From Humean Truthmaker Theory to Priority Monism

NOUS 44:1 (2010) 178–198

From Humean Truthmaker Theoryto Priority Monism1

ROSS P. CAMERON

University of Leeds

1. Introduction

The Humean is a resister of mysterious brute necessity; when there is ne-cessity, she claims, we must be able to give an explanation of the necessity.In particular, the Humean objects to brute necessary connections betweendistinct contingent existents. The truthmaker theorist holds that when aproposition is true, there must be some thing (or things) that makes it true:some things which couldn’t exist and the proposition fail to be true.2 The pri-ority monist holds that while there may be many things, there is necessarilyonly one fundamental thing, with the many other things being ontologicallydependent on this one fundamental thing.

Connections have been drawn between truthmaker theory and prioritymonism. Jonathan Schaffer—who has been largely responsible for the recentresurgence of interest in priority monism—has argued that one of the benefitsof priority monism is that it allows for a neat and parsimonious theoryof truthmakers which solves the problem of negative facts.3 That gives usone way of arguing from truthmaker theory to priority monism: prioritymonism affords an advantageous theory of truthmaking, so the truthmakertheorist has good reason to be a priority monist. In this paper I intend tooffer a different argument from truthmaker theory to priority monism: thetruthmaker theorist has to be a priority monist, provided she doesn’t wantto be committed to objectionable necessary connections between distinctcontingent existents.

2. The Problem of Contingent Intrinsic Predication

Here is an object called ‘Ball’. Ball is red, but it might not have been;it might have been blue. So the truthmaker for <Ball is red> cannot be

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From Humean Truthmaker Theory to Priority Monism 179

Ball, since Ball could exist and that proposition be false, and the existenceof a truthmaker necessitates the truth of any proposition which the truth-maker actually makes true. So what is it then that makes it true that Ball isred?

This is the problem of contingent intrinsic predication. In the literature,two options dominate as to its solution. One option is that the truthmakerfor an object a contingently satisfying the intrinsic predication ‘ . . . is F’ is thestate of affairs of a instantiating a universal: either the universal of F-nessor some other universal(s), instantiation of which is sufficient for an objectto satisfy the predicate ‘ . . . is F’.4 Another option is that the truthmaker isa trope (or some tropes): either the particular being F of a or the particularbeing G of a (together with the particular being H of a, together with . . . etc),the having of which is sufficient for an object to satisfy the predicate ‘ . . .is F’.5

And, of course, there are further sub-options once we choose betweenthese two main options. Suppose we opt for states of affairs. We are then facedwith the question: are the states of affairs ontologically dependent on theparticulars and universals that are their constituents, or are the constituentsdependent on the state of affairs, or is neither dependent on the other? (I’llsay more about ontological dependence later.) If we opt for tropes we mustask: what is the relation between objects and their particularised properties?Is there more to an object than its particularised properties (is substance-attribute theory true6), or do the tropes taken together exhaust what there isto the object (is bundle theory true7)?

3. The Humean Denial of Necessary Connections

How is one to choose between the options? I will approach my answer tothis question via discussion of Lewis’ objection to truthmaker theory. Lewischarged that in solving the problem of contingent intrinsic predication thetruthmaker theorist would violate the Humean denial of necessary connec-tions between distinct contingent existents. He asks us to consider some thingA which is intrinsically but contingently F. The proposition <A is F> musthave a truthmaker, B, which is distinct from A but which couldn’t exist and<A is F> be false. But the truth of <A is F> necessitates the existence ofA; so since the truth of that proposition is necessitated by the existence of Bthen, by the transitivity of strict implication, the existence of B necessitatesthe existence of A. Lewis says:

B is entirely distinct from A . . . yet B’s existence is necessarily connected towhether or not A has F. Necessarily, if A has F . . . then B must exist; neces-sarily, if A had lacked F . . . then B would not have existed . . . The demand fortruthmakers just is a demand for necessary connections.8

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Now actually, the first of these necessary connections isn’t a commitmentof any sane version of truthmaker theory. The truthmaker theorist does nothold that in general there is only one possible truthmaker for any giventruth; it does not follow, then, that if A is F then B would, of necessity, haveexisted, for <A is F> might have been made true by something else. The strictimplication from the truth of the proposition to the existence of that whichin fact makes it true is invalid because there are many potential truthmakersfor the proposition. But the second of the necessary connections is good,given truthmaker necessitarianism: necessarily, if the truthmaker exists, theproposition is true; so if the truth of the proposition necessitates the existenceof a thing distinct from that truthmaker, as it will in the case of contingentintrinsic predications, then we have a necessary connection between distinctcontingent existents.

What should the truthmaker theorist say? She might take Lewis to taskon his pronouncement that B is “entirely” distinct from A. If one thoughtthat B is the state of affairs of A being F then one would hold that B isn’tentirely distinct from A, because it has A as a constituent. If one thoughtthat B was A’s particular F-ness and held that A was itself simply a bundleof tropes then, again, one would hold that B isn’t entirely distinct from A,because B is one of the component tropes that make up A. The thoughtis that whilst A and B are definitely not one and the same thing, they arenot wholly distinct either: on one option (states of affairs) A is a constituentof B, on the other option (trope bundle theory) B is a constituent of A.But necessary connections, our truthmaker theorist might claim, are onlyobjectionable when they hold between wholly distinct contingent existents. Anecessary connection between a thing and its constituents is unobjectionable.So whilst some of the options above (such as substance-attribute trope theory)might commit us to objectionable necessary connections, not all of themdo; so adherence to the Humean denial of necessary connections at mostplaces constraints on the truthmaker theorist’s ontology, it doesn’t rule outtruthmaker theory altogether.

This is the response Richard Fumerton makes on behalf of the truthmakertheorist to the Lewisian charge as put forward by Fraser MacBride againstappealing to states of affairs as truthmakers.9 Fumerton says,

MacBride claims that states of affairs offend against the Humean principle thatthere can be no necessary connections between distinct states of affairs. The stateof affairs of a’s being F is distinct from both a and F—a can exist without thestate of affairs a’s being F and so can F . If Hume didn’t recognize that there canbe complex wholes that require the existence of their parts but are not simplyidentical with the set or sum of their parts, he should have. Anyone interestedin defending states of affairs is going to junk the version of the principle thatMacBride attributes to Hume.10

The idea that necessary connections are objectionable if they hold betweenwholly distinct contingent existents but benign if the objects participating in


the necessary connection overlap is not uncommon. But what is the princi-pled difference between the cases? I can see why one would think there wasa difference if one held the following two claims.

Compositional Essentialism: For all objects x and y, if x is a part of y then,necessarily, if y exists then x exists and is a part of y.

Formally11: ∀x∀y(x<y → �(E!y → (E!x & x<y))).

Compositional Sufficiency: For all objects x and y, if x is a part of y then,necessarily, if x exists then y exists and has x as a part.

Formally: ∀x∀y(x<y → �(E!x → (E!y & x<y))).Were compositional essentialism and compositional sufficiency true (and

provided we had an explanation for these essentialist theses) then there wouldbe no puzzle in the obtaining of necessary connections between overlappingobjects. Suppose we have two houses, H1 and H2, which share a wall, W.There would be no puzzle in the existence of H1 necessitating the existenceof H2 (or vice-versa), for we could argue as follows. Necessarily if H2 didnot exist then W would not exist since, by compositional sufficiency, W isessentially a part of H2. But if W did not exist then H1 would not existsince, by compositional essentialism, H1 essentially has W as a part. Bythe transitivity of the strict conditional, then, it follows that, necessarily, ifH2 did not exist then H1 would not exist. Similar reasoning will yield that,necessarily, if H1 did not exist then H2 would not exist. So H1 and H2, whileboth contingent existents, necessarily coexist.

So I can understand why, on the assumptions of compositional essential-ism and compositional sufficiency, necessary connections are only bad if theyobtain between wholly distinct entities. Unfortunately, neither of those thesesis, in general, true. Compositional sufficiency is not in general true: entitiesneed not have composed the thing they actually compose. Had my atomsbeen scattered across the universe, it’s not that I would have been scatteredacross the universe. The bricks that compose my house might never have beenbrought together, but they would have remained the very same bricks. Like-wise, compositional essentialism is not in general true: at least some entitiescould have differed in at least some of their parts. I would survive the lossof a leg; a table survives the loss of one of its atoms; a house survives one ofits bricks being replaced by another. (Now, of course, the defenders of com-positional essentialism will wheel out some elaborate story about why thesepropositions seem to be true even though they aren’t—such as Chisholm’stheory of entia successiva12—but given the support these propositions havefrom intuition we should only accept such a story if we are given strongreason to accept compositional essentialism—and I have never seen such areason.)

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Given that a thing could have had different parts, and that the parts of athing might not have been parts of that thing, there seems to be no reason tohold that necessary connections between overlapping objects are in generalany better than necessary connections between wholly distinct objects. Itwould be as remarkable were the existence of one of the overlapping housesH1 and H2 to necessitate the existence of the other as if two wholly distincthouses were such that they necessarily coexisted. And so I can’t see that it’sof any consolation to the truthmaker theorist that she can claim that thenecessary connections she’s committed to hold not between wholly distinctthings but only between a thing and its constituents.

This might seem unduly pessimistic. One might argue as follows. “Look,it’s true that you could have had different parts (you might have been bornwithout legs, say). And it’s true that the house could have been made ofdifferent bricks. But it hardly follows that a state of affairs could have haddifferent constituents. Why? Because, as is well known, the composition re-lation that builds states of affairs out of particulars and universals is notmereological composition.13 What holds of one composition relation needn’thold of another. So yes, a mereological whole has its mereological parts con-tingently. But the composition relation that binds particulars and universalstogether into a state of affairs binds them tighter than a mere mereologicalsumming; that is why the existence of the state of affairs necessitates theexistence of its constituents.”

I have no problems with the consistency of this response; I just don’t seethe motivation for such a position. It’s a perfectly consistent option to holdthat there are a plurality of compositional relations and that CompositionalEssentialism and/or Compositional Sufficiency are true when restricted tosome of the compositional relations and false when restricted to others. Pro-vided that the compositional relation that binds particulars and universalstogether into a state of affairs obeys Compositional Essentialism, or providedthat that the compositional relation that binds tropes together into a bun-dle obeys Compositional Sufficiency, then at least some truthmaker theoristsface no objection from the Humean denial of necessary connections. Myproblem with this is that I don’t see what independent motivation there isto think that there are such composition relations obeying such essential-ist principles. Were it in general true that when a complex object is com-posed of simpler entities it has those simpler entities as parts/constituentsessentially, or were it in general true that things essentially belonged to anycomplexes to which they actually belong, then I would have no qualmsabout accepting the claim that this holds a fortiori in the case of a partic-ular or a universal belonging to a state of affairs, or a trope belonging toa bundle. But since these claims aren’t in general true, I need convincingthat it’s true in these cases. One can say that it’s a different compositionrelation in this case—one that obeys the requisite essentialist principle; butunless one can give an independent reason (i.e. a reason other than: this is


how things must be for truthmaker theory to work) for accepting this, onehasn’t really explained away the necessary connection in question, merelyembraced it.

The initial hope—and what is suggested in Fumerton’s remarks above—was that the truthmaker theorist is simply committed to the kind of neces-sary connections that any ontologist commits to on reflection. The necessaryconnections truthmaker brings, so the hopeful thought goes, are just thosenecessary connections that we all believe in, whether we’re truthmaker the-orists or not: necessary connections between complexes and their parts. Butthe hopeful thought is hopeless: we don’t all believe in these necessary con-nections. So the truthmaker theorist can’t claim innocence on the groundsthat her necessary connections are no worse than anyone else’s. She has nec-essary connections, while her opponent simply need not. Appealing to a newcomposition relation that conveniently churns out the right essentialist re-sults isn’t going to satisfy her Humean opponent. The Humean will simplyask: what right do you have to assume that this composition relation obeysthe necessary essentialist principles when it’s not in general true that compo-sitional relations obey them? I can’t think of a good answer to this question.The truthmaker theorist who went down this route would simply have to an-swer that it’s stipulated that this is how these compositional relations work.But then if we’re going to allow ourselves to say that why go in for all thistalk of compositional pluralism in the first place? Why not simply stipulatethat the necessary connections we commit to in truthmaking are acceptableones? Proclaiming some necessary connections acceptable whilst not beingable to point to a principled difference between those and the unacceptableones is no worse than claiming that some compositional relations obey therequisite essentialist principles whilst not being able to point to a principleddifference between those compositional relations and the ones that don’tobey the essentialist principles. In neither case are we explaining the neces-sary connections that the Humean objects to: we’re simply building it intoour theory that they’re unobjectionable. Now it’s not obvious that in thatcase the Humean wins the debate (why is the denial of necessary connectionsso inviolable?14); but it’d be nice if we can do more than aim for a stand-offhere.

4. Acceptable Necessary Connections and Ontological Dependence

I think it right that the truthmaker theorist ought to attempt to explainwhy her necessary connections are of a benign kind; but for the reasonsabove I don’t think she should say this is because the necessitated and thenecessitating entity overlap in some sense. Rather, she should look for someother principled reason for accepting some necessary connections, and saywhy the necessary connections truthmaker theory commits one to are of thiskind.

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To make headway on such a project, we can start by looking at certainnecessary connections that one might be committed to independently ofbeing a truthmaker theorist. Here are two commonly held claims:

NUS: Necessarily, if there are some things, the Xs, then there is a thing whichis the sum of the Xs.15

NST: For all possible things x, Necessarily, x exists if and only if the singletonof x exists.16

If NST is true then there are necessary connections galore: pick any thingyou like and you will be able to find some other thing such that the existenceof either necessitates the existence of the other. But NST is widely held.17

NUS doesn’t commit us to necessary connections in quite the same sense,because nothing about NUS commits us to the claim that it is the same thingin each world containing the Xs that is the sum of the Xs.18 For all that issaid by NUS, the Xs could compose some thing y but it be possible thatthey all exist and y not exist, provided the Xs would in that world composesome other thing z (z �=y). But nevertheless, NUS still seems to violate thespirit of the Humean denial of necessary connections. Assuming, with theorthodoxy, that strong composition as identity is false, then when the Xscompose something there is a new thing that is the sum of the Xs. Why onearth, then, should it be impossible for the Xs all to exist and it fail to bethe case that we get some new thing. Natural principles of recombinationsuggest that we should be able to get a possible world by keeping the Xsbut taking away the thing they compose, and we shouldn’t have to introducesome new thing into the world in order to keep it possible. Imagine I toldyou that whilst you could exist and I fail to exist, this is only possible if youintroduce some new thing into the world (that is, the only possible worldscontaining you but not me are worlds containing some thing which doesn’tactually exist). Wouldn’t that be a bizarre claim, against the whole spirit ofthe Humean denial of necessary connections? Whence then the difference inthe case of composition?19

In previous work I’ve attempted to explain away the necessary connectionsbrought about by NUS and NST.20 The starting thought is that even though asingleton is not its member and a sum is not its parts, there is a relationship ofontological dependence between the distinct entities. A sum is ontologicallydependent on its parts, if priority pluralism is true—and vice-versa if prioritymonism is true; an impure21 set is ontologically dependent on its members.

I proposed the following analysis of ontological dependence: X is onto-logically dependent on the Ys iff the Ys, and not X itself, are truthmakers for<X exists>. The idea is that what there is fundamentally are just those thingsthat are needed to make true the true sentences of our best theory. Otherthings might exist; but these things will be merely derivative entities: theywill be ontologically dependent on some of the fundamental entities, which


is to say that they exist in virtue of the fundamental entities, which is to saythat the fact that they exist is made true by some of the fundamental entities.

Let’s suppose priority pluralism and universalism are true: that is, thatfundamentally everything is mereologically simple, but that for any collectionof things there is a complex object that is composed of those things and whichis ontologically dependent on them. Universalists are fond of defending theirview by claiming that complex objects are nothing ‘over and above’ thesimples composing them: that they were an “ontological free lunch” and“no addition of being”.22 They tend to be less fond of telling us what thismeans.23 But once we accept that existence claims can be true without beingmade true by what is said to exist we have to hand a satisfying explanation.Complex objects are no addition of being—they are an ontological freelunch; nothing ‘over and above’ the simples that compose them—because theontology needed to ensure the existence of complex objects is just an ontologyof simples. It is true to say that complex objects exist; but what grounds thetruth of statements concerning the existence of complex objects—what makesthem true—are just the simples. And so the truth of NUS is un-mysterious:the reason it’s necessary that when you’ve got some things you’ve also gottheir sum is simply that the things themselves will make it true that there issome thing that is their sum.

If complex objects and their simple parts are both fundamental, combi-natorial reasoning about possibilities seems to entail that we should be ableto take the sums away and leave the simples as they are. But if the fact thatthe sum exists is made true by those simples then the necessary connectionis perfectly explainable; it follows immediately from truthmaker necessitar-ianism.24 Since a, b and c make it true that there is a sum of a, b and c,it follows straightforwardly from truthmaker necessitarianism that in everypossible world in which you have a, b and c it is also true that the sum of a, band c exists. This necessary connection, I claim, is perfectly benign. We don’thave a necessary connection between elements of fundamental ontology, onlya necessary connection between a fundamental being and something which isontologically dependent on it, and this is explained simply by what it meansfor one thing to be dependent on another.25

Similarly, suppose (one form of ) priority monism is true. Suppose thatfundamentally there is only the one complex object that is the sum of everything: the world. Every proper part of the world is, we suppose, ontologicallydependent on the world, which is to say that for every thing x, the world,and not x (except in the case where x is the world), makes it true that x exists.The explanation for NUS in this case, if it is true, is simply that if the worldmakes it true that some things, the Xs, exist and makes it true that somethings, the Ys, exist, then the world also makes it true that there is something that is the sum of the Xs and the Ys.

This alone can’t explain every necessary connection however, for the sim-ple reason that necessary connections can run both ways while ontological

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dependence is asymmetric. (If the Xs but not the Ys make it true that the Ysexist then the Ys cannot make it true that the Xs exist; either the Ys do sometruthmaking work or they don’t: if they do then they make it true that theyexist, if they don’t then a fortiori they don’t make it true that the Xs exist.)Consider one half of NST: necessarily, if x exists, x’s singleton exists. Thisis perfectly explainable, if what I’ve said above is right. {x} is ontologicallydependent on x; which is to say just that <{x} exists> is made true not by{x} but by x. So of course the existence of x necessitates the truth of <{x}exists>: that just follows, as above, from truthmaker necessitarianism. Butwhat explains the other half of NST: necessarily, if {x} exists, then x exists?It’s not the case that {x} makes true <x exists>, so the same story can’t apply.

I think what explains why the existence of {x} necessitates the existenceof x is that x is a truthmaker for <{x} exists> in every world in which <{x}exists> is true. <{x} exists> couldn’t have been made true without beingmade true by x. Since it’s necessary that every truth has a truthmaker, itfollows that if a proposition p couldn’t have been true without being madetrue by a, then p can’t be true and a not exist. So if <{x} exists> couldn’t havebeen made true without being made true by x, then <{x} exists> can’t betrue without x existing. Since {x} can’t exist without <{x} exists> being true,it follows that {x} can’t exist without x existing. So this necessary connectionis perfectly explainable if it is explainable why <{x} exists> couldn’t havebeen made true without having been made true by x. So what explains that?I think that’s simply a matter of linguistic convention. It’s just part of themeaning of talk about sets that we don’t let anything deserve the name ‘thesingleton of x’ unless it has x as its sole member, and it’s part of the theoryof truthmaking under offer that this can’t be the case unless x makes it truethat that set exists. And so it’s just part of the meaning of talk about setsthat <{x} exists> will not count as true unless it is made true by x. There’sno deep necessity here, just a reflection on how we use our language.

And of course, if what I’ve said above is correct, then if some fundamentalthing A makes it true both that B exists and that C exists, and if it is alsonecessary that <B exists> and <C exists> are made true by A, if they aremade true at all, then there will be a perfectly benign necessary connectionbetween B and C. Necessarily, if B exists then C exists; but that’s simplydue to the fact that if B exists then A must exist to make it true that Bexists; and if A exists then C must also exist since A makes it true that Cexists.

I now make the conjecture that every necessary connection is of this kindand to be explained in this manner. That is, that whenever there is a neces-sary connection it is explained by the relations of ontological dependencethat hold between the necessitated and the necessitating entities; which isto say that it is explained by the truthmaking relation that holds betweensome entities and the fact that other entities exist. Here is the principle indetail:


No Unexplained Necessary Connections: For all objects/pluralities of objectsx/the Xs and y/the Ys, if the existence of x/the Xs necessitates the existence ofy/the Ys then either:

(i) x/the Xs is a truthmaker/are truthmakers for <y exists>/<the Ysexist>, (which is to say that y/the Ys is/are ontologically dependent onx/the Xs);

or (ii) y/the Ys is/are necessarily a truthmaker (or is necessarily one of theplurality that are the truthmakers26) for <x exists>/<the Xs exist>;meaning: necessarily, if x/the Xs exists, y/the Ys make(s) it true (or atleast is/are among the plurality of entities that makes it true) that x/theXs exist(s), (which is to say that in every world in which x/the Xs exists,x/the Xs is/are ontologically dependent on y/the Ys (or is ontologicallydependent on a plurality of entities amongst which y/the Ys number));

or (iii) both x/the Xs and y/the Ys exist in virtue of z/the Zs and necessarilyif either <x exists>/<the Xs exist> or <y exists>/<the Ys exist> aremade true, then they are made true by z/the Zs.

(Option (iii) will play no part in the following discussion; I insert it forthe sake of completeness, but in none of the options which I go on to discussare the necessitated and the necessitating entities plausibly both derivativeon a common ground. Each of the cases to be considered is a case where atleast some of the entities involved in the necessary connection are supposedto be fundamental existents; and so it is options (i) and (ii) above that arecandidates to explain such a connection.)

On what grounds do I assert No Unexplained Necessary Connections? Itis a cautious conjecture; if what I’ve said above is correct, then we alreadyknow that there are some necessary connections of the kinds that fall underone of the options above. These necessary connections, I have argued, areperfectly benign. Now, perhaps there are other kinds of acceptable necessaryconnections: necessary connections that hold between entities where no re-lation of ontological dependence holds; but if we constrain our truthmakertheory only to admit necessary connections of the kind permitted by NoUnexplained Necessary Connections then we are not reliant on that being thecase. If the necessary connections we commit to in doing truthmaker theoryare benign according to No Unexplained Necessary Connections then they arebenign whether or not No Unexplained Necessary Connections is correct insaying that the only necessary connections that are benign are those of types(i), (ii) or (iii); and so we do not leave ourselves hostage to fortune whenanswering the Humean objection. I propose, then, to adopt an ontology thatsatisfies No Unexplained Necessary Connections. This lets us rule out someof the ontological options considered earlier.

5. Narrowing Down the Options

Suppose we hold that the truthmakers for contingent intrinsic predicationsare states of affairs of particulars instantiating universals. Then we had better

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hold that the state of affairs is the only fundamental existent and that theparticulars and the universals are ontologically dependent on the state ofaffairs.27 That is, if there is a state of affairs of A being F, both the par-ticular A and the universal F had better be ontologically dependent on thestate of affairs; which is to say that the state of affairs had better make<A exists> and <F exists> true, not A and F themselves.28 For this is theonly way in which it is explainable that the existence of the state of affairsnecessitates the existence of A and the existence of F (and, indeed, that itnecessitates not only their existence but also that it necessitates that the for-mer instantiate the latter). If each of A, F and the state of affairs of A beingF were fundamental existents then a necessary connection here would be asunpalatable as a necessary connection between you and I. There must befree recombination amongst the fundamental existents; whenever there is anecessary connection, there must be ontological dependence to explain thenecessary connection. If the state of affairs was ontologically dependent onthe constituent particular and universal, then likewise it would be inexpli-cable why the existence of the state of affairs necessitated the existence ofthe particular and the universal that are its constituents. For although thereis ontological dependence here, it is the existence of the dependent entitynecessitating the existence of the fundamental entities; and that’s only ex-plicable if it’s necessary that the fundamental entities make it true that thedependent entity exists—that obviously isn’t the case here, however, sinceboth A and F can exist and the state of affairs of A being F not exist. (Thatwould be the case were A not F but some other thing was F.) (Compare thecase of the existence of the singleton of a, a dependent entity, necessitatingthe existence of a, a fundamental entity. That’s only acceptable because it’snecessary that if {a} exists then a makes it true that {a} exists. Likewise, thestates of affairs case would only be acceptable if it were necessary that if thestate of affairs existed then the constituents would make it true that the stateof affairs existed. But we know that that is false because it’s not actual thatthe constituents make it true that the state of affairs exists; and we knowthat because the constituents could exist and the state of affairs not exist,and this entails, given truthmaker necessitarianism, that the constituents donot make it true that the state of affairs exists.)

So if we are to appeal to states of affairs as truthmakers, and if we are tosatisfy No Unexplained Necessary Connections, then the states of affairs hadbetter number amongst the fundamental components of our ontology, andthe particulars and universals that are their constituents had better not.

Call the view that only the states of affairs, and not their constituents, arefundamental ‘Tractarian Factism’, because this seems to be the position ofWittgenstein in the Tractatus.29 Perhaps that’s what any believer in states ofaffairs would claim to believe anyway; but I think that some of the projectsstates of affairs theorists concern themselves with are a red herring if only thestates of affairs are fundamental. Consider for example the work on specify-ing the mode of composition by which states of affairs are constructed from


particulars and universals.30 That project only makes sense, or so it seemsto me, if we’re thinking of the particulars and universals as part of funda-mental reality. If particulars and universals are not fundamental existentsbut derivative entities existing in virtue of the states of affairs then there isno sense in which states of affairs are composed out of the particulars anduniversals that are their constituents. The constituents are a mere ontologicalby-product of the states of affairs—they are no ‘addition in being’. Trying tosay how it is they compose to form a state of affairs supposes that the state ofaffairs comes about as a result of the constituents; this gets things exactly thewrong way round on the Tractarian view: the constituents come about as aresult of the state of affairs. There’s no need to posit compositional structureto the states of affairs: the state of affairs of A being F ‘gives rise’ to theexistence of A not because the state of affairs comes with a built in structurebut simply because the simple state of affairs makes true the sentence ‘Aexists’. And there’s nothing that needs explaining here: it’s simply a matterof how we use our language that that sentence gets made true by that stateof affairs.

What if we are attracted to the idea that the truthmakers for contingentintrinsic predications are not states of affairs but rather tropes? Well if that’sthe case then, given truthmaker necessitarianism, tropes had better be non-transferable, in the sense that the tropes that make it true that A is F couldn’tall exist without belonging to A. If <A is F> is made true by some tropesthen there must be some subset of A’s tropes that couldn’t all exist withoutit being the case that A is F; and so there must be some subset of A’s tropesthat couldn’t all exist without all belonging to A. Now maybe just one tropedoes the job: maybe A’s F-ness makes it true that A is F, in which case ithad better be the case that A’s F-ness couldn’t exist without belonging to A;or maybe no proper subset of A’s tropes makes it true that A is F, and so toguarantee that A is F you need all of A’s actual tropes to exist; or maybe thereis a privileged ‘core’ of A’s tropes—some, but not all, of A’s tropes—thatdo the job. It doesn’t matter: in any case, there is some subset of A’s tropesthat couldn’t all exist without A existing (in order for A to be F). This,I think, pushes us towards bundle theory rather than substance-attributetheory.

According to the bundle theorist, objects are simply what you get whenyou get a plurality of tropes together. An object is nothing over and above itsparticularised properties: it is ontologically dependent on those properties;which is to say that the fact that the object exists is made true by the tropes,and hence it is no mystery that the tropes can’t (all) exist without the objectexisting.31 Were we substance attribute theorists, on the other hand, we wouldhave unexplained necessary connections. Suppose substance-attribute theoryis true and that the tropes are fundamental; then either the bare substratumis also fundamental or it is ontologically dependent on the tropes. But itcan’t be the latter; at least not if the spirit, rather than simply the letter,

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of substance-attribute theory is to be preserved. The idea behind substance-attribute theory is that there’s more to an object than its properties: theremust be something to ‘bind together’ the tropes into an object.32 The idea isthat the bare substratum is needed to do something that the tropes can’t doalone. The bare substratum is needed to ground the unity amongst the tropes:it is what explains why this bunch of tropes goes together to make an objectrather than that bunch—because the former and not the latter all belongto a common bare substratum. But if the bare substratum is ontologicallydependent on the tropes that belong to it then all the work is being done bythe tropes themselves; the bare substratum is simply an idle wheel. It mightbe true to say that a bare substratum exists; but what was motivating thesubstance-attribute theorist wasn’t simply that she wanted to proclaim thetruth of the sentence stating that there was more to the world than tropes.She was motivated by the thought that you needed the bare substratum todo what mere bundles of tropes couldn’t do on their own; and this is notthe case if the bare substratum is ontologically dependent on the tropes: thetropes are doing all the truthmaking work.

Hence, if we are really to be substance-attribute theorists, and if the tropesare fundamental, then both the bare substratum and the tropes that belongto it must be ontologically fundamental. But then, since tropes are non-transferable, we have a necessary connection amongst fundamental ontology:necessarily, if A’s redness exists (or if some subset of A’s tropes exist) then Ais red; and necessarily, if A is red then A’s bare substratum exists; so neces-sarily, if A’s redness exists (or if some subset of A’s tropes exist) then A’s baresubstratum exists. This is unacceptable: necessary connections amongst fun-damental existents are ruled out by No Unexplained Necessary Connections.(And it’s also just highly intuitive that there should be free recombinationamongst the fundamental entities.) So substance-attribute trope theory withthe tropes taken as fundamental is not a runner.

The substance-attribute theorist would only have a hope, I think, if sheheld that only the bare substratum is fundamental and that the tropes are notfundamental but ontologically dependent on the bare substratum. But thenshe couldn’t hold that tropes were non-transferable. For if No UnexplainedNecessary Connections is to be upheld, the existence of a dependent entity (orsome dependent entities) can only necessitate the existence of a fundamentalentity if it is necessary that if the dependent entity/entities exist(s) then thefundamental entity makes it true that the dependent entity exists. But that’snot true in this case. It’s not actual that the bare substratum makes it the casethat the tropes exist, a fortiori it is not necessary. We know that the bare sub-stratum doesn’t actually make it true that the tropes that belong to it exist, be-cause it could exist and those tropes not exist. (We know this because it couldhave had different properties. Ex hypothesi, it is contingent that A is F. If thetropes are non-transferable then they can’t exist without A being F. So if A’sbare substratum can’t exist without those tropes existing then A’s substratum


can’t exist without A being F. Which is to say that A can’t exist without beingF. Contradiction.). So the substance-attribute theorist would have to simplyabandon non-transferability. That means, of course, abandoning the idea thatthe tropes themselves make true the intrinsic predications. The substance-attribute theorist would be driven instead to positing a relation that heldbetween the bare substratum and the trope: a relation that bound the tropeto that bare substratum. But of course, this relation can’t be non-transferableeither, for reasons similar to the above, so there must be another relationto hold together the previous relation and the bare substratum and thetrope. And thus does Bradley’s regress beckon!33 And so I think substance-attribute theory should simply be abandoned; bundle theory is far more ben-eficial if we are motivated to secure the truth of No Unexplained NecessaryConnections.

We’ve narrowed down the options we opened the chapter with to two: aTractarian ontology of fundamental states of affairs and a bundle theory oftropes. On neither ontology are ordinary objects like you and I fundamentalconstituents of reality, so both of them might be thought to be revisionary;but I don’t consider that a reductio of anything that’s been said. Can wefurther narrow down these two options to a unique winner? I think so.In the next section I will argue that the truthmaker maximalist—one whothinks that every truth has a truthmaker—who constrains themselves by NoUnexplained Necessary Connections should also be a priority monist. This inturn, I think, tells in favour of states of affairs over the bundle theory. Andso the position the Humean truthmaker theorist is left with is that there isone fundamental entity: the totality state of affairs that says how the worldas a whole is.

6. From Maximalism to Monism

Truthmaker maximalism says that every truth has a truthmaker. There mustbe truthmakers both for ‘positive’ truths, and for ‘negative’ truths such asnegative existentials. In that case, we need to account for the truth of the factthat all the truthmakers that there are are all the truthmakers that there are.It doesn’t appear that the truthmakers themselves make this true, becausethey could seemingly all exist and yet there be some extra truthmakers inaddition. So it looks like we’re forced into admitting some new entity: a‘higher-order’ truthmaker that makes it true that all and only the actualfirst-order truthmakers are all and only the first-order truthmakers. So, forexample, Armstrong introduced his totality fact: the higher-order state ofaffairs of all and only the actual first-order states of affairs being all andonly the first-order states of affairs.34

But here’s the problem. The existence of such a higher-order truthmakermust, of course, necessitate the existence of each of the first-order truth-makers, otherwise it’s not doing the job it was introduced to do. But in

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that case, given No Unexplained Necessary Connections, it had better be thecase either that the higher-order truthmaker makes it the case that each ofthe first-order truthmakers exists or that it is necessary that the first-ordertruthmakers make it the case that the higher-order truthmaker exists. Weknow the latter is false; it’s not necessary that the first-order truthmakersmake it the case that the higher-order truthmaker exists because it’s not evenactual; and we know that because the first-order truthmakers could all existand the higher-order truthmaker fail to exist—this would be the case werethe actual first-order truthmakers to exist alongside some extra first-ordertruthmakers. It was due to that possibility that we needed the higher-ordertruthmaker in the first place! So if No Unexplained Necessary Connections istrue, the first-order truthmakers had better all exist in virtue of the higher-order truthmaker. But that’s to say that the first-order truthmakers are allontologically dependent on the higher-order truthmaker; which is to say thatthere’s only one fundamental existent: the higher-order truthmaker. And soin attempting to secure No Unexplained Necessary Connections we’ve woundup with priority monism: the claim that, necessarily, exactly one fundamentalthing exists.

The truthmaker theorist who wants to uphold No Unexplained NecessaryConnections but not be committed to priority monism could, of course, claimthat it is a necessary truth that the number of truthmakers is what it actuallyis. That is, that there couldn’t have been more or fewer truthmakers than thereactually are. In that case, what makes it true that the actual truthmakers areall and only the truthmakers is just the actual truthmakers: since presumablythey are collectively a perfectly good truthmaker for the fact that there are ntruthmakers (since each of them makes it true that a truthmaker exists, andthere are n of them), and the fact that they are all and only the truthmakersis entailed by the fact that there are n of them, provided that it’s necessarythat there be exactly n truthmakers.

But if that’s the best hope for a Humean truthmaker theorist to resistpriority monism, then there’s not much hope at all, for it’s pretty implausiblethat the number of truthmakers that there are is a non-contingent matter.Or rather, that’s pretty implausible unless priority monism is true. If it’snecessary that there’s exactly one fundamental thing, then of course, sincethe truthmakers are fundamental entities (that’s part of what it means tobe fundamental), the number of truthmakers is a non-contingent matter.But if there could have been a plurality of fundamental beings, then it’s notclear why there should not be possible pluralities of differing cardinalities.The whole point of accepting No Unexplained Necessary Connections was toresist commitment to unexplained brute necessities!

Instead of admitting an entity that guarantees that these truthmakersare all and only the truthmakers that there are, thus driving us towardsunexplained necessary connections, and instead of holding that for some n


it’s necessary that there are exactly n truthmakers, thus committing us tobrute necessary truths (which are in any case independently implausible),the priority pluralist could always attempt to introduce an entity that madeit true that there were exactly n truthmakers without making it true thatthere were exactly these n truthmakers (i.e. the actual ones).35 Such an entitywould ground the truths that need to be grounded without necessitatingthe existence of any of the other truthmakers, since obviously it could existwithout any of the other truthmakers existing, provided there existed n-1 truthmakers which don’t actually exist. But this doesn’t sound like toohopeful a strategy. For starters, it’s not clear how the story would go inthe case where there are infinitely many truthmakers, since in that case youcould have extra truthmakers existing (thus changing what is true) withoutincreasing the number of truthmakers that there are; but put this problem toone side. Consider the alleged state of affairs of there being exactly n statesof affairs (it’s not clear what the story would be in the case of tropes). That’sreally different from what we usually think states of affairs are like: it’s dedicto, whereas states of affairs are typically de re. It would be like havinga state of affairs of something being F without that state of affairs being astate of affairs of any particular thing being F. States of affairs are aboutparticular things being a particular way: they are not about some thing orother being some way or other. You don’t get to introduce a state of affairsinto your ontology just by pointing to some truth, p, and introducing thestate of affairs that p; you only get to introduce a state of affairs by pointingto some thing(s) and to some way(s) that/those thing(s) are. So while I’mhappy with the state of affairs of these states of affairs being all and onlythe first-order states of affairs—a state of affairs that says de re of somefirst-order states of affairs that they are all and only the first-order statesof affairs—I am not happy with the de dicto state of affairs that says thatthere are n states of affairs without saying of any states of affairs that thosestates of affairs are the n states of affairs. What are the constituents of sucha state of affairs? It’s not a state of affairs of some particular thing or thingsinstantiating a property.

I want to make a similar response to a suggestion made in correspondenceby Louis deRosset. deRosset suggested to me that the pluralist believe not inthe state of affairs of there being exactly n things but rather in the state ofaffairs, call it Capstone, of there being no first-order states of affairs otherthan the first-order states of affairs S1 to Sn. Capstone does the job, becauseits existence together with the existence of S1 to Sn guarantees that there areno states of affairs other than S1 to Sn and Capstone. But Capstone won’tlead the pluralist to a conflict with No Unexplained Necessary Connectionsbecause its existence does not necessitate the existence of any of S1 to Sn,since any proper sub-plurality of S1 to Sn can exist and it be true that nofirst-order state of affairs other than that sub-plurality exist. ‘There is nothing

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other than the Xs’ can be true either if all the Xs exist and nothing else does,or if some but not all of the Xs exist and nothing other than one of theXs exist; indeed, it is true even if there is nothing at all. But I still don’tthink Capstone is a de re state of affairs in the required sense. The fact thatthe name of the state of affairs references some other states of affairs is notenough to make the former state of affairs about the latter states of affairsin the relevant sense: it must be about those states of affairs in the samesense that the state of affairs of A being F is about A: it must take A as aconstituent and bind it to the universal F.

In essence, the argument of this paper is very simple: If truthmaker max-imalism is true there must be a higher-order state of affairs that guaranteesthat there are no first-order states of affairs other than the actual first-orderstates of affairs. This higher-order state of affairs must be de re about thefirst-order states of affairs; that is to say, it must be a state of affairs ofthose first-order states of affairs being a certain way (namely, exhausting thefirst-order states of affairs). For a state of affairs to be about some thingbeing a certain way it must have both the thing and the way as a constituent:that’s how states of affairs work. The existence of a state of affairs necessi-tates the existence of its constituents (if they didn’t, they wouldn’t be doingtheir job as truthmakers). So the existence of the higher-order state of af-fairs necessitates the existence of the first-order states of affairs. And so thehigher-order state of affairs had better be prior to the first-order states ofaffairs to avoid mysterious necessary connections; and so priority monismis true.

The only good way to guarantee the truth of the contingently true claimthat there are n first-order truthmakers then, I claim, is by admitting ahigher-order truthmaker for the fact that these n things are all and only thefirst-order truthmakers. That forces us to accept the necessary connectionthat, necessarily, if the higher-order truthmaker exists, each of the first-order truthmakers does also. In which case, the first-order truthmakers hadbetter exist in virtue of the existence of the one fundamental higher-ordertruthmaker.

So I think the Humean truthmaker theorist must simply embrace prioritymonism. This, I think, tells in favour of Tractarian factism over the tropebundle theory36; for it’s clear how we can have one single state of affairs—thetotality fact that says how the world is in its entirety—that accounts for theexistence of every derivative thing and grounds every truth, but it’s less clearhow you could have a single trope that did this job. One could say that it’s thetropes (plural) of the world as a whole that are all and only the fundamentals.That’s still in the spirit of priority monism, despite there being a plurality offundamental beings, because the fundamental beings are all particularisedproperties of the world as a whole as opposed to its proper parts. But this isonly going to solve our problem if there is some n such that it’s a necessarytruth that n is the number of tropes belonging to the world as a whole. And it’s


again far from obvious why that should be the case. Couldn’t the world losea trope without having it replaced? Or lose two but have it only replaced byone? Or gain a trope without losing any? Until we’re given a good reason toanswer these questions in the negative, the scales fall in favour of Tractarianfactism over the trope bundle theory. Insofar as we’re concerned only withsatisfying priority monism, there are other options over Tractarian factism,of course. The view that there’s necessarily one fundamental substratum—theworld—along with its tropes which ontologically depend on it, is a perfectlyacceptable priority monist view, qua priority monism. But, of course, we havealready argued against the substance-attribute theory above, on the groundsthat it violates No Unexplained Necessary Connections. Tractarian factistmonism seems to be the best bet if one wants to be a truthmaker theorist andresist unexplained necessary connections. All that there is, fundamentally, isthe big totality fact: the grand state of affairs that says how the world is in itsentirety. Every truth is true in virtue of this one totality fact. At least, that’swhat is the case if truthmaker maximalism is correct; you may feel free tomodus ponens or modus tollens at your pleasure.

Notes1 Thanks to Elizabeth Barnes, Louis deRosset, Jonathan Schaffer, Robbie Williams and an

anonymous referee for helpful discussion.2 I assume here that the truthmaker theorist accepts what is known as Truthmaker Neces-

sitarianism: the doctrine that if A makes p true then it is metaphysically impossible for A toexist and it not be the case that p is true. There are other conceptions of truthmaking out there,such as that the truthmaking relation supervenes not merely on the existence of the truthmakerbut on the intrinsic natures of the truthmaker and the proposition, but I will simply assume thenecessitarian view in this paper. For discussion of the necessitarian view and its rivals see my‘Truthmakers, Realism and Ontology’, in Being: Contemporary Developments in Metaphysics,Robin LePoidevin (ed), Royal Institute of Philosophy Supplement, 83, p. 107–128, (2008).

3 Jonathan Schaffer, ‘The Least Discerning and Most Promiscuous Truthmaker’, forthcom-ing in The Philosophical Quarterly.

4 See, inter alia, D.M. Armstrong, A World of States of Affairs, Cambridge: CambridgeUniversity Press, (1997).

5 See, inter alia, John Heil, From an Ontological Point of View, Oxford: Clarendon Press,(2003).

6 As, e.g., Heil, ibid., thinks.7 As, e.g., Peter Simons thinks. Simons, ‘Farewell to Substance: A Differentiated Leave-

taking’, Ratio Vol. XI No. 3, p. 235–252, (1998).8 David Lewis, ‘A World of Truthmakers?’, in Lewis, Papers in Metaphysics and Epistemol-

ogy, Cambridge: Cambridge University Press, (1999), p. 215–220, at p. 215.9 Fraser MacBride, ‘Lewis’ Animadversions on the Truthmaker Principle’, in Helen Beebee

& Julian Dodd (eds) Truthmakers: The Contemporary Debate, Oxford: Oxford University Press,(2005), p. 117–40.

10 Richard Fumerton, Review of Beebee and Dodd (eds.), Truthmakers: The ContemporaryDebate, Notre Dame Philosophical Reviews, http://ndpr.nd.edu/review.cfm?id=5921

11 Where ‘x<y’ is to be read as ‘x is a (proper or non-proper) part of y’, and ‘E!x’ is to beread as ‘x exists’. I’m not assuming that the notion of ‘parthood’ here is mereological. Perhaps

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there are multiple composition relations, and it is one of the non-mereological notions of ‘part’that holds between the constituents of a state of affairs and the state of affairs itself, or betweena trope and the bundle of which it is a constituent. I want to abstract away from these issuesfor the moment however; we’ll come back to them soon below.

12 Roderick Chisholm, Person and Object: A Metaphysical Study, London: George Allen &Unwin Ltd., (1976).

13 See Armstrong, ibid. p. 119–123. Lewis’s complaint against an ontology of states of affairsis precisely that it needs ‘non-mereological composition’, which he finds mysterious as mereologyis meant to be the general theory of composition. See David Lewis, Parts of Classes, Oxford:Blackwell, (1991), p. 57. For discussion see Kris McDaniel, ‘Structure Making’, AustralasianJournal of Philosophy, Vol. 87 No. 2, (2009), p. 251–274.

14 For some scepticism concerning the denial of necessary connections see Jessica Wilson,‘What is Hume’s Dictum, and Why Believe It?’, forthcoming in Philosophy and PhenomenologicalResearch. For my part, I am guided by the thought that possibility is the default mode, and thatwe should grant the possibility of a proposition unless we have an explanation for the necessityof its negation.

15 Adherents of NUS are legion. See, inter alia, Armstrong, ibid. p. 120; Lewis, ibid. p. 79–81; Theodore Sider, Four-Dimensionalism: An Ontology of Persistence and Time, Oxford: OxfordUniversity Press, (2001), p. 121–132.

16 See, inter alia, D. M. Armstrong, ‘Classes Are States of Affairs’, Mind, Vol. 100, No. 2,(1991), p. 189–200; Kit Fine, ‘Essence and Modality’, Philosophical Perspectives, Vol. 8, (1994),p. 1–16.

17 Armstrong, ibid., attempts to analyse singletons as states of affairs precisely so that hecan say that a singleton and its member are distinct but not wholly distinct; but of course, if whatI said above is correct, this doesn’t help to make the necessary connections any less mysterious.

18 See Ben Caplan and Kris McDaniel, ‘Mereological Myths’, ms, for a dissolution of thetendency of philosophers to draw fallacious de re modal conclusions from this de dicto necessity.

19 See my ‘The Contingency of Composition’, Philosophical Studies, Vol. 136, No. 1, (2007),p. 99–121, for an argument that the compositional facts do not hold of necessity.

20 Ross Cameron, ‘Truthmakers and Ontological Commitment’, Philosophical Studies, Vol.140, No. 1, p. 1–18, (2008). An earlier version of the idea received discussion in my ‘Truthmakersand Necessary Connections’, Synthese, Vol. 16, No. 1, (2008), p. 27–45, but resulted in quitedifferent conclusions.

21 Why just impure sets? Shouldn’t the same hold of pure sets? Maybe; but I’m simply notconcerned with impure sets here. If there are such things, then presumably they necessarily exist.In which case they don’t provide even a prima facie counter-example to the denial of necessaryconnections between contingent existents. If there’s a necessary connection between pure setsthat’s just because they all exist of necessity (if at all). There’s no mystery at all in the factthat necessary existents necessitate one another’s existence: at least, no further mystery over andabove the fact that these things couldn’t but have existed.

22 See Armstrong, A World of States of Affairs, p. 12; Lewis, Parts of Classes, p. 80.23 There are exceptions of course. Some of them tell us that what it meant was that complex

objects are identical to their parts. But if many-one identity is the price to pay, then it reallydoes seem that there’s no such thing as a free lunch. For a defence of composition as identitysee in particular Donald Baxter, ‘Many-One Identity’, Philosophical Papers, Vol. 17, No. 3,(1988), p. 193–216 and Baxter, ‘Identity in the Loose and Popular Sense’, Mind, Vol. 97, No.388, (1988), p. 575–582. The view is also discussed, but not quite endorsed, by Lewis, Partsof Classes, p. 81 and Theodore Sider, ‘Parthood’, The Philosophical Review, Vol. 116, (2007),p. 51–91.

24 Just to clarify: I’m suggesting that ‘There is a sum of the Xs’ is made true by the Xs, notthat ‘The thing which is actually the sum of the Xs exists’ is made true by the Xs, which is whytruthmaker necessitarianism explains only the truth of NUS and not the truth of de re claimthat the existence of the Xs necessitates the existence of the thing which is actually their sum.


‘The thing which is actually the sum of the Xs exists’ still doesn’t require a complex object asits truthmaker, however: it can be made true by the Xs together with their intrinsic propertiesand the non-mereological relations the Xs bear to one another and perhaps to other thingsas well.

25 What of truthmaker necessitarianism itself—doesn’t it lead to unexplained necessities?I think not: the necessary connection between an element of ontology and the truth of somesentence can be explained simply by how we use language, in a way that a necessary connectionbetween two elements of ontology could not be.

26 This qualification is necessary to deal with non-singleton sets. Necessarily, if a and b bothexist then {a,b} exists: no problem, because a and b collectively make it true that {a,b} exists.And necessarily, if {a,b} exists then a and b both exist. No problem, because, necessarily, if {a,b}exists then what makes it true that {a,b} exists is a and b (collectively). But also: necessarily, if{a,b} exists then a exists. Without the qualification this would be ruled out by No UnexplainedNecessary Connections, since it’s neither the case that {a,b} makes it true that a exists, nor is itthe case that, necessarily, a makes it true that {a,b} exists. But there’s clearly no more problem inthe existence of {a,b} necessitating the existence of a as there is in it necessitating the existenceof a and b. If A’s existence necessitates the existence of a plurality of things, and that’s perfectlyexplainable, then there’s obviously no further mystery as to why A’s existence necessitates theexistence of each member of that plurality.

27 I will speak as if the ‘property’ parts of states of affairs are universals, but I should saythat there’s no barrier to taking them to be tropes. Indeed, on the Tractarian view both theproperty part and the particular part are mere abstractions from the state of affairs anyway,and so the question as to whether we take the property part to be a trope or a universal isn’treally an ontological one but a conceptual one.

28 Of course, this is perfectly compatible with <A exists> and <F exists> also being madetrue by other entities other than A and F, such as the state of affairs of A being G and the stateof affairs of B being F respectively.

29 Ludwig Wittgenstein, Tractatus Logico-Philosophicus, London: Kegan Paul, Trench andTrubner, (1922). Although I’m no Wittgenstein scholar, and make no pretensions to be engagingin exegesis here.

30 E.g. Kris McDaniel, ‘Structure Making’, Australasian Journal of Philosophy, Vol. 87No. 2, (2009), p. 251–274.

31 I’ll assume, what I think is plausible, that all A’s tropes are needed to make <A exists>true. In that case A’s F-ness, while it might make it true that something is F, won’t make it trueon its own that A is F, for it won’t be sufficient to make it the case that it’s A that is F. Rather,each contingent intrinsic predication will be made true by the totality of A’s tropes. But thesame points hold if you think a proper subset of A’s tropes, perhaps even the single trope of A’sF-ness, makes it true both that A exists and that A is F.

32 See Heil, From an Ontological Point of View and C.B. Martin, ‘Substance Substantiated’,The Australasian Journal of Philosophy, Vol. 58, (1980), p. 3–10.

33 F.H. Bradley, Appearance and Reality, Oxford: Clarendon Press, (1983).34 Armstrong, A World of States of Affairs, p. 196–201. There’s no need to go any higher;

the higher-order state of affairs is sufficient to make it true that it’s the only the higher-orderstate of affairs. See my ‘Truthmaker Necessitarianism and Maximalism’, Logique et Analyse,Vol. 48, Nos. 189–192, (2005), p. 43–56.

35 This was suggested to me by Robbie Williams.36 The argument from the previous section that forced us to choose between these two

option still stands; for even though we are no longer claiming that the state of affairs of Ball’sbeing red, e.g., is absolutely fundamental (since we are now embracing priority monism), wemust still hold that it is more fundamental than its constituent, Ball. After all, we still haveto explain why the existence of the state of affairs necessitates the existence of Ball, and thisis not explained by the fact that the existence of both is grounded in the totality state of

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affairs. Why not? Because both entities could exist without the actual totality fact existing, butnevertheless there is no world (not just no world where the actually totality fact exists) wherethe state of affairs of Ball’s being red exists but Ball does not. The only way to explain this isto hold that the state of affairs of Ball’s being red, whilst not being absolutely fundamental,is more fundamental than Ball. And so, even if no state of affairs but the totality state ofaffairs is absolutely fundamental, the derivative states of affairs are still more fundamental thantheir constituent particulars and universals. Hence, states of affairs are Tractarian rather thanArmstrongian.

From Humean Truthmaker Theory to Priority Monism

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