise isitself universally quantified, not atomic. So it can’t be arguedthat the truthmakers forFa,Fb…Fnput together already discharge the task of making ∀xFxtrue because they entail it (Russell 1918–9: 236–7;Hochberg 1969: 335–7).

It follows that if maximalism is true then negative and universaltruths have bespoke truthmakers, i.e., not just combinations oftruthmakers for atomic truths. So what might the truthmakers be forsuch truths?

Before turning to consider answers to that question, note two otherchallenges to maximalism. (1) Take the most encompassing negativeexistential of all: absolutely nothing exists. Surely this statementis possibly true. But if it were true then something would have toexist to make it true if the principle that every truth has atruthmaker is to be upheld. But then there would have to be somethingrather than nothing. So combining maximalism with the conviction thatthere could have been nothing rather than something leads tocontradiction (Lewis 1998: 220, 2001: 611). So unless we already havereason to think there must be something rather than nothing—asboth Armstrong (1989b: 24–5) and Lewis (1986: 73–4) thinkthey do—maximalism is already in trouble. (2) Milne raise thecharge that the sentence (M): This sentence has no truthmaker, cannothave a truthmaker because if it had a truthmaker it would be true andif it was true it wouldn’t have a truthmaker becausethat’s what it says.Ergo it cannot have a truthmaker.But if it has no truthmaker (M) is true. So there is at least onesentence, (M), that lacks a truthmaker (Milne 2005). For furtherdiscussion, see Rodriguez-Pereyra (2006c), Milne 2013 and Barrio andRodriguez-Pereyra 2015.

2.2 Truthmakers for Negative Truths

Russell’s favoured class of truthmaker for negative truths wasnegative facts, but, he reflected,

There is implanted in the human breast an almost unquenchable desireto find some way of avoiding the admission that negative facts are asultimate as those that are positive. (1919: 287)

He was right that our desire for positive facts and things makes usawkward about acknowledging that negative facts or things are thetruthmakers of negative truths. Nonetheless, discussions aboutwhether there are positive or negative facts are fraught by thedifficulty of telling whether a fact is negative or positive. This isbecause, as Russell noted, there is “no formal test” or“general definition” for being a negative fact; we“must go into the meanings of words” (1918–19:215–6). Statements of the form “a isF” aren’t invariably positive, witness:“so-and-so is dead”, nor are statements of the form“a isn’tF” always negative,witness: “so-and-so isn’t blind”. But itdoesn’t follow from the fact that a syntactic test cannot begiven that there is nothing to the contrast between positive andnegative. Molnar suggests that the contrast can be put on a soundscientific footing. For Molnar, natural kinds are paradigm instancesof the positive, to be identified ona posteriori grounds(2000: 73). To say that a thing belongs to a natural kind identifiedin this way is to state a positive fact. To state a negative fact isto negate a statement of a positive fact.

It’s a very natural suggestion that if the negative claim thata isn’tF is true it’s made true by theexistence of something positive that’sincompatiblewitha’s beingF (Demos 1917). For example,the truthmaker for the claim that kingfishers aren’t yellow isthe fact that they’re blue because their being blue isincompatible with their being yellow. But what makes it true thatthese colours are incompatible? The notion ofincompatibilityappears itself to be negative—a relation that obtains betweentwo states when it’snot possible for them to obtaintogether. So this proposal threatens to generate a regress:we’ll need to find another positive truthmaker for the furthernegative claim that yellow and blue are incompatible, something whoseobtaining is incompatible with the state of yellow and blue’sbeing compatible, and so on (Russell 1918–9: 213–5, 1919:287–9; Taylor 1952: 438–40; Hochberg 1969: 330–1).There’s another worry: it’s not obvious that there areenough positive states out there to underwrite all the negative truthsthere are. Even though it may be true that this liquid is odourlessthis needn’t be because there’s something further about itthat excludes its being odorous (Taylor 1952: 447; Mulligan, Simons,& Smith 1984: 314).

One could circumvent the threatened regress by denying that theincompatibilities in question require truthmakers of their ownbecause they’re necessary truths and such truths are alegitimate exception to maximalism—because “they are truecome (or exist) what may” (Simons 2005: 254; Mellor 2003: 213).There is some plausibility to the idea that tautologies don’tstand in need of truthmakers; their truth is settled by thetruthtables of the logical constants. But material necessarytruths—such as that expressed by “yellow is incompatiblewith blue”—appear to make just as substantive demands uponthe world as contingent truths do (Molnar 2000: 74). In a sense theyappear to make even more of a demand since the world must be soendowed that it could not in any circumstances have failed to live upto the expectations of material necessary truths. It’s apeculiar feature of our philosophical culture that even thoughit’s almost universally acknowledged that Wittgenstein’splan (1921: 6.37) to show all necessity is logical necessity ended infailure—indeed foundered upon the very problem of explainingcolour incompatibilities—that so many philosophers continue tothink and talk as though the only necessities were formal ones so thatnecessary truths don’t need truthmakers (MacBride 2011:176–7).

Russell reluctantly chose to acknowledge negative facts astruthmakers for negative truths (but see Veber 2008 for a defence ofthe incompatibility view of negative truths). He just couldn’tsee any way of living without them. But negative facts are an unrulybunch. Try to think of all the ways you are. Contrast that with theeven harder task of thinking of all the ways you aren’t! Ifnegative truths are acknowledged as truthmakers they will have to beindefinitely numerous, unbounded in their variety; choosing to livewith them is a heavy commitment to make (Armstrong 2004: 55).What’s worse, if negative facts are akin to positivefacts—as their name suggests—then they must be made up outof things, properties and relations arranged together. But,primafacie, many of these things, properties and relationsaren’t existing elements of reality. So unless, like Meinong, webelieve in the non-existent, we’ll have to admit that negativefacts aren’t configurations of their constituents and so anentirely different kind of entity from positive facts altogether(Molnar 2000: 77).

It is for such reasons that Armstrong counsels us to adopt a moreparsimonious account of what makes negative truths true (2004:56–9). Armstrong’s own account lies at the oppositeextreme to Russell’s. Whereas Russell posited indefinitelymany negative facts to make negative truths true, Armstrongposits justone thing that’s responsible for makingthemall true, what he calls a ‘totality fact’.Since Armstrong also posits totality facts as truthmakers for generaltruths, let us turn to the matter of truthmakers for generaltruths.

2.3 Truthmakers for General Truths

Armstrong’s grand design is to sweep away the difficulties thatattend the admission of negative facts by positing a special kind ofgeneral fact that also serves as the truthmaker for general truths.Russell admitted general facts too but he acknowledged that, “Ido not profess to know what the right analysis of general factsis” (Russell 1918–9: 236–7). But Armstrong has gonefurther and assigned to general facts the following structure: ageneral, or totality fact consists in a binary relationT oftotality that holds between an aggregate on the one hand anda property on the other when the aggregate comprisesall theitems that fall under the property in question (Armstrong 1989b:93–4, 1997: 199–200, 2004: 72–5).

Consider the following example to get a sense of what Armstrong has inmind. China, France, the Russian Federation, the U.K. and the U.S.A.comprise the permanent membership of the UN Security Council. So theaggregate (A) of them bears the totality relationTto the property (P) of being a permanent member of theCouncil (T(A,P)). Since the aggregatebears that relation to that property, there can be no other permanentmembers of the Council who aren’t already included in it. So thetotality factT(A,P) suffices for thegeneral truth that China, France, the Russian Federation, the U.K. andthe U.S.A areall its members. It also suffices for the truthof the negative existential that there areno other membersof the Council. So once we’ve recognised thatT(A,P) exists, there’s no need to recognise additional bespoketruthmakers for these negative truths.

Now, according to Armstrong, we can avoid the need to posit negativefacts by affirming “the biggest totality state of all, the oneembracing all lower-order states of affairs”, i.e., theexistence of a totality state that consists in an aggregate of all the(1^st order) states of affairs there are related byT to the property ofbeing a (1^st order)states of affairs (2004: 75). It’s a defining feature ofArmstrong’s metaphysics that the world is “a world ofstates of affairs, with particulars and universals only havingexistence within states of affairs” (1989: 94). Consequentlythis totality state, the biggest one, comprises a vast swathe of whatexists—whether particulars, universals or states of affairs thatconsist in particulars having universals. So it follows from theexistence of this totality fact that there are no more (1^storder) states of affairs that are not already included in theaggregate of states thatT relates to the property ofbeing a (1^st order) states of affairs. Nor arethere any particulars or (1^st order) universals had bythose particulars that are not constituents of the state of affairsincluded in that aggregate. It also follows that there are no moreparticulars or (1^st order) universals. So this totalityfact serves as truthmaker for all these negative truths.

It is sometimes objected that such totality facts are just negativefacts in disguise: “Totality statements state the non-existenceof certain entities, they state ‘no more facts’”; sowe should reject totality facts if we are dissatisfied with negativeones (Molnar 2000: 81–2). Armstrong responds to this charge withequanimity: “It is not denied, of course, that the totalling oralling relation involves negation. It sets a limit to the things ofthat sort” (2004: 73). But if negation has indeed been smuggledinto the description of the role thatT performs incomprising a totality state then it is difficult to avoid thesuspicion that Armstrong has simply exchanged many negative facts forone big one. But we may think of Armstrong’s contribution in adifferent way. There are two ostensible concerns that negative statesof affairs present. First, there is a concern about their number.Second, there is a concern about, so to speak, theirnegativity. Armstrong has addressed the first concern byshowing how we may reduce the number of negative states of affairs.Armstrong judges that the second concern doesn’t need to beaddressed—because, as Armstrong reflects, we cannot eliminatenegation from our description of the world.

According to C.B. Martin, Armstrong’s proposal conflicts withcommon sense because we already recognise in ordinary discourse thatdifferent negative truths have different truthmakers—not justone as Armstrong proposes (1996: 59). For example, we recognise thatwhat makes it true that there is no oil in this car’s engine isdifferent from what makes it true that there are no dodos left. Whatmakes claims like these true are absences, lacks, limits, holes andvoids, where these are conceived not as things but as“localised states of the world”, robustlyfirst-order and “causally relevant” to what goes on(Martin 1996: 58, 65–6; Taylor 1952: 443–5). But, as manyphilosophers have argued, when we talk about an absence having causaleffects what we’re really saying can be understood withoutreifying negative states and appealing instead to the actual effects,or the counterfactual effects, of a positive state (Molnar 2000:77–80; Armstrong 2004: 64–7; Lewis 2004; Beebee 2004)

It has also been objected that Armstrong’s position gives riseto a “paradox of totality” (Armstrong 1989: 94, 1997:198–9, 2004: 78–9; Cox 1997: 53–60; Molnar 2000:81). Take the totality state of affairs that comprises all the(1^st order) state of affairs. Since this (2^ndorder) state is itself a state of affairs it follows that the initialaggregate of (1^st order) states of affairs failed tocomprise all the states of affairs there are. So there must be afurther totality state that comprised the aggregate of all of them.But this (3^rd order) state is also a state of affairs so itwill need to be added to the mix too, and soadinfinitum.

Armstrong responds to this objection with equanimity too:

we can afford to be casual about this infinite series. For after thefirst fact of totality these “extra” states of affairs areall supervenient. As such, we do not have to take them withontological seriousness. (1989b: 94)

To understand this we need to appreciate that Armstrong’s notionofsupervenience is non-standard. For him: “an entityQ supervenes upon entityP if and only if it isimpossible that P should exist andQ not exist” or, inother words that the existence ofP entails the existence ofQ. (Armstrong 1997: 11). He also holds a non-standardconception of ontological commitment,viz. that “Whatsupervenes is no addition of being” (Armstrong 1997: 12, 2004:23–4). Armstrong’s idea is (roughly) that to be a genuineaddition to being is to be a net (indispensable) contributor to theschedule of truthmakers for all the truths. But supervenient entitiesare superfluous as truthmakers. If the existence of anRentails the existence of a certainS which in turn entailsthe truth ofP, thenR already makesP trueso there is no need to includeS in the inventory oftruthmakers. It follows that supervenient entities, likeS,are no addition of being (Lewis 1992: 216).

Now bring this non-standard conception of ontological commitment tobear upon the envisaged infinite series of totality facts. It isimpossible that the 2^nd order totality fact comprising allthe 1st order states of affairs exist and the 3^rd ordertotality fact comprising all the 1^st and 2^ndorder states not exist. So the 3^rd totality fact—orany other state higher-order than it—is entailed by theexistence of the 2^nd order totality state. So all of thesen > 2 higher-order totality states supervene on it.That’s why Armstrong doesn’t think we need to take any ofthem with ontological seriousness.

What should we make of this non-standard conception of ontologicalcommitment in terms of truthmaking: that to be is to be atruthmaker? An argument is owed that we can’t legitimatelycommit ourselves to the existence of things that perform theoreticalroles outside the theory of truthmakers. Why shouldn’t we allowthat there are other theoretical roles for existing things to perform?Indeed it’s a very real possibility that when we come tounderstand the capacity of the truthmakers to make truthbearers truewe will find ourselves embroiled in commitment to the existence ofother things in their explanatory wake that aren’t truthmakersthemselves (MacBride 2011: 169). In fact Armstrong himself should havebeen one of the first to recognise this. For it has been an abidingfeature of Armstrong’s world view that we are obliged toacknowledge not only states affairs, which are truth makers, but alsoproperties and relations, constituents of states of affairs, whicharen’t. Cameron (2008c) has proposed that Armstrong’sconception shouldreplace the standard one that to be is tobe the value of a variable. But there’s the further difficultythat this threatens to cut off the branch the advocates of truthmakertheory are sitting on: if they disavow that existential quantificationis ontologically committing then they will be left without a means ofexpressing what, according to truthmaker theory, are the existingtruthmakers (Schaffer 2010: 16–7).

More generally still, can we make any sense of the idea of “anontological free lunch”? Why is something supervenient noaddition to being? Even if we only ever came to recognise theexistence of one supervening entity would we not thereby haveadded at least one extra item to our inventory of things thatexist? Of course in the special case where the supervening entity isconstituted by the entities it supervenes upon—i.e.,the things that are already there—it makes some sense to saythat it’s not adding anything new; but what Armstrong et al.declare to be ontological free lunches aren’t typicallyconstituted from the entities upon which they supervene (Lewis 1992:213, Melia 2005: 74–5). Accordingly Schulte (2011a, 2011b)argues that no necessitarian or grounding account of truthmaking canmake sense of the notion of an ontological free lunch, maintaininginstead that truthmaker theory needs to be augmented with the ideathat we are offering a reductive explanation when we make anexplanation in terms of truthmakers. Where does this leave us? So longas Armstrong’s non-standard conception of ontological commitmentremains controversial, it also remains controversial whether theinfinite series of totality facts to which Armstrong is“committed” may be welcomed as an ontologicalfree-lunch.

2.4 Optimalism

One way to respond to these difficulties is to abandon maximalism infavour of optimalism, to deny that universal and negative statementsneed truthmakers. But Merricks argues the optimalist “wayout” is blocked. Negative truths need truthmakers if any truthsdo, but they can’t have them. So, according to Merricks, we mustgive up thinking that truths need truthmakers in the first place(2007: 39–67).

Here’s why Merricks thinks so. In order to avoid theover-generation of truthmakers for necessary truths (etc.)Merricks imposes a relevance constraint : “a truth-maker must bethat which its truth is about”, so akin to Smith’srequirement that a truthmaker fall within the subject matter of theproposition it makes tree (Smith 1999, Merricks 2007: 28). But canthis constraint be satisfied in the case of negative existentials,such as the statement there are no hobbits? This statement isn’tabout hobbits, because there aren’t any, and other apparentcandidates, such as the universe’s exhibiting the globalproperty ofbeing such that there are no hobbits in it,appear hoaxed up and artificial (2007: 43–55). Even if onefollows Merricks this far, one may still think that negativeexistentials are the principled exception that proves the rule that atruthmaker for a positive truth must be what its truth is about. But,so far as Merricks is concerned, this is throwing the baby out withthe bathwater:

I deny that if we set aside the intuition that “a truth, anytruth” depends on being we are left with the equally compellingintuition that all truthsexcept negative existentials dependon being. (2007: 41)

He further suggests that this position is theoretically disingenuousbecause no one would consider retreating to it from full-blownmaximalism unless he or she had already been “spooked” byhis or her failure to find truthmakers for negative truths; or ifthey held onto the view that truth is correspondence (Merricks 2007:40–1; Dodd 2007: 394; Cameron 2008a: 411). Merricks surmisesthat if we have any reason to commit to truthmakers, we have onlyreason to commit outright to a truthmaker for every truth(maximalism). But since maximalism cannot be sustained because of thelack of things for negative existentials to be about, Merricksrecommends the rejection of truthmakers altogether.

But optimalists aren’t just “spooked” or“timid” maximalists. They stand on their two feet with aprincipled position of their own that need neither be based upon“gerrymandered intuition” nor adopted as a consequence ofa forced retreat from maximalism. If maximalism is intellectual heirto Russell’s logical atomism, then optimalism (at least in theform under consideration) is heir to Wittgenstein’s version ofthe doctrine according to which it is only atomic propositions thatrepresent the existence of states of affairs. The optimalists’idea is that once truthmakers have been supplied for the atomictruths there is simplyno need to posit further truthmakersfor the molecular ones. All we need to recognise is that an atomicstatementP is true whenever a truthmaker forPexists, thatP is false if and only if no truthmaker forP exists. Once the existence and non-existence of thetruthmakers has settled the truthvalues of all the atomicstatements, the logical operations described by the truthtables thensettle the truth and falsity of all the molecular statements (anotherstory must be told about what the truthmakers are for thenon-extensional constructions—another elephant in the room). Inparticular, the truthtable for negation—that tells us what“~” means—assures us that ifP is falsethen ~P is true. So all it takes to make ~P true isthat no truthmaker forP exists. Thus Mulligan, Simons, andSmith:

it seems more adequate to regard sentences of the given kind as truenot in virtue of any truth-maker of their own, but simply in virtue ofthe fact that the corresponding positive sentences have notruth-maker. (1984: 315; see also Mellor 2003: 213–4, 2009;Simons 2000:7–8, 2005: 255–6)

Optimalists also think that general truths are true without need forbespoke truthmakers (like totality facts) because they are logicallyequivalent to truths that don’t need truthmakers. For example, auniversal quantification ∀xFx is logically equivalent to thenegative statement ∼∃x∼Fx. Since the latter is negative,it’s true, if it is, because no truthmaker exists for∃x∼Fx. Then because the former is logically equivalent tothe latter, the optimalists concludes that ∀xFx isn’ttrue in virtue of a bespoke truthmaker of its own but simply becauseno truthmaker for its negation exists (Mellor 2003: 214; Simons 2008:14–5).

Jago (2012, 2018: 81–102) presents a dilemma againstnon-maximalists (optimalists). Here’s a sketch. Thenon-maximalist will accept (at least) two types of true proposition:those requiring truthmakers (‘positive’ propositionssaying how reality is) and those that don’t (‘negativepropositions’ saying how reality isn’t). (Some truepropositions may be a mix of the two. These are true derivatively).Now consider proposition P: <Jo knows that Shamima doesn’thave an aunt>. Suppose P is true. Here’s the first horn ofthe dilemma. P is a true positive proposition, so there must be atruthmaker T for it. By necessitation and the factivity of knowledge,whatever T might be, it must necessitate the nonexistence ofShamima’s aunt. But a truthmaker which necessitates thenonexistence of something, so is a ‘negative fact’,belongs to a maximalist ontology – an ontology thenon-maximalist purportedly eschewed. Here’s the second. If thenon-maximalist can provide truthmakers for P that aren’tnegative facts then the maximalist can use the same truthmakers fornegative propositions. So either the non-maximalist doesn’tevade the negative facts of the maximalist or the maximalist can adoptthe non-maximalist strategy in order to avoid negative facts whilstcontinuing to hold that every truth has a positive truthmaker. Furtherdefences of and challenges for the optimalist or non-maximalist arediscussed in Simpson 2014, Skiles 2014, Griffith 2015, Schipper 2018,Asay 2020: 71–91, Jago 2020.

2.5 Truth Supervenes Upon Being

Optimalism retains the original demand for truthmakers but restrictsit to atomic statements. Optimalism accordingly disavows a commitmentto truthmakers for negative statements and statements of generality.But Bigelow⎯also wary of the commitments that maximalismengenders to negative and totality facts⎯ weakens whattruthmaking means to a point where negative and general statementsdon’t require bespoke truthmakers of their own (1988:131–3). He offers the following principle to capture the kernelof truth in truthmaking worth saving.

(Truth Supervenes on Being)

If something is true then it would not be possible for it to befalse unless either certain things were to exist which don’t, orelse certain things had not existed which do (Bigelow 1988: 133).

This principle allows atomic truths to have truthmakers⎯becauseit would only be possible for them to be false if certain things hadnot existed: their truthmakers. But it also allows negative truths tobe true without them. The statement that there are no dragons gets tobe true because it would only be possible for that statement to befalse if something which hadn’t existed (dragons) did exist.Such statements are true not because they have truthmakers butbecause they have no counterexamples, “they lackfalse-makers” (Lewis 1992: 216, 2001: 610).

General truths are also true for lack of false-makers. The statementthat everything is physical (if true) is true because it would only bepossible for the statement to be false if something that hadn’texisted did,viz. something that wasn’t physical. Sowhen truthmaking is understood in this weakened sense there is noneed to acknowledge, e.g., an additional totality fact to make it truethat there are only five coins in my pocket; it’s enough that ifI hadn’t stopped adding coins that statement would have beenfalse because then there would have been at least one other coin in mypocket (Heil 2000: 236–240; Bricker 2006).

Despite their differences, optimalism and (Truth Supervenes UponBeing) share a key idea in common—that a negativeexistential truth isn’t true because something exists, butbecause something doesn’t,viz. a truthmaker for itscontradictory, a false-maker for it. C.B. Martin has objected thatthis doesn’t obviate the need to posit truthmakers for negativeexistentials. This is because a statement that there are nofalse-makers for a negative existential truth is itself a negativeexistential truth. So this statement “can’t be used toexplain or show how the latter needs no truth-making state of theworld for it to be true” (1996: 61). Lewis takes Martin’sobjection to be that this account of the truth of negative truthsisn’t informative. Take the statement that there are nounicorns. Why is it true? Well because there are no unicorns.That’s not much of an explanation! But, Lewis retorts, thepositive existential statement that there is a cat is true becausethere is a cat. That’s “No explanation at all, and nonethe worse for that” (Lewis 2001: 611–12).

Lewis argued that the doctrine that truth supervenes upon being is anuncomfortable halfway house. He began by arguing that the retreat frommaximalism was always necessary. He pointed out how deeplycounterintuitive it is to suppose that negative existentials are truebecause their truthmakers exist. It seems, offhand, that they aretrue not because some things do exist but because some don’t.“Why defy this first impression?” (1992: 204). But, moreimportantly, Lewis pointed out that maximalism was incompatible withwhat he took to be the Humean principle governing our thought aboutmodality: that anything can co-exist with anything else that’sdistinct. But it is theraison d’être of anytruthmaker for the negative existential truth that there are nounicorns—if there is one and whatever else it is like—thateven though it is distinct from all unicorns it cannot co-exist withany of them. Why? Because otherwise it would make it true that thereare no unicorns even in circumstances where unicorns existed.Alternatively, suppose that any putative truthmaker is not distinctfrom all unicorns but shares some common part with them. But evenallowing this would not explain why the truthmaker excludes theexistence of unicorns. If anything, the sharing of a common part wouldmake it more mysterious why the truthmaker excludes their existence.Similarly it is theraison d’être of anytruthmaker for a general truth that such-and-such are all the factsthere are that it refuses to co-exist with any other facts even thoughit is distinct from them. So if we’re to hang onto the Humeanprinciple that anything can co-exist with anything else, we’dbetter give up the demand for truthmakers for negative and generaltruths—in other words, give up maximalism (Lewis 1992: 205,2001: 610–11).

Lewis also argued that we can’t stop here—just giving upmaximalism—because even the truthmakers for atomic statementsconflict with his Humeanism. An atomic, contingent statement‘a isF’ isn’t made true bya orF or even the mereological fusiona+Fbecause they can exist even in circumstances wherea andF are unrelated, say whena isG ratherthanF whilstb isF instead. For thisreason, many maximalists make common cause with optimalists and positanother fundamental kind of thing to perform the truthmaking role forcontingent predications: facts that consist in objects, properties andrelations inhering together; in this case the fact thata isF (Armstrong 1989a: 41–2, 1997: 115–6; Mellor1995: 24).

Now facts aren’t mereological fusions, Lewis argued, becausefacts require more for their existence than the existence of theirconstituents, its also being required that their constituents inheretogether for facts to exist. Assuming that only mereological fusionshave parts, it follows that the constituents of facts aren’tparts of facts, hence that facts are entirely distinct from theirconstituents. But even thougha andF are entirelydistinct froma isF, the existence ofa isF necessitates the existence ofa andF.More generally, the obtaining of a fact necessitates the existence ofits constituents even though the fact and its constituents areentirely distinct. So facts conflict with Lewis’s Humeanismaccording to which any distinct things may coexist or fail to coexist.So we cannot posit facts as truthmakers for contingent statementswithout going against Humeanism (Lewis 1992: 200, 1998: 215–6,2001: 611). Armstrong replied that mereology isn’t the only formof composition, i.e. the constituents of facts are parts of them in anon-mereological sense, hence facts aren’t distinct from theirconstituents after all (Armstrong 1997: 119–122). Lewis’sreply was that the only way to make sense of something’s being aconstituent of a state of affairs, without being a mereological part,was that it lies in a necessary connexion to that state of affairs;but necessary connexions are what we should seek to avoid (Lewis 2001:611; MacBride and Janssen-Lauret 2022: 79–83).

Other maximalists and optimalists, posit tropes rather than facts astruthmakers for contingent predications (Martin 1980; Mulligan,Simons, & Smith 1984: 295–304, Lowe 2006: 186–7,204–5) Tropes, in the non-transferrable sense, are particularinstances of properties that are existentially dependent upon theirbearers. But Lewis’ reasoning can be easily extended to showthat non-transferrable tropes cannot serve as the truthmakers forcontingent statements without contradicting Humeanism. If tropef is a property thata bears rather than a part ofa, thenf is wholly distinct froma.Nevertheless, the existence off necessitates the existenceofa even though they are distinct Alternatively iff is a part of the bundle of tropes that constitutea andf is non-transferrable, then the existence off necessitates the existence of some other distinct tropesthat are also parts of this bundle. So Humeanism is violated eitherway.

In order to avoid contradicting Humeanism, Lewis recommended a furtherweakening of (Truth Supervenes upon Being). According toLewis, the kernel of truth in truthmaking is the idea thatpropositions have asubject matter. They areaboutthings so whether they are true or false depends on how those thingsstand. This led Lewis to endorse (2003: 25):

(Subject matter)

Any proposition has a subject matter, on which its truth valuesupervenes.

Equivalently,there cannot be a difference in the truthvalue of aproposition without a difference in its subject matter. Thismight consist in (1) an increase or decrease in the population ofthings that fall within the subject matter; or (2) a shift in thepattern of fundamental properties and relations those things exhibit(Lewis 2001: 612). Now the truth value of “a isF” supervenes upon its subject matter without thereneeding to be any existing thing distinct froma orF that necessitates their existence; it is enough that thestatement would have been false ifa had been something otherthanF. So it also follows, although Lewis didn’texplicitly trace out this consequence, that we can avoid contradictingHumeanism by abandoning optimalism in favour of (Subjectmatter).

In an intriguing twist to the plot, Lewis subsequently appeared towithdraw his doubts about truthmakers and embrace them after all(2003: 30, Lewis & Rosen 2003: 39). Here’s a rough sketch toget across the idea. There is a way of interpreting ‘fact’talk that doesn’t embroil speakers in a commitment to necessaryconnexions between distinct existences. To talk about the fact thata isF isn’t to talk about something distinctfrom botha andF. It’s talk aboutaitself, albeit in a qualified way, namelyasF or‘qua F’ as Lewis puts it. SoaquaF qualifies as a truthmaker for the statementthata isF becausea qua F cannot existunlessa isF. So ifaqua Fexists then the statement thata isF is true. Butthere are no restrictions thereby imposed on what can or cannotcoexist. That’s because whilsta qua F cannot existunlessa isF,a without the qualification‘qua F’ can exist even ifa isn’tF, for example asa qua G. So we can havetruthmakers for contingent predications likea isFafter all becausea can just be an ordinary thing. In thesame way that ordinary objects likea can serve astruthmakers for contingent predications, Lewis & Rosen (2003)suggest that the entire world—“the totality of everythingthere actually is”—can serve as the truthmaker fornegative existentials. Take the worldqua unaccompanied byunicorns. In the conversational context just set up, the world has nocounterparts that are inhabited by unicorns. So the worldquaunaccompanied by unicorns is essentially lacking in unicorns andtherefore qualifies as a truthmaker for the statement that there areno unicorns. When building the case for (Subject Matter)Lewis had deliberately remained neutral about the metaphysics ofmodality (2001: 605). But to explain what ‘qua F’constructions mean, Lewis broke his neutrality and availed himself ofhis favoured theory of counterparts according to which‘a is essentiallyF just in case all ofa’s counterparts (includinga itself) areF’ (2003: 27). So, roughly, ‘a quaF’ stands for all ofa’s counterparts that areF.

Has Lewis shown how it is possible to garner truthmakers forcontingent predications and negative existentials without positingtotality facts or tropes that ensnare us in a web of necessaryconnections? We need to be clear about what Lewis was doing. Hewasn’t belatedly recognising what he had previously denied, thatthe truthmaking role is genuine, but then ingeniously coming up withthe idea thatqua-versions of things perform this role justas effectively as states of affairs, only without necessaryconnections between distinct existences. Rather, Lewis’ aim inthis paper is to damn the very idea of truthmakers with faint praise.By showing howqua versions of things performed thetruthmaking role just as effectively as facts or tropes Lewis aimedto show how explanatorily light weight the truthmaking role trulywas.

There are various criticisms of detail to be made. MacBride (2005:130–2) points out that Lewis failed to provide truthmakers forrelational predications and argues that it is very difficult to seehow the lacuna can be filled when the class of eligible truthmakers isrestricted by Lewis to the class of ordinary things. So, for example,sequences cannot serve as truthmakers for relational predicationsbecause sequences aren’t ordinary things. Bricker (2015:178–9) raises a difficulty with Lewis’s use of counterparttheory. Lewis maintains that whether a is a truthmaker foraisF will depend upon whatever counterpart relation is evokedin context. Bricker argues that this is incompatible withinterpreting the maximalist principle that every truth has atruthmaker as a single assertion--because it will only be a singleassertion if there is a uniform interpretation in terms of a singleprivileged counterpart relation. Lewis might reply that the maximalistprinciple needn’t be taken as a single assertion but as a schemawhere different instances evoke different counterpart relationseven if we didn’t appreciate this hitherto. But, infact, there seems no reason for Lewis to make that concession becausehe is able to say what the maximalist principle amounts to in oneclosed formula which Bricker (2017: 174) provides:(TMC) For every true propositionP, thereexists some entityT and some admissible counterpart relationsuch that, for every worldW, ifT has a counterpart(under that relation) inW, thenP is true inW. Nonetheless Bricker’s own proposal (2017:177–80) about how to provide an account of truthmaking in termsof a single counterpart relation is of independent interest.

3. What Motivates the Doctrine of Truthmakers?

3.1 To catch a cheater

What is the motivation for adopting a theory of truthmakers, whethermaximalist or optimalist? Sider describes the “wholepoint” of adopting a theory of truthmakers thus: to“Catch the cheaters” who don’t believe intruthmakers (Sider 2001: 40–1; see also Merricks 2007:2–3). But this is a bit like saying that the point of a benefitsystem is to catch out benefit frauds. It’s only if there issome antecedent point in favour of truthmakers that there can beanything wrong with leaving them out. Nonetheless, it is possible thatwe can come to appreciate the need for truthmakers by appreciatingwhat is lacking in theories that neglect them. This is how C.B. Martinand Armstrong came to recognise the necessity for admittingtruthmakers (Armstrong 1989b: 8–11, 2004: 1–3). Considerphenomenalism: the view that the physical world is a construction outof sense-impressions. One obstacle for this view is the need to makesense in sense-impression terms of true claims we make about theunobserved world. Martin noticed that the phenomenalist could onlyappeal to brute, ungrounded counterfactuals about possible experienceto do so. But counterfactuals do not float free in a void. They mustbe responsive to an underlying reality, the reality that makes themtrue. For Martin this was the phenomenalists’ fatal error: theirinability to supply credible truthmakers for truths about unobservedobjects. The same error afflicted Ryle’s behaviourism with itsbrute counterfactuals about non-existent behaviour and Prior’spresentism according to which there is nothing outside the present andso there is nothing for past-tensed and future-tensed truths to beheld responsible to. We come to appreciate the need for truthmakersas the common need these different theories fail to fulfil.

According to Lewis, this demand for truthmakers represented anoverreaction to what was undoubtedly a flaw in phenomenalism (1992:217). We can already understand what’s wrong with phenomenalismwhen we appreciate that it fails to provide an account of the thingsupon which the truth of counterfactuals about sense impressionssupervene, i.e., when we see that it fails to satisfy (SubjectMatter). This leaves under-motivated the claim that phenomenalismshould also be faulted for failing to supply truthmakers to groundcounterfactuals about sense-impressions. The same reasoning applies tobehaviourism and presentism; they also fail to satisfy (SubjectMatter). So there’s no need to adopt truth makers to catchcheats. All we need to do is to recognise the strictures (SubjectMatter) places upon us.

It’s a further flaw of Martin and Armstrong’s reasoningthat even if we accede to the demand for truthmakers it doesn’tfollow that even idealism is ruled out. According to Armstrong if weforsake the demand for truthmakers we thereby challenge “therealistic insight that there is a world that exists independently ofour thoughts and statements, making the latter true or false”(1997: 128). But even an idealist could accept that there aretruthmakers whilst thinking of them as mind-dependent entities. Soacceding to the demand for truthmakers doesn’t tell uswhat’s wrong with idealism (Daly 2005: 95–7). Bergmann,the grandfather of the contemporary truthmaker movement, was explicitabout this: “the truth ofS must be groundedontologically. On this first move idealists and realists agree”(Bergmann 1961: 229). The realist-idealist distinction cuts across thedistinction between philosophers who admit truthmakers and those thatdon’t (Dodd 2002: 83–4).

The demand for truthmakers doesn’t help “catchcheaters” at all. Just acknowledge, e.g., some brutecounterfactual facts about sense data, or brute dispositions to behavein one way or another, or brute facts about what happened in the pastor will happen in the future. What’s unsatisfactory about theseposits isn’t that if they existed they’d fail to make truestatements about unobserved objects or statements about mental statesthat failed to manifest themselves in actual behaviour or statementsabout the past or future. The problem is that we have difficulty inunderstanding how such facts or dispositions could be explanatorilysound (Horwich 2009: 195–7). Whatever we find lacking intheories that posit such items, it isn’t that they fail toprovide truthmakers, because they do.

Here’s another way to make the point. The demand fortruthmakers turns out to be vacuous. Are the facts the“cheater” posits questionable in some further way as‘metaphysically strange’ or ‘spooky’? Thosefacts are specified in terms of counterfactual or dispositionaltruths, so those facts are questionable if and only if truths of thesekinds are. If there is some reason to find such truths questionable,then that alone is the reason for querying behaviourism orphenomenalism; the demand for truthmakers was extraneous.

An alternative line is this: ‘One must approach the question ofwhich truths have truthmakers on a case-by-case basis’ Asay(2020: 23–7, 2023: 24). One consequence is that a philosophicaltheory is not immediately open to criticism on the ground that itallows truths which lack truthmakers. The ‘catchingcheaters’ strategy is thereby weakened: it is not a defaultassumption that any given truth has a truthmaker and so the burden ofargument does not lie with (say) the phenomenalist or thebehaviourist. Whether their theories are at fault in not positingtruthmakers for certain truths becomes a matter of debate and lackseasy resolution.

3.2 Truth Depends on Being

Armstrong’s original motivation for introducing truthmakers involvedappeal to the following intuition.

It seems obvious that for every true contingent proposition there mustbe something in the world (in the largest sense of“something”) which makes the proposition true. Forconsider any true contingent proposition and imagine that it is false.We must automatically imagine some difference in the world. (Armstrong1973: 11; c.f., Bigelow 1988: 126)

Armstrong assumes that the word ‘some’ in ‘somedifference’ should be interpreted objectually, i.e. as havingthe function of ranging over a domain of a entities which are suchthat their presence and absence corresponds to the truth and falsityof continent propositions. With this assumption in place it is easy tothink that there must be some things that we’re quantifying overwhen we say that there’s some difference in the world thatconstitutes the difference between these circumstances,viz. truth makers. However, it shouldn’t be assumedwithout argument that quantifier words are objectual, i.e. range overan associated domain of entities (Prior 1971: 31–4). Williamsonargues in particular that that the truth maker principle in factinvolves irreducible quantification into sentence position and‘we shouldn’t assume that quantification into sentenceposition is objectual ‘For “value” is a noun, not asentence’ (1999: 263) So one might acknowledge the intuitionthat there is some difference between the circumstances in which aproposition is true and the circumstances in which it is false butwithout our having to think that there exists something thatwe’ve quantified over that makes it so.

There’s another logical presupposition made by Armstrong andother proponents of truthmakers that’s relevant here. The use ofthe truthmaking idiom is often conceived as equivalent to the use of anon-causal ‘because’. So saying:S is madetrue byT, is equivalent to saying:S is truebecauseT exists. The logical presupposition made byArmstronget al is that the relevant use of‘because’ expresses a relation between a truthbearer andsome worldly item, a fact or a trope. But this presupposition ischallenged by philosophers who hold that “because”so-employed is a connective conceived on the model of logicaloperators (“&”, “∼” etc.) i.e., as anexpressions that link sentences but without expressing a relationbetween things picked out by those sentences. But, they reason, if‘because’ is connective then so is the ‘makestrue’ construction because they are equivalent. But then, theyreason, there’s no need to introduce truthmakers as items thatstand at one end of thetruthmakingof relation with truestatements at the other, no need to because it’s onlysuperficial features of the grammar of our language that suggest thereis a truthmaking relation to stand at the ends of. (Künne 2003:150–; Hornsby 2005: 35–7; Melia 2005: 78–9;Schnieder 2006a: 29–37; Mulligan 2007).

Typically philosophers who maintain that “makes true” is aconnective do not argue for this conclusion directly but encourage usto dwell upon the fact that it natural to hear the“because” that occurs in equivalent constructions as aconnective. When we hear, e.g., “It is true that the rose is redbecause the rose is red” we don’t naturally hear it asexpressing a binary relation between two things. So we shouldn’thear, or at least don’t have to hear, “It’s truethat the rose is red in virtue of the rose’s being red” or“the rose’s being red makes it true that the rose isred” as a expressing a binary relation between a truth andtruthmaker either. Künne has gone further and suggested that thetruthmaking connective is really the “because” ofconceptual explanation (2003: 154–5; Schnieder 2006a:36–7). He hears the equivalence between,

(R)

He is a child of a sibling of one of your parents, which makes himyour first cousin

and,

(R*)

He is your first cousin because he is a child of a sibling of oneof your parents.

Künne tells us that the “because” in (R*) isthe “because” of “conceptual explanation”.Since (R) and (R*) are equivalent, he concludes thatthe “makes” construction in (R) is just acumbersome way of expressing the “because” of conceptualexplanation in (R*). Künne then invites us take the useof “makes” in (R) as a model for understandingthe truthmaking construction,

(S)

The fact that snow is white makes the statement that snow is whitetrue.

This enables us to see that (S) does “not affirm arelation of any kind between a truth vehicle and something in theworld” (Künne 2003: 155). Why? Because it is equivalentto,

(S*)

The statement that snow is white is true because snow iswhite.

a claim that makes no (explicit) mention of facts.

Does all this mean that we should join Bigelow in his retreat to(Truth Supervenes Upon Being) or step back with Lewis to(Subject Matter)? The problem is that these supervenienceprinciples don’t seem a satisfactory resting place either, notif our concern is to understand how true representations can touchupon an independent reality, i.e., something non-representational.First, it is familiar point that just appealing to a systematicpattern of modal co-variation between truths and their subjectmatters—so that there is no difference in the former without adifference in the latter—doesn’t provide us within anyinsight into the underlying mechanism or mechanisms that sustains thisdependency (Molnar 2000: 82–3; Heil 2003: 67; Daly 2005:97–8; Melia 2005: 82–3). Second, if possible worlds areconceived as maximal representations then these supervenienceprinciples (understood in the idiom of possible worlds) fail toarticulate what it is for a representation to touch upon being,something non-representational: “For the idea that every truthdepends on being is not the idea that every truth isentailed by propositions of a certain sort” (Merricks2007: 86).

A third reason for being unsatisfied with Lewis’ (SubjectMatter) is based upon the observation that the supervenienceinvolved is symmetric. Just as there is no difference in thedistribution of truthvalues amongst the body of propositions withouta reciprocating difference in their subject matter, there is nodifference in their subject matter without a difference in thedistribution of their truthvalues (Armstrong 2004: 7–8). But wealso have the firm intuition that the truth or falsity of aproposition depends upon the state of the world in a way in which thestate of the world doesn’t depend upon the proposition’struth or falsity. This means that a supervenience principle like(Subject Matter) cannot be used to articulate the asymmetricway in which truth so depends upon being; for this, it is argued, weneed to rely upon a robust asymmetric notion of truthmaking(Rodriguez-Pereyra 2005: 18–19). Bricker (2015: 180–183)replies on Lewis’s behalf that the oft-heard complaint thatsupervenience by itself is not a dependence or ontological priorityrelation is besides the point. Rather, Bricker argues, themetaphysical punch of Lewis’s doctrine that truth supervenesupon being “has little to do with the ‘superveniencepart’ and everything to do with the ‘being’ part andthe conception of fundamentality that informs it”, where by‘fundamental’ Bricker means Lewis’s theory ofnatural properties and relations.

But is there really anything so mysterious about the asymmetricdependence of truth upon being that we need anything as heavy duty astruthmaking or supervenience+naturalness to explain it? A number ofproposals have been made for explaining the felt asymmetry in otherterms. Horwich (1998: 105; 2008: 265–66) argues that asymmetricdependence of truth upon being arises from the fact that we can deducep from the proposition thatp is true. But we canequally deducep fromp is true so this fails toestablish an asymmetric dependence (Künne 2003: 151–52;Rodriguez-Pereyra 2005: 27).

Hornsby argues instead that there is explanatory asymmetry between itsbeing the case thatp and the proposition thatp istrue, because the latter requires more to be the case than theformer, (e.g.) that there are propositions (Hornsby 2005: 44). Doddsuggests a cognate alternative: that the felt asymmetry of truth uponbeing arises from the fact that the identity of the proposition that pis partially determined by the worldly items it’s about, so wecan’t understand what is required for the proposition thatp to be true without already having an understanding of whatit is forp to be the case (Dodd 2007: 398–400). Moreradically, Tallant (2018) seeks to entirely replace truthmaker theorywith explanatory considerations: every truth is explained withoutappeal to any truthmaker: <p> is true because p and <p> istrue iff p.

MacBride (2014) offers a semantic account of the felt asymmetry interms of the interlocking mechanism of reference and satisfaction thatexplains the truth of a proposition. Whilst we can deduce from thetruth of the proposition thatp thatp is the case,MacBride argues that we can’t (ultimately) explain its being thecase thatp in terms of the truth of the proposition thatp because its being the case thatp is alreadyassumed by the truth of that proposition, that is, has alreadyperformed a role in the semantic mechanism whereby the truthvalue isdetermined. By contrast, its being the case thatpisn’t determined by a semantic mechanism but by whatever worldlyfactors, if any, that gave rise top’s being the case.Saenz (2018) replies that whilst reference and satisfaction may beused to explain that propositions are true, they still “do not,in any sense, account for the world ‘making it’[sic] that propositions are some way” (a similar pointis made by Mulligan et al 1984: 288, see sec. 3.5 below for furtherdiscussion). But Saenz risks begging the question by making theadditional demand on the character of the felt asymmetry of truth andbeing that it consists in more than an asymmetric relationship betweentruth and being. Saenz holds that the felt asymmetry consists in therequirement that the world makes propositions true but whether we needto appeal to the idea of the world making propositions true in thefirst place is the point at issue. Finally, Liggins (2012) argues thatthe felt asymmetry between truth and being is best explained in termsof the asymmetry of grounding, although the asymmetry of grounding iscontested as is grounding itself.

3.3 Truth: Correspondence and Deflationism

An alternative motivation for adopting the truthmaker principle isthat it inherits whatever the attractions where for the correspondencetheory of truth.

Anybody who is attracted to the correspondence theory of truth shouldbe drawn to the truth-maker [sic]. Correspondence demands acorrespondent, and a correspondent for a truth is a truth-maker.(Armstrong 1997: 14; see also 1997: 128–9, 2004: 16–7)

According to Armstrong, the “truth-maker principle” (akamaximalism) just is what we are left with once we drop the assumptionfrom the correspondence theory that the relation between truth bearersand truthmakers is one-one. Of course, the truthmaking relation,however it is explicated, cannot be the relation of correspondence interms of whichtruth is defined—for whereas the latteris symmetric, the former isn’t (Beebee & Dodd 2005b:13–4). But this doesn’t prevent truth being defined usingthetruthmaking relation, albeit in a more roundabout wayaccording to the following pattern,

(C)

S is true ⇔ (∃x)(Sis-made-true-byx).

Of course such a definition will only succeed if the relationexpressed by “is-made-true-by” can itself be explicatedwithout relying upon the notion oftruth itself or othernotions that implicitly presuppose it, e.g., entailment (Merricks2007: 15). This is no doubt one of the reasons that principles oftruthmaking are typically not put forward as definitions of truth(David 2009: 144). Another objection made by Horwich is that it isimplausible to suppose that an ordinary person understands the notionof truthvia the heterogeneous principles that govern theprovision of truthmakers for different types of propositions.It’s more plausible to suppose that we first grasp what truthis, and only subsequently figure out what truthmakers are requiredfor the various kinds of propositions there are (Horwich 2009:188).

Several philosophers have argued that the kinds of truthmaking we havebeen considering don’t presuppose the notion oftruthbut operate at a far more subterranean level. Bigelow writes,“The force behind Truth-maker lies deeper than worries about thenature of truth and of truth-bearers” (Bigelow 1988: 127, 2009:396–7; Robinson 2000: 152; Lewis 2001: 605–6; Horwich2009: 188–9, Bricker 2015: 169). Here’s their reasoning.Suppose we understand what it is to be truthmaker in terms ofentailment. Then whatever the range of truths we think are capable ofbeing rendered true, the “guts” of our truthmakerprinciple can be stated using the schema,

(Schema)

IfP, then there must be something in the world whoseexistence entails thatP.

This schema is equivalent to the infinitely many conditionals thatfall under it:

(i1)

If the donkey is brown, then there must be something in the worldwhose existence entails that the donkey is brown;

(i2)

if the Parthenon is on the Acropolis then there must be somethingin the world whose existence entails that the Parthenon is on theAcropolis; and so on.

Note that neither “true” nor “truth” shows upanywhere in the schema or its instances. Arguably the only role thatthe notion oftruth performs is the one thatminimalist or deflationary theories of truth emphasize, that ofenabling us to capture all of that unending string of conditionals ina single slogan,

(Slogan)

Forany truth, there must be something in the world whoseexistence entailsthat truth.

But since truth is serving hereonly as a device ofgeneralization, the real subject matter of (Slogan) isalready expressed by the conditionals (i1), (i2)etc. Since they make no explicit mention of eitherpropositions or truth, a theory of truthmakers is neither a theoryabout propositions nor a theory about truth. If so, then the theory oftruthmakers can neither gain inspiration from, nor be tarred by thesame brush as the correspondence theory of truth. Nor need the theoryof truthmakers be bedeviled by concerns about the nature of truthbearers.

One may nevertheless wonder whether Bigelow and Lewis have thrown thebaby out with the bathwater. MacBride (2013a) argues that if we do notallow ourselves the general thought that truthbearers are true orfalse depending upon how things stand in the world then it is unclearwhat, if any, credibility (i1), (i2) etc. have. Forwhy should there be something in the world whose existencenecessitates that (e.g.) cats purr? Why can’t cats purr, eventhough there is nothing whose existence entails that truth? SinceSlogan is intended to be just shorthand for its instances,(i 1), (i 2) etc. it followsSlogancan’t be any more credible or motivated than its instances. If,however, we allow ourselves a conception of truth which isn’tdeflationary, i.e. a substantial conception whereby truth is conceivedas a relation borne by a truthbearer to something worldly that existsindependently of us, then, MacBride argues, we will have anindependent reason for positing something worldly the existence ofwhich necessitates the truth that cats purr etc.

Asay draws another connection with minimalism or deflationary theoriesof truth. He argues that truthmaking should not be used in the serviceof defining truth because, “As on deflationary accounts (e.g.,Horwich 1998), it may be that all there is to the property of truth isthat it is the property that a sentence ‘p’ has if andonly if p” (2023: 14). But, as Alston (1996: 37–8)thought, some kind of deflationism might be the correct theory of theconcept of truth, whilst leaving open the possibility that there ismore to be said about the property of truth than the concept of truthsupplies—which truthmaking might supply. Moreover, unless Asay thinksthe truthmaker principle analytically follows from minimalism abouttruth, he is committed to saying that, at least in many instances,there is more to be said about the property of truth than what Horwichallows. (For further discussion of deflationism in connection withtruthmaking see McGrath 2003, Vision 2005 and Thomas 2011).

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Acknowledgments

This entry was originally based upon a course on truth makers thatMacbride gave in Cambridge, Michaelmas 2012. For subsequent revisionshe is grateful to Helen Beebee, John Bigelow, Jeremy Butterfield, RossCameron, Julian Dodd, Dominic Gregory, Ghislain Guigon, Jane Heal,John Heil, Herbert Hochberg, Jennifer Hornsby,Frédérique Janssen-Lauret, Nick Jones, David Liggins,Jonathan Lowe, Mike Martin, Hugh Mellor, Peter Milne, Kevin Mulligan,Laurie Paul, Bryan Pickel, Stephen Read, Gonzalo Rodriguez-Pereyra,Jonathan Schaffer, Jeroen Smid, Peter Simons, Tim Williamson, Ed Zaltaand two anonymous referees for SEP.