Negative Properties

NOUS 45:3 (2011) 528–556

Negative PropertiesNICK ZANGWILL

Durham University

“Annihilation’s forces meet resistance

From something coarse asserting its existence

Goethe, Faust, Part One, Faust’s Study (ii)

“The absence of a property is not itself a property”

Moses Maimonides

Guide for the Perplexed, book I, chapter LXXIII, seventh proposition

“What is not . . . has its share in existence”

Plato, The Sophist (260d)

§1. Reality and Power

§1.1I shall explore and connect two issues about negative properties. One con-cerns whether they are real or genuine properties. The other is whether theydetermine other properties.

The view I am attracted to, and would like to hold, is the extreme viewthat positive properties (PPs) are real or genuine, but negative properties(NPs) are not. The reason for holding this extreme view would be that PPshave a causal or metaphysical determining role whereas NPs do not. Realproperties earn their keep, they do work; but NPs are idle and do nothing,and hence are not real.

Although I have much sympathy for this extreme view, there are seriousdifficulties with it. For NPs clearly cannot be denied some causal and meta-physical determining role. After all, NPs generate causal counterfactuals: ifthe sailors had not lacked vitamin C then they would not have got scurvy;

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if the passengers had not failed to wear seat belts, they would not have beenhurt. And NPs are among the necessary conditions of PPs causing other PPs:being rained on causes one to get wet but only if one fails to wear protectiverainwear. Similarly, for events: dropping an egg will cause it to break onlyif Superman fails to show up and catch it before it hits the ground. Thenon-preemption of the cause event is necessary for the effect. Even if we putcausal powers to one side, NPs cannot be denied some metaphysical power.NPs determine other NPs, just as PPs determine other PPs. For example,not being colored determines not being blue. Not being divisible into wholenumbers by 2 determines not being divisible into whole numbers by 4. Notbeing H2O determines not being water. And not being blue determines notbeing blue or being a kangaroo. Furthermore, all properties, positive andnegative, are self-determining. You cannot take all that away from NPs. Soit is unwise to say that NPs play absolutely no determining role and aretherefore not at all real.

§1.2The view I shall defend is this:

PPs are more real than NPs.

The thesis amounts to inegalitarianism about properties. I think that weshould discriminate against NPs. There is a metaphysical hierarchy, and PPshave a superior place in that hierarchy with respect to NPs. The view Iendorse is that PPs have a greater degree of reality than NPs.

This claim about the reality of PPs and NPs is connected with a claimabout determination:

PPs have more determining power than NPs.

As we saw, we should not say that NPs have no determining power. Like thereality of properties, determining power is not black and white. The idea isthat NPs do not play as great a determining role as that played by PPs. PPsexceed NPs in power. I assert the degreed version of inegalitarianism ratherthan the more extreme absolutist version because I think that NPs cannot bedenied some determining role; it is just that they have less of a determiningrole than PPs. NPs are less efficacious than PPs, and this is connected withthe fact that they have a lesser degree of reality. It is this claim that I pursuein this paper. Before I begin the argument, I want to make some furtherremarks about the thesis to be defended.

§1.3How exactly are claims about reality and about determination related? Threeviews are:

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(1) PPs are more real than NPs because they have greater determining power.(2) PPs have more determining power than NPs because they are more real.(3) PPs are more real than NPs and they have more determining power.

My view is (2), but this will not be important in this paper. I think thatdetermining power and degree-of-reality are explanatorily linked, and I thinkthat PPs are more powerful than NPs because they are more real. But I shallnot defend this way of linking reality with determination. In this paper, Iappeal to determination epistemically—to tell us when a property is relativelyreal. I argue that since PPs are more powerful than NPs, we are entitled tohold that they are more real than NPs.

§1.4I believe that we need to resurrect the idea that there are degrees of reality, asmany philosophers thought in other eras. I sympathize with Plato, Descartesand the medieval philosophers in embracing the idea of degrees of reality.This idea is useful, and perhaps indispensable, all over philosophy. It seemsto be a peculiarly modern prejudice to think that either something is real orit is not. It is not plausible that reality is either black and white, and thereare no persuasive arguments that it is. The idea of degrees of reality is quiteintuitive and has been popular in the history of philosophy. TraditionallyGod was thought to be the most real thing. This was connected with Hisbeing all-powerful and also with His being a creator, in the sense of beingwhat everything else depends on. Everything depends on God, while Hedepends on nothing except Himself. He and only He is self-sustaining. Platohas a not dissimilar view of the world (at least in his middle period), since hethought that the forms are more real than anything else and material thingshave their share in being only in virtue of the forms, while the existenceof the forms is not at all dependent on the existence of material things.Philosophers have sometimes used the idea of substance to express the idea ofsomething that is not dependent for its existence on anything else. Substanceis an unexplained explainer. This idea is common in medieval philosophyand also in Locke. These days, many think that primary being is physicalreality (properties, facts, events, laws), which is the unexplained explainer.Other aspects of reality, such as its chemical, biological and perhaps mentalproperties only obtain in virtue of basic physical reality. Physical reality isprimary being, which is more real than what depends on it. (There mayalso be hierarchies within the physical.) However, whether God or physicalreality or an elephant or a tortoise stand at the base of the world makes littledifference to the fundamental idea that there are more or less fundamentallevels of being, where the less real depends on the more real. A simple andintuitive illustration, although of objects rather than properties, is that ofholes, which are real (you can trip of over them) but also less real than theirbrute surroundings, in virtue of which they exist. Holes depend on their


surrounding material just as the material world has been thought to dependon God.

§1.5I shall not define what it is for a property to be positive or negative. I relyon an intuitive sense of which properties are NPs. I shall not attempt to givea non-circular definition of negativity. Some philosophers say that they donot understand the distinction between PPs and NPs, and that they have nointuitive grasp of which is which. I don’t believe them! Perhaps they can viewthis paper as an attempt to give sense to this distinction.

One source of elucidation that we should be especially wary of is a lin-guistic elucidation. There is no straightforward mapping from negated pred-icates to NPs. For example, being empty is a NP, and not being emptyis a PP. Linguistically negative ascriptions often fail to pick out NPs. If Idescribe people as impolite, do I imply (semantically, not conversationally)that they are rude? Rocks, worms, and the Milky Way, are neither politenor rude. Politeness and rudeness are not contradictory properties but con-traries. If impoliteness implies rudeness then it is a PP; but if impolitenessjust amounts to not being polite, then it is a negative property. Similarly, alinguistically disjunctive ascription may not pick out a disjunctive property.We might describe something as either an African emerald or a non-Africanemerald (Jaegwon Kim’s example; see Kim 1993: 321). This picks out thenon-disjunctive property of being an emerald. We cannot either define thenegativity or the disjunctivity of a property in linguistic terms. We mustrely on an intuitive grasp of the distinction between positive and negativeproperties.

Even if there are some cases that are hard to classify as positive or negative,there are still many other cases that are uncontroversially positive or negative,and so the questions we are interested in can be raised for those clear cases.Some philosophers might go further and deny the distinction even in theapparently clear cases; but I don’t believe them if they claim to have nointuitive grasp of the distinction. I hope that this paper enables them tograsp it knowingly.

§1.6If we discriminate against NPs, it commits us to denying the identification ofproperties with sets of (actual and possible) things (Lewis 1986). For thereis a set of non-blue things just as there is a set of blue things. And sincemany non-blue things are just as real as many blue things, the set of non-blue things cannot be less real than the set of blue things. There are possibleworries about the size of sets that might prevent us admitting that there is aset of all of the things that are not blue, which includes London buses andthe number 2 and all sets. But it is a consequence of what I am arguing here

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that even if there were such a set—the set of all non-blue things—it wouldnot constitute a genuine property, or as genuine a property as blueness.Corresponding to any genuine property, there is a set of actual and possiblethings that instantiate that property; but not all members of sets of actualand possible things are united by being the instantiators of a fully genuineproperty.

The set conception of properties contrasts with four other standard viewsof properties: a property, such as blueness, might be (1) a Platonic universal,(2) an Aristotelian universal, (3) a fusion of tropes, or (4) a resemblance re-lation. Suppose that it is a Platonic universal. Then it is in virtue of bluenessthat blue things are blue. So the property in virtue of which blue things areblue is not identical with the set of actual or possible blue things. (A setis metaphysically dependent solely on the existence of its members, not onthe properties of its members.) Even if it is necessary that a set exists if itsmembers exist, on the Platonist view, the properties and the sets of thingsare distinct. Suppose instead that blueness is an Aristotelian universal. Thenit is wholly present in its instances. But if so, the Aristotelian universal isnot identical with any or all of the things in which it is present or even withthe set of any or all of them. Again, suppose we prioritize tropes, and wethink of the general property of blueness as the mereological sum of tropesof a certain sort—all the particular bluenesses—that are actual, or actualand possible. Then it is not merely the things that are in question but theirtropes. Blueness is the mereological sum of all the bluenesses. But on thetrope view, things are members of the set of blue things in virtue of pos-sessing the relevant tropes; they do not possess the tropes in virtue of beingmembers of the set of blue things. Lastly, suppose that blueness is a resem-blance relation among objects. Then such a resemblance relation betweenobjects is more than a matter of the objects related. A set of objects is deter-mined just by the objects in question, not by relations between them, suchas resemblance. Hence on Platonic, Aristotelian, trope or resemblance views,properties are no kind of set-theoretic or mereological construction out ofthings.

There is surely a significant intuitive difference between properties andthings. Things and properties are completely different—like eggs and oranges;and the same is true of sets of things and properties, for a set of things isanother thing. If we can argue that non-blue things do not share a fullyreal property, in the way that blue things then that confirms the intuitivedifference.

§1.7There has been discussion recently of negative facts and negative truths (forexample Molnar 2000 and Armstrong 2000). The issues these raise are relatedto the topic of this paper, but they are not the same issue. I put the issue ofnegative truths to one side, since our concern here is not particularly with


semantic facts, positive or negative. Perhaps falsity is a negative semanticfact. Still, the issue over negative facts and properties is more general. Anegative fact might be the existence of an object or event that possesses anegative property. Or it might also be the non-existence of an object with apositive property. These are two kinds of negative facts. There is a dangerthat a unitary theory of both will ignore this difference. We are interested inthe first kind of negative fact.

§1.8It might be argued that the view that there are no negative facts is self-refuting, since it would seem that on that view it is a negative fact thatthere are no negative facts! Perhaps. But the view that there are no negativeproperties does not seem to suffer from this problem. Or does it? What ifbeing real is a property, as some say that existence is? Then the thesis mightbe that NPs have the NP of not being fully real. Is this thesis self-refuting?I think not. For even if being real is a property (or a fully real property),that does not mean that not being real is also a property (or a fully realproperty). So the negative thesis about NPs does not necessarily attributea property to NPs, even on the (questionable) assumption that reality is aproperty. Suppose that the NP of non-reality is a property but only to a lowdegree. Then to attribute non-reality to NPs is not to attribute much of aproperty to them. (Non-reality determines non-blueness, which is at least aminor achievement.) So the thesis that NPs are not fully real does not ascribea very robust property to NPs, and there is no problem about self-refutation.Of course, Plato’s beard is lurking nearby since it seems that NPs must bereal in order to have the NP of not being real. But this is at least not theproperty form of the self-refutation worry, which is that if NPs have the NPof non-reality, then that NP (of non-reality) is real, since it is had by NPs.But if the property of non-reality has a low degree of reality, there is nodifficulty here.

§2: The Asymmetrical Determination Thesis and the Basic Argument

§2.1Our problem is how to argue either for the crude or for the sophisticatedinegalitarian view. The problem addressed in this paper is that of showingthat PPs have greater determining power than NPs, and this involves pointingto the precise respects in which they have greater power and showing howwe can know that they have greater power in those respects.

I take the notion of determination to be basic, not to be explained inother terms. (I am also not distinguishing the determination of A by B fromthe dependence of A on B.) However, a natural approach, if we seek toknow where there are determination relations, is to appeal to conditionals or

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necessitation relations. Consider conditionals. Conditionals are not implausi-ble candidates for criteria or symptoms of determination relations (causal ormetaphysical). But there are cases of determination without conditionals andof conditionals without determination. So conditionals relating NPs and PPscannot be taken infallibly to signify determination. The situation is similarwith necessitation, which is also a plausible criterion or symptom of determi-nation. It is sometimes thought that determination and necessitation are thesame. But this is a mistake, as Kit Fine has shown (Fine 1995). Necessitationis not universally correlated with determination and lack of necessitation isnot is not universally correlated with lack of determination. Nevertheless, inmany cases, necessities, like conditionals, are symptomatic of determination.They can be used as defeasible criteria. We need to be cautious when we seekto locate determination relations by appeal to conditionals or necessity; weneed to be wary of a scenario where the criteria are misleading. But, usedwith care, the criteria may be enlightening where a conditional or necessityrelation holds in virtue of a determination relation.

§2.2My First Thought about the respect in which PPs have greater determiningpower than NPs was this.

NPs have less determining power with respect to PPs than other PPs have withrespect to PPs.1

However, this proves hard to show. The trouble with the First Thought isthat neither conditionals nor necessesitation allow us to distinguish the waythat PPs determine PPs and the way that NPs determine PPs. NPs are clearlyamong the necessary conditions for a PP to determine what it does, and theconditionals in question are true in virtue of those necessity relations. Forexample, it is necessary that causes not be preempted if they are to havetheir effects. Striking one billiard ball against a second one causes the secondball to move unless something prevents it. Non-prevention is necessary if thecause is to yield the effect. Even if one says that the true cause is the entirestate of the world at a time, the ‘totality property’—that those facts are allthe facts—is itself a NP or implies a NP. (I say more about totality propertiesbelow.) That NP generates counterfactuals and it is a necessary condition forthe effect. There is no way around this. So, unfortunately, neither conditionalsnor necessitation relations license the anti-negative stance, since NPs satisfythose criteria, and there seems to be no non-ad hoc way of dealing withthis. It is doubtful whether conditionals or necessitation relations can beemployed in such a way that NPs can be seen to fall short by comparisonwith PPs in the determination of PPs (see further Zangwill 2003).


§2.3In this paper I shall pursue a line that is different from, but related to, theFirst Thought: instead of trying to find a difference between PPs and NPs intheir determining role with respect to PPs, I want to try to find an asymmetrybetween PPs and NPs in their determining role with respect to each other.I call this thesis the Asymmetrical Determination Thesis. The thesis I amattracted to could be crudely stated by saying that a thing’s PPs determine itsNPs, but its NPs do not determine its PPs—or: being determines non-being,but non-being does not determine being. The extreme claim would be:

PPs determine NPs, but NPs do not determine PPs.

However, we can soften this thesis to make it a matter of degree:

PPs determine NPs to a greater degree than the degree to which NPs determinePPs.2

The Asymmetrical Determination Thesis—extreme or degreed—describesthe respect in which PPs have greater determining power than NPs, andhence are more real. I shall argue for the degreed version of the AsymmetricalDetermination Thesis, and then, at the end of this paper, I will use that as abasis from which to argue for the First Thought. In fact I think that thereis no arguing for the First Thought apart from arguing from the (degreed)Asymmetrical Determination Thesis.

§2.4I noted that we should not reduce determination to conditional or necessi-tation relations, but that such relations are plausible candidates for relationsthat are symptomatic of determination relations. In particular, what is called‘supervenience’ is a modal relation that many philosophers might be temptedto reach for in thinking about the determination relation between PPs andNPs. Although we should not characterize the claim that PPs determine NPsin terms of the notion of supervenience, the idea of supervenience, neverthe-less, can be deployed as a criterion of determination, one that is potentiallydefeasible, but which, in the absence of defeat gives us reason to believe ina determination relation. Thus the Asymmetical Determination Thesis I ampursuing might be thought to be supported by the fact that although NPssupervene on PPs, PPs do not supervene on NPs.

The following two claims have some plausibility: if something has a NPthen it has some PP that suffices for its having that NP; but it seems not tobe the case that if something has a PP, then it has some NP that sufficesfor its having that PP. For example, if there is something which is not waterthen it has some PP, such as being gold, such that being gold is sufficientfor it not being water. But PPs do not supervene on NPs: it is not the case

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that if something has a PP then it has some NP that is sufficient for itshaving that PP. For example, if something is water, then there is no NP thatit has—such as not being gold—which is sufficient for being water. A tortoiseis neither gold nor water. Being gold suffices for not being water and beingwater suffices for not being gold, but not being gold does not suffice forbeing water and not being water does not suffice for being gold. In this way,it seems that PPs have more efficacy than NPs.

Moreover, there are also factual conditionals running from PPs to NPs,which gives us more reason to believe that PPs asymmetrically determineNPs.3 By contrast, there are no factual conditionals running from NPs toPPs, which gives us some reason to believe that no determination relationholds. And in both cases there is no defeating complication that defeats theconditional criterion. The factual conditional [if something is water then itis not gold] holds, which is criterial for the obtaining of a determinationrelation. And there is no defeating complication such that it holds without adetermination relation. So the factual conditional [if something is water thenit is not gold] holds in virtue of a determination relation. By contrast, theconditional [If something is not gold, then it is water] fails, which is criterialfor the lack of a determination relation.

The necessitation relations in question are strict. In many cases, in par-ticular in cases of cross-time causation, causes produce effects only if otherthings are equal. The reason is that we must include non-preemption in thestrict sufficient conditions for the cause to produce the effect. By contrast,PPs are strictly sufficient for NPs, but NPs are not strictly sufficient for PPs.There is no problem here with pre-emption not being operative. For, if wecan speak in such terms, in absolutely all ‘possible worlds’, water is not gold,whereas there are possible worlds (including the actual one) in which thereis non-gold that is water. We have strict sufficiency and conditionals in onedirection but not in the other. Hence determination relations flow one waybut not the other.

This is the basic argument for metaphysical inegalitarian. In the nextsection, I look at some neighbouring issues, and in section 4, I explore somedevelopments and ramifications. I then pick up the dialectical thread againin section 5.

§3. Three Comments on the Basic Argument

§3.1My topic is negative properties; but there are important parallel issues aboutconjunctive and disjunctive properties. Although I will not pursue theseissues, I want to mention that my view of these properties is completelydifferent. I am very tolerant of them. I grant a high degree of reality toboth conjunctive properties and disjunctive properties. It is only NPs thatI have a problem with. (The only writer I have come across with a similar


combination of views is James Van Cleve (Van Cleve 1989).) David Arm-strong tolerates conjunctive properties but not disjunctive properties or NPs(Armstrong 1978, 1989, 2000). David Mellor tolerates neither (Mellor 1995).And some—I call them ‘Boolean hooligans’—tolerate them all. However,the determination criterion cheerfully admits both conjunctive propertiesand disjunctive properties. For if being A causes being B and being C causesbeing D, then it is very difficult to see how it can be denied that being Aand C causes being B and D, or that being A or C causes being B or D (seeHirsch 1993, pp. 63–65).

David Armstrong has tried to argue against the causal efficacy of dis-junctive properties by arguing that if x’s being A causes y’s being B, thatdoes not mean that x’s being A or C cause y’s being B. Armstrong con-cludes that that the disjunctive property adds no real power in this case(Armstrong 1978, 1989). The inference seems to be that disjunctive prop-erties play a lesser determination role with respect to non-disjunctive prop-erties than non-disjunctive properties. I agree with Armstrong that if beingA causes being C, that does not mean that being A or B causes being C.He is right about that. Consider the conditional criteria: where A causesB, even though the counterfactual [If not-(A or C) then not B] usuallyholds, the factual conditional [If (A or C) then B] will often fail. But allthis shows is that the causal role of disjunctive properties is not simplyinherited from one of their disjuncts. It does not begin to establish thequite general thesis that disjunctive properties lack efficacy. That is anothermatter.

Some philosophers would concede that disjunctive properties should beaccorded some determining role, but say that disjunctive properties are likeNPs in that this role is very limited. Perhaps disjunctive properties have con-siderable determining roles with respect to other disjunctive properties andwith respect to themselves, but not with respect to non-disjunctive properties.However, some disjunctive properties clearly do have determining role withrespect to non-disjunctive properties. For example, being over 6 foot tall is adisjunctive property that may play an important role. Certainly, being over6 foot tall seems to be a better explanation of why I bumped my head ona doorway that was 6 foot high than my being exactly 6 foot 1.37 inchestall. (Some explanations may be good because they pick on some aspect ofthe situation that we happen to be interested in; but others are good be-cause of the properties they appeal to.) Tall people often bump their headsagainst things. An example of non-causal disjunctive determination is this:being blue determines being coloured, and so does being red; thus beingeither blue or red determines being coloured. By contrast, being blue or twodoes not determine being coloured. So say the conditional criteria, at anyrate. Thus disjunctive properties have a substantial metaphysical determiningrole.4 A blanket denial of disjunctive determination (causal or metaphysical)runs up against these kind of examples.

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It might be argued that determining power varies with the degree ofreality of properties, it seems that conjunctive properties should be said to bemore real than their conjunct properties, and disjunctive properties shouldbe said to be less real than their disjunct properties and the correspondingconjunctive properties. I do not mind conceding this so long as the verysubstantial causal and metaphysical determining role of disjunctive propertiesis recognized.

§3.2Causal and metaphysical efficacy are not closed under logical entailment.First consider causal determination: it might be that a lorry’s weighing 200tons caused a bridge to collapse. Weighing 200 tons entails weighing 200tons or weighing one ton. But the lorry’s weighing 200 tons or one tondid not cause the bridge to collapse. The counterfactual holds here but notthe factual conditional. (If the disjunctive property were not instantiated,then the bridge would not have collapsed; but it is not the case that if thedisjunctive property is instantiated, then the bridge collapses.) This is not todeny that disjunctive properties have causal roles. That would be implausible.It is just to say that their causal roles are not simply inherited from one oftheir disjuncts. And this is because causal efficacy is not closed under logicalentailment. Thus the fact that NPs are entailed by PPs does not ensure thatthey have causal efficacy.

What about metaphysical determination? Is it preserved under logicalentailment? Being 6 foot tall metaphysically determines being more than3 foot. And being 6 foot tall logically entails being 6 foot tall or being 2 foottall. But being 6 foot tall or 2 foot tall does not metaphysically determinebeing more than 3 foot tall. So metaphysical efficacy is not preserved underentailment. Neither causal nor metaphysical power is automatically preservedunder logical entailment, although there are special conditions in whichpower is transmitted.

§3.3The issue over the status of negative objects and events does not run parallelto the issue over the status of NPs. The most plausible position, in my view,is that they are dependent or supervenient objects and events. For example,it is plausible that there are only holes because there are hole-linings. (Lewisand Lewis 1970, Casati and Varzi 1994.) The hole in a bagel depends on thedough hole-lining. But if they are dependent or supervenient entities, whynot allow that they are causally active, exactly as we might allow that manydependent or supervenient properties are causally efficacious? But we musttread carefully (and avoid the holes)! Negative objects have PPs. For example,a hole might be three feet across. It is these PPs of the negative objects that arecausally efficacious. A hole’s not being round might be causally significant,


but only because of PPs of the hole. Negative entities can only have causalroles if they have PPs with causal roles. By contrast, negative entities withonly NPs would be entirely mute. I don’t believe in them.

§4. Mixed Disjunctions

§4.1Is every property positive or negative? That is: is the distinction exhaustive?And is it exclusive? Are there some properties that fall into both or neithercategories? In particular, what about the conjunction or disjunction of a PPand a NP? Call these ‘mixed conjunctions’ and ‘mixed disjunctions’. Aremixed disjunctions positive or negative, both or neither? So far we have en-dorsed the general principle that NPs on their own do not determine PPs.This is no less true of mixed disjunctive properties. Mixed disjunctive proper-ties, on their own, do not determine PPs. So I maintain that mixed disjunctiveproperties are NPs. By contrast, mixed conjunctions are PPs, since they candetermine PPs by themselves. So mixed disjunctive properties and mixedconjunctive properties are comfortably classifiable as negative or positive,and these properties give us no reason to deny that the distinction betweenPPs and NPs is exclusive and exhaustive.

§4.2How does this tie in with the closure of negativity and positivity under logicalimplication? We do not want to say that any property which is logicallyentailed by a PP is a PP, because mixed disjunctions would then be classifiedas PPs (since Px logically entails [Px or not-Qx]). By contrast, we shouldendorse the claim that any property which logically entails a PP is a PP. Thisis reversed for NPs: any property which is logically entailed by a NP is a NP,but it is not the case that any property which entails a NP is a NP. That is,where ‘F’ and ‘G’ stand for properties, ‘⇒’ means ‘logically entails’, we have:

If (G is a PP) & (F ⇒ G) then (F is a PP)

If (G is a NP) & (G ⇒ F) then (F is a NP)

It is not the case that if (G is a PP) & (G ⇒ F) then (F is a PP).

It is not the case that if (G is a NP) & (F ⇒ G) then (F is a NP)

Moreover, since disjuncts entail disjunctions, it follows from lines 1 and 2 ofthis schema that a disjunction exclusively of PPs is a PP, and a disjunctionexclusively of NPs is a NP. It is equally clear that a conjunction exclusivelyof PPs is a PP, and a conjunction exclusively of NPs is a NP.5

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§4.3There are special cases of mixed disjunctive and conjunctive properties thatare formed of a property and its negation. Mixed disjunctive properties, suchas being either blue or not-blue, are necessary properties, while mixed con-junctions, such as being both blue and not-blue, are impossible properties.6

The above principles of closure for positivity and negativity yield the con-sequence that necessary properties, such as being blue or not blue or beingsuch that x = x or being such that water = H2O or being self-identical, fallout as NPs!7 They don’t determine anything except some other necessaryproperties. On the other hand, impossible properties, such as being bothblue and not blue, fall out as PPs! They determine everything. The formerseems okay, but the latter seems worrying. Do impossible properties reallyhave such impressive determining power? Does something being both blueand not-blue really determine its being an elephant?

We could simply restrict the thesis about determination to contingentproperties. But that seems ad hoc. In response to this worry, I offer twostrategies.

The first strategy is to say that although there can be things (objectsor events) that have necessary properties, there cannot be things that haveimpossible properties. (In fact, everything, actual and merely possible, hasnecessary properties and it seems that nothing actual or possible has im-possible properties.) So there seems to be an asymmetry between necessaryand impossible properties, which is that things can possess necessary proper-ties but not impossible properties. There is surely something pretty dubiousabout a property that nothing can possess, although some philosophers haveembraced this idea. Surely, a property that nothing can possess is not a gen-uine property. If a thing exists, it must possess some genuine properties; butequally if a property is genuine, a thing can possess it. Perhaps impossibleproperties are not genuine properties. Perhaps there are other ways to fail tobe genuine besides being negative. If so, being a PP does not imply being agenuine property.

The second strategy is to point out that although being both blue andnot-blue determines being an elephant, it also determines not being an ele-phant. So the impossible property cannot really be said to determine a PPsince it cannot both determine that something has a PP and also that itlacks it. Presumably, if something exists, or is merely possible, it must haveproperties, and that means having those properties rather than their op-posites. And if a property determines, it must determine some propertiesrather than their opposites. In this slightly more demanding sense, impos-sible properties do not have determining power. We found ourselves dis-cussing necessary and impossible properties because they are special cases ofmixed disjunctive and conjunctive properties. Mixed conjunctive propertiesusually have determining power in non-impossible cases, due to the posi-tive conjunct. But where the negative conjunct is logically or metaphysically


incompatible with the positive conjunct, then the whole mixed conjunctiveproperty fails to determine anything—where that means determining some-thing and not its opposite. Therefore, on this view, although most mixedconjunctive properties are positive, impossible mixed properties are not. Theimpossible mixed conjunctive properties might be NPs or neither NPs norPPs (in which case the distinction is not exhaustive after all). On both views,necessary and impossible properties are not PPs. And perhaps they are alsonot genuine properties. That would be a commonsensical conclusion.

On the other hand it might be more theoretically elegant to ignore theworry and embrace the view that necessary properties are NPs and impossibleproperties are PPs. All we have is a sense of unease, not an articulatedobjection to the view.

§5. Complex Conjunctive Negative Properties

§5.1Let us now return to the basic argument. The Asymmetrical DeterminationThesis depends on two theses. I take it that the first—that PPs by themselvesdetermine NPs—is not controversial. But the converse negative thesis—thatNPs by themselves do not determine PPs—can be questioned. The thesisthat NPs never by themselves determine PPs seems intuitively attractive. Butwe probably cannot set much store by this intuition. (Intuitions do not takeus very far in metaphysics.)

The major source of resistance to the Asymmetrical Determination Thesiscomes from the appeal to complex conjunctions of NPs. Perhaps they dodetermine PPs, by themselves? (As we saw in §4, a conjunction exclusivelyof NPs is itself a NP.) I claimed that NPs, like not being gold, do notdetermine PPs, such as being water. But perhaps a complex conjunctionof all of a thing’s NPs does determine its PPs. A thing’s being orange isnot determined by its being non-blue. And something’s being orange is notdetermined by its having the property of not being all the other colors apartfrom orange, because the thing with that complex NP might be a number orGod, with no colors at all. But what if we add that the thing also has thenegative category properties of not being a theological object, not being anumber, and so on? Perhaps possessing such a lengthy conjunctive NP doesdetermine possessing the PP of being orange. Suppose that there are onlytwenty possible properties, and suppose that there is something that has theconjunctive NP of not having nineteen of them. (Some of these propertiesmight be negative category properties such as not being a number.) It mightbe argued that it must have the twentieth. And the same seems to followeven if the number of conjuncts is infinite. So it might be argued that certaincomplex conjunctive NPs do determine PPs, by themselves, which means thatthe Asymmetrical Determination Thesis is incorrect.

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§5.2In §2.4 I deployed the notion of supervenience to make the case for theAsymmetrical Determination Thesis. It seemed that if a thing has an NPthen it has a PP that suffices for that NP; but the controversial issue iswhether if something has a PP then it has a NP that suffices for that NP.In that section, I considered only simple negative properties, such as notbeing gold, which clearly do not suffice for being water. But supervenience,at least in a Jaegwon Kim-style formulation, quantifies over NPs; it saysthat if something has a PP then there is some NP such that if it instantiatesthat NP, it suffices for its having the PP (Kim 1984a). And one candidateNP is a very complex conjunctive NP. Perhaps such NPs do determine PPs.Appealing only to examples such as not being gold would be to make a badinductive inference.

One reply might be that we should distinguish two notions of superve-nience. A covariation notion says that if two things that are similar in Brespects, then they must be similar in A respects, or that if things differ in Arespects, then they must differ in B respects.8 Kim’s notion seems different: itsays that if something has an A property then that thing has some B propertythat necessitates (is sufficient for) the A property (Kim 1984a).9 The two no-tions certainly look different in form. Two differences seem notable. Firstly,Kim’s notion says that something with A properties must have B properties,whereas the covariation notion does not seem to say that. Secondly, Kim’snotion does not seem to talk about other things besides the thing with the Aproperty, unlike the covariation notion.

Supposing that these two notions are distinct, we can consider how itwould impact on the Asymmetrical Determination Thesis. It is true that iftwo things are the same in respect of all their PPs then they must be the samein respect of all their NPs. So, in the covariation sense, NPs supervene onPPs. But the opposite also seems to hold. It seems that if two things are thesame in respect of all their NPs then they must also be the same in respect ofall their PPs. This seems to imply that NPs and PPs are mutually covariant,and thus neither has metaphysical priority. However, we might think that theAsymmetrical Determination Thesis is safe if we deploy Kim’s formulation;for Kim’s notion, unlike the covariation notion, seems to preserve the ideathat PPs do not supervene on NPs—or so it seemed in §2.4.

However, the two notions are in fact logically equivalent. They only su-perficially look different. There is an explanation of why they look different.They would be different if we could assume that it is not the case that thenegation of a property is also a property (that is, that propertihood is not‘closed under negation’). The trouble is that this assumption is too near thecontroversial issue we are considering. Consider the idea that things withA properties must have B properties. If we include not having a B propertyas a B property then both notions of supervenience entail that things withA properties must have B properties. Surprisingly, therefore, psychophysical


supervenience, of either the covariation or Kim varieties, does not rule out theexistence of Cartesian non-physical souls, which are minds that lack positivephysical properties. But it does mean that Cartesian souls are very boring!For all Cartesian souls must think the same thing, and their thoughts neverchange.

If we allow that propertihood is preserved under all logical operations—that is, if we are a ‘Boolean hooligan’—then two the notions of supervenienceare equivalent, and PPs and NPs are mutually supervenient according toboth notions. The trouble is that if we deny that propertihood is closedunder negation, then we cannot use supervenience to argue against NPs.Either way, we are short of an argument for metaphysical inegalitarinism,given that certain complex conjunctive NPs seem to determine PPs.

§5.3A second possible reply is this. Suppose a thing is not colours C1 to Cn

(where what follows is a list of all the colors except orange), not a number,not a theological object, and so on, through all the possible categories ofthings. My opponent’s idea, which I deny, is that the conjunction of allthese negative properties of the thing together make it orange. Now, it iscontroversial whether “All Xs are Ys” implies “There are Xs that are Ys”,10

but it certainly implies “There are no Xs that are not Ys”. All-facts entailnegative facts. Hence the second-order property of a thing of having all theproperties of a certain sort entails that the thing has a certain second-orderNP: it has the second-order NP of not having other PPs of that sort. Similarly,the second-order property of a thing, of having all the NPs of a certain sortentails the second-order NP of not having other NPs of that sort. Both theproperty of not having other PPs of a sort and of not having other NPs of asort are second-order NPs.

Now we are interested in a particular property—the property that is theconjunction of all of a thing’s NPs except one. We have just accepted that ifa conjunction is of absolutely all of a thing’s NPs, it means that there are noother NPs that the thing has, which is a second-order NP. But what about theproperty of being the conjunction of all of a thing’s NPs except one? This is aPP! For it implies that if a thing had it, it would have all NPs apart from theremaining NP. So the thing would fail to have that remaining NP. But failingto have a NP means having the corresponding PP. Consider the propertyof not having some particular NP—for example, not having the property ofbeing non-orange. This is just the property of being orange. It is a PP, since,to put it loosely, two NPs make a PP. Hence the complex property of havingall NPs apart from not being orange entails the PP of being orange. Thenegative all-except-one property is in fact a PP, in disguise. So it might beargued that there is no difficulty here for the Asymmetrical DeterminationThesis; for the conjunction of all of a thing’s NPs except one is a PP, since itis a conjunction of many NPs plus one PP. Hence that complex conjunction

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can determine a PP. And that is because it is a PP and not a NP. No wonder,then, that it can determine the PP. So we can retain the idea that no numberof purely NPs on their own can ever determine a PP. We can never derive theconclusion that something has a PP unless the premises contain the assertionthat something has a PP. (It’s like Hume on ‘is’ and ‘ought’.)

The trouble with this reply is that it is not clear that the complex con-junctive property that we are interested in is indeed the property of havingall the NPs except one. We must distinguish between the property that is aconjunction of all of a thing’s properties, and the property of having all ofa thing’s properties. The former does not imply that the thing has no otherproperties; only the latter, second-order property, implies that. A complexconjunction of all of a thing’s NPs does not imply that it has no other NPs.The mere conjunction of all of a thing’s NPs except for the property of not-being-orange does not imply not having the property of not being orange(that is, being orange). So the complex conjunctive NP seems really to be aNP, not a PP in disguise, and perhaps—for all we have been shown—it doesdetermine the PP of being orange without including a positive property indisguise as one of its conjuncts.

§6. Empty Space-time Points and the Positive Existence Principle

§6.1The reply to the problem of complex conjunctive NPs that I favour is asfollows. Consider empty space-time points. The fact that the lengthy con-junctive NP is instantiated at some space-time point does not entail thatanything exists at that point that has the remaining PP (orangeness). Forthere might be nothing at all of any sort at that point. The NP can be in-stantiated at that point without being instantiated by a thing that occupiesthat point. If so, the instantiation of the lengthy complex NP alone does notdetermine the instantiation of a PP. For the empty space-time point lacksthe PP of being orange. The NP is instantiated without the PP; so the NPdoes not determine the PP.

It might be replied that an empty space-time point is a thing. Perhaps aspace-time point is a thing with various positive relational properties, and itmay not have positive intrinsic properties. But even if it is a thing, the emptyspace-time point is not orange. So the complex NP that the empty space-timepoint instantiates still does not determine being orange.

On some views, existence is a property of things, and if so existence wouldbe a PP. But even if an empty space-time point has this PP in addition to theconjunctive NP, that does not mean that it instantiates orangeness.

There might have been no space-time points. There might only have beenabstract objects and God. Such a purely non-physical world is perhaps athing. But it is not an orange thing, despite having the lengthy conjunctiveNP. Furthermore, perhaps the world might have been entirely empty—not


just no spatio-temporal things, but also no space, no time, no abstract objects,no deities: nothing. An entirely empty world might nevertheless be a thing.But such an empty world is not orange, despite having the lengthy conjunctiveNP. So, again, the lengthy conjunctive NP does not determine orange.11

Both the conditionals and the necessitation relations fail in this case.Both criteria indicate that NPs do not determine PPs, and the criteria arenot defeated. So there is no reason to think that a determination relationobtains despite their failure.

§6.2There is now an interesting complication, which raises deep metaphysicalissues. Suppose that some space-time point is not empty—that is, supposesomething exists there. Then does the instantiation of the complex conjunc-tive NP by that thing mean that it must have some PP? Perhaps it does. But itdoes so only if we assume the principle that an existing thing must have somePP or other (besides the property, if it is such, of merely existing, and besidesthe ‘haecceity’ property, if it is such, of being the particular thing that it is).If this principle has no name, it deserves one. Some philosophers may havestated this principle, but I don’t know about it; so I suggest the name ‘ThePositive Existence Principle’. The instantiation of the complex conjunctiveNP at a space-time point means that it has a PP only if something existsat that point and we can assume the Positive Existence Principle. Is thisgood news for negativity and its determining power? Not necessarily—forthe instantiation of the complex conjunctive NP by a thing alone does notnecessitate that the thing has the PP—only the instantiation of the complexNP by that thing plus the Positive Existence Principle that an existing thingmust have some PP. By contrast, the instantiation of a PP by a thing does byitself necessitate the instantiation of many NPs by that thing. We do not haveto assume a Negative Existence Principle that anything that exists must lacksome properties. For example, something that is orange is thereby not blue.That necessitation does not depend on the Negative Existence Principle. Bycontrast, it is not necessary that if something has the complex conjunctiveNP then it is orange unless the Positive Existence Principle holds. Perhaps itis true that things that exist cannot instantiate all properties: they must lacksome properties. Nevertheless, PPs necessitate NPs by themselves and not bymeans of that principle. So there is a metaphysical asymmetry. It is true thatif a thing exists and it has the complex conjunctive NP then it must have theremaining PP, given the Positive Existence Principle; but it is not true thatthe instantiation of the complex conjunctive NP itself necessitates the PP. Aswe saw, an empty space-time point, or even a whole world, might instantiatethe complex conjunctive NP but not instantiate the PP. The instantiation ofthe conjunctive NP only necessitates the instantiation of the PP if somethingexists within a world that instantiates the conjunctive NP. But this is only

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because of the Positive Existence Principle that an existing thing must havesome PP or other. PPs need no such help.

§6.3Here it is crucial to remember the distinction between determination andnecessity (Fine 1995). In the case of the complex conjunctive NP, the con-ditional and necessity relations hold despite the lack of a determinationrelation. The criteria are defeated by the obtaining of a distinct necessaryfact (the Positive Existence Principle) in the way that if Socrates is wise then2 + 2 = 4 is necessary despite there being no determination relation betweenSocrates’ being wise and the mathematical fact that 2 + 2 = 4. NPs andPPs may be mutually necessarily connected. But the necessitation relationsflowing from PPs to NPs hold solely in virtue of the determination of NPsby PPs, whereas necessitation relations flowing from NPs to PPs depend inpart on the Positive Existence Principle. What this shows is that NPs are notcompletely responsible for PPs in the way that the PPs are completely re-sponsible for NPs. That is, NPs necessitate PPs only if the Positive ExistencePrinciple holds, whereas PPs necessitate NPs come what may, just becausethey determine them. The Positive Existence Principle is one fact (if it is afact), and NPs only generate PPs given that fact (if it is one). By contrast,PPs generate NPs by themselves, without the help of distinct facts.

There is a benign dilemma: either the Positive Existence Principle is trueor it is false. If it is false, then something (such as a space-time point) can havethe complex conjunctive NP but not have a PP; so NPs do not necessitate PPsand do not determine PPs. But if it is true, then perhaps the instantiation ofconjunctive NPs means that it is necessary that certain PPs are instantiated;but the NPs do not have it within themselves to bring about the instantiationof those PPs, and so do not determine them. By contrast the generation ofNPs by PPs is entirely the responsibility of those PPs.

§6.4The Positive Existence Principle comes to the same thing as the thesis thatthere cannot be bare particulars, if we take a bare particular to be a thing thatonly has NPs. I assume that we are not operating with a strong conception ofa bare particular, which would be a thing without any properties, positive ornegative. (And I assume in addition that we are not counting existence andhaecceity properties as PPs.) In terms of bare particulars, weakly construed,the argument is that the PPs of a thing determine its NPs, but a thingthat instantiates a NP—even a complex conjunctive NP—may be a bareparticular (a thing with only NPs). Only if we assume that there cannot bebare particulars, that is, by assuming the Positive Existence Principle thata thing must have some PPs, does the complex conjunctive NP generate aPP. By contrast, PPs generate NPs without the help of such a metaphysicalprinciple. Hence the Asymmetrical Determination Thesis is secure.


Suppose that it is necessary that there are no bare particulars and that thePositive Existence Principle holds necessarily. Then it is necessary that if thecomplex conjunctive NPs are instantiated then the PPs are instantiated, giventhe necessity of the Positive Existence Principle (the necessary lack of bareparticulars). Nevertheless, the NPs do not determine the PPs by themselves,whereas PPs do determine NPs by themselves. In terms of supervenience, wemight say: if there can be bare particulars, then PPs do not supervene onNPs and are not determined by them. But if there cannot be bare particulars,then although PPs do supervene on NPs, supervenience is not criterial fordetermination and PPs still have metaphysical primacy.

§7. Infinitely Disjunctive Haecceities and the Power of Positive Properties

§7.1Let us now consider an argument against the metaphysical primacy of PPsover NPs. This argument goes as follows. Each non-blue thing has the prop-erty of being the very thing it is. That property is its haecceity (= “primitivethisness”). But there is also a property that is the disjunction of the haec-ceities of all the actual and possible things that are not blue. Each suchhaecceity is a PP. So the large disjunction of haecceities of all the things thatare not blue is also a PP, since, in general, a disjunction of PPs is also a PP.Call that lengthy disjunctive haecceitical property ‘DH’. Now it seems thatnon-blueness determines DH. Hence NPs do determine PPs, by themselves,contrary to the Asymmetrical Determination Thesis.12

Although it is not uncontroversial that the haecceitical property of beingsome particular thing is a genuine property, let us agree that it is for the sakeof argument. Then I think we must concede that if something is non-blue thenit is DH (and also that if something is blue then it is not DH). Determinationrelations are often revealed by the obtaining of such conditionals linking thedeterminer with the determined. Since such conditionals obtain, why isn’tthere a determination relation?

§7.2One reply would be to deny that if something is non-blue then it is DH on thegrounds that something must exist and be non-blue if that thing is DH. Anunoccupied space-time point might be non-blue without anything existingthere that has a haecceity. The problem with this reply is that an unoccupiedspace-time point may be a thing with its own haecceity. If it is not a thingwith its own haecceity, then the empty space-time point is non-blue but alsonot DH, and the Asymmetrical Determination Thesis is safe, since it is nottrue that if something is non-blue then it is DH. But if an empty space-time point is a thing, it will have a (positive) haecceital property, and thathaecceital property will be one of the disjuncts of DH. (At this point, thisargument does better than the first argument considered in section §5.2.)

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Surely—we might continue—there might have been absolutely nothing.The absence of blue things does not determine that something is DH sinceonly things that exist have haecceities, and the absence of blue things does notof itself determine that anything exists—not even space-time points, and noteven possible things if one thinks that possible things are things. An entirelyempty world, which has no space-time points, and no God or abstract objects,is not blue but also not DH.

But this reply does no better than the last, for even an empty world isan entity in its own right with its own haecceity. So that whole world doesinstantiate DH. Thus there is nothing actual or possible which is non-bluebut not DH, and the argument from DH properties against the AsymmetricalDetermination Thesis is back on track.

§7.3A better reply to the disjunctive haecceity argument is to emphasize degreesof determining power. What the disjunctive haecceity argument depends on isthe idea that whatever is non-blue exists and therefore has its own haecceity.Although the argument does show that being non-blue determines beingDH—let us concede that—it is surely not very exciting. For all it says is thatif something exists (or is possible) and is non-blue, then it has the haecceitalproperty that is consequential on its existence. Determining such a propertysurely is not much of an achievement. So DH is not very powerful.

Suppose that someone insists that it is nevertheless some achievement: thatcredit should be awarded to NPs. Well, we can agree—but according to thedegreed version of the Asymmetrical Determination Thesis, degrees of realityare correlated with degrees of determining power, and it is enough for theAsymmetrical Determination Thesis to show that NPs do relatively poorlyon this score. It needn’t be an all or nothing matter. Being non-blue leavesa lot open, whereas being orange leaves less open. Being orange determinesmore than being non-blue. We can concede that NPs are not completelypowerless with respect to PPs because they determine DH properties, butNPs are not as powerful as ordinary PPs (with respect to other PPs). For,although PPs determine DH PPs, they also determine many other non-DHPPs as well. And that is enough to discriminate against NPs in favor of PPs.

Imagine cowboys herding cattle into a coral in a plain in Arizona. In asense, the fence of the coral delimits an area ‘outside’ it, just as much as itdelimits an area ‘inside’ it. It delimits the rest of the surface of the earth.Nevertheless, one area is larger than the other. Similarly, let us concede thatnon-blueness determines a PP, just as orangeness determines PPs. But beingorange leaves less open than being non-blue. Thus being orange is moreefficacious than being non-blue, and is thus more real.

§7.4It might be objected that the idea that one property determines more prop-erties than another will not work if both properties determine an infinite


number of properties, since one infinite set may be just as large as the other.But while NPs (by themselves) determine an infinite number of NPs, theyonly determine one PP—the DH property. By contrast, PPs (by themselves)determine an infinite number of NPs. Therefore PPs are quite a bit morepowerful than NPs in this respect. (One cow is a lot less than an infinitenumber of cows.) A reply might be that if we allow that there are distinctlogically equivalent properties, such as DH and (DH or DH) and (DH orDH or DH), then we will end up with NPs determining an infinite numberof such DH properties. But then we can simply say that PPs determine manyNPs that are not logically equivalent, whereas NPs determine PPs that areall logically equivalent. So PPs have more determining power than NPs.

§7.5It is not implausible that every actual and possible thing has, in additionto its haecceity property, some total unique non-haecceity PP, presumablya conjunctive PP. Then it might be suggested that we could take all suchunique non-haecceital properties and disjoin them to form a complex dis-junctive property. This property is a property that no blue thing has and itis a property that only non-blue things have. Such a disjunctive property, itseems, is determined by non-blueness. But if this is what is suggested, wecan point out, once again, that there is only one such property. By contrast,PPs determine many NPs. The only problem would be if each actual andpossible thing had an infinite number of uniquely identifying PPs. But thereis little reason to believe this if we are including possible things. Supposethat the disjoined PPs are not unique. Then it is difficult to see why someblue thing could not also have that property. For example, suppose that thereare just two non-blue things and one is fluffy but not round and the otheris round but not fluffy. Then there might surely be a blue round thing anda blue fluffy thing, and if so being non-blue would not determine beingeither fluffy or round. Hence there can only be one disjunctive propertythat non-blueness determines—the disjunction of total unique properties—but determining that is not a very impressive manifestation of determiningpower.

§7.6Infinitely disjunctive haecceity properties are interesting. It is not clear thatthey are examples of genuine properties that are determined by NPs. But evenif they are, there remains an asymmetry in the determining power of NPsand PPs with respect to each other, even if some PPs are infinitely disjunctivehaecceital PPs. The primacy of being over non-being is not threatened bythese PPs.

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§8. Negative Totality Properties?

§8.1A problem for the Asymmetrical Determination Thesis might be thoughtto derive from totality facts. Bertrand Russell and David Armstrong arguedthat whatever facts there are, there is also the totality fact that those factsare all the facts—that there are no other facts (Russell 1918, Armstrong1978, 1989). So there must be negative facts about the world in addition topositive facts. What is important for us is that this negative totality fact isnot determined by the positive facts.

We could also run a parallel argument in terms of objects (or events):even if we list all the objects, there is always a totality fact that those objectsare all the objects. But there is an interesting category difference. For such atotality fact about the objects is not itself an object. Can’t we construe theworld itself as an object—the world-object? This is inadvisable since as soonas we have an object we can ask whether it is one of many objects there are,or whether it is perhaps the only object (a big lonely object), which wouldimply that there are no other objects. But then the totality fact that there areno other objects is not given in the lonely world-object. Hence it looks as ifwhether we consider facts or objects, we must admit that there are negativefacts about those facts and objects that are not determined by the positivefacts and objects.

§8.2Our question is whether the situation for properties is similar. Any object(such as apple) has many PPs and it lacks many PPs. Those it lacks are itsNPs. Suppose that we list the PPs of an object. That list would leave openwhether those were all of its PPs—that is, the list would leave open whetherthere were other PPs that it has. The thing must have a second-order NPof having no other PPs. Now let us ask the question: are all the NPs ofan object determined by its PPs? Certainly many of them are. But it seemsthat not all of them are—especially the second-order totality NP. But thisseems not to be consistent with the primacy of PPs over NPs. Another suchexample is the NPs of empty space-time points and empty worlds. In section6, I appealed to empty space-time points and empty worlds in order to showthat the complex NPs that are determined by a PP do not determine that PP.But what determines the complex conjunctive NPs of the empty space-timepoint or empty world? It seem not to be determined by PPs? Again, it is hardto square this with the primacy of PPs over NPs.

§8.3Now the Asymmetrical Determination Thesis, in a strong form, says not justthat all PPs determine NPs and that a thing’s NPs do not determine any ofits PPs, and also that a thing’s PPs determine all its NPs. The totality NP


certainly conflicts with that, for it is not determined by PPs. The same goesfor the NPs of empty space-time points and empty worlds.

However, we can soften the Asymmetical Determination Thesis. It needs tobe stronger than the weak claim that there are some PP/NP pairs that standin asymmetrical determination relations. It should be the intermediate thesisthat all PPs determine NPs and no NP determines any PP. This allows thatsome NPs are not determined by PPs. We should avoid a strong AsymmetricalDetermination Thesis that implies claims that all NPs are determined by PPs.For totality properties and the NPs of empty space-time points and emptyworlds are not determined by PPs.

To repeat: the intermediate thesis is: all PPs determine some NPs, andno NP determines any PP. The strong thesis is: all PPs determine NPs, andno NP determines any PP, and all NPs are determined by PPs. Totalityproperties and the NPs of empty space-time points or empty worlds onlycreate a problem for the strong but not for the intermediate AsymmetricalDetermination Thesis. That a thing’s PPs determine some of its NPs and athing’s NPs do not determine any of its PPs is still a significant asymmetryin the mutual determination of PPs and NPs, even if some NPs are notdetermined by PPs.

§9. Atomism of Powers

§9.1So far I have argued that NPs play less of a determining role with respectto PPs than PPs play with respect to NPs. I now want to return to my FirstThought—which I put to one side earlier on—that there is a difference in thedetermining role of PPs and NPs with respect to PPs. I still find intuitivelyattractive the view that is that although the instantiation of a NP can causeother NPs to be instantiated, nevertheless NPs do not play as substantial acausal role with respect to PPs that PPs play with respect to PPs. Armedwith the Asymmetrical Determination Thesis, let us now return to the FirstThought. That thought unraveled because it seemed that both PPs and NPswere causally relevant to producing PPs. Both conjoined together to forma sufficient condition for the positive effect (or for the probability of thepositive effect). However, this does not mean that we have no choice butto concede that the causal efficacy of NPs stands to PPs exactly as upper-level metaphysically determined properties stand to lower-level determiningproperties. I seek to undermine the thought that if NPs are determinedby PPs, then they should do as well as many other sorts of PPs that aredetermined by basic physical PPs, such as (positive) chemical properties or(positive) mental properties on the usual materialist views according to whichsuch properties are perfectly real and have causal powers (Kim 1984b). Onthat view, NPs have considerable causal status, rather than being relativelyepiphenomenal.

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§9.2Sydney Shoemaker claimed, insightfully in my view, that it is essential to a(positive) property to make a certain contribution to the powers of thingsthat possess them (Shoemaker 1984, 1998). I modify this to say “causal ormetaphysical powers”. Part of what Shoemaker means, or perhaps part ofwhat I think he ought to mean, is that these powers are atomistic, even thoughthose powers are typically manifested in combination with the instantiationof other PPs. A PP always makes some contribution on its own. I shall callthis the principle of the Atomism of Causal Powers. By contrast with PPs,NPs on their own make no contribution at all. They are mere absences. Andabsences, by themselves, can do nothing.

§9.3In support of this, consider that some causal powers are intrinsic while othersare extrinsic. Being an iron key of a particular shape gives a thing the powerto open a particular door in the right circumstances. But it is a ‘contextual’or ‘circumstantial’ power. An iron thing of that shape might easily lack thepower to open a door—for example if the door had a different lock fitted.Those are circumstances in which contingent and non-nomic things distinctfrom the key are different. By contrast, the key has the power to melt at500 degrees centigrade. This is an intrinsic power. That power does notdepend on any contingent and non-nomic matter of fact distinct from it. Itis determined by its intrinsic nature plus the laws. Having a power dependson the laws of nature; and in circumstances where they differ, the powers alsodiffer. Intrinsic powers depend merely on the intrinsic properties of thingsplus the laws of nature; but the extrinsic powers of a thing also depend oncontingent and non-nomic facts about things that are distinct from it.

Now the trouble with NPs is that there is no distinction between the causalpowers had by a thing with the NP just in virtue of having that property plusthe laws, and those it has in virtue of the NP and the laws together with theproperties of contingent and non-nomic things that are distinct from it. Butwith PPs, we can distinguish the causal contribution of the property in itselffrom the causal powers that it has only in combination with other distinctcontingent things. Of course, it is important that the intrinsic casual powersof PPs are not interfered with by distinct contingent and non-nomic thingsif they are to manifest themselves in the context of other factors. Still, a PPbrings causal powers to that situation, which may or may not be manifested.By contrast, NPs bring nothing.

§9.4The same is true of the metaphysical determinative power of NPs by PPs.The conjunctive NP, not being less than 6 feet long and not being more than6 feet long, does not determine being exactly 6 feet long unless it is conjoined


with the PP of being a physical object. NPs determine PPs (such as being6 feet long) only in conjunction with PPs. But it is not true that PPs ontheir own determine nothing. Being 6 feet long determines being more than2 feet long and it determines being a physical object, as well as not beingover 8 foot and not being a mathematical object. But the conjunctive NP,not being less than 6 feet long and not being more than 6 feet long, on itsown, does not determine any PPs, although it does determine other NPs, likenot being less than 4 feet long. (As with causal explanations, when we givemetaphysical explanations of PPs, we may mention NPs, but not becausethose properties themselves play the same full determining role that PPsplay; we mention them to draw attention to the PPs that play the dominantdetermining role.)

§9.5We can therefore rescue and reinstate the First Thought. There is, after all,a respectable sense in which we can say that PPs depend, if not solely, thenprimarily, on PPs. PPs determine PPs, or play the major role in determin-ing PPs, while NPs are metaphysically epiphenomenal with respect to PPs,or relatively epiphenomenal with respect to them. We can and should bemetaphysical inegalitarian about the properties that determine PPs. NPs donot play the same dominant role in determining PPs that PPs play. TheFirst Thought wasn’t far off. What partly reinstates the First Thought is thecombination of the Asymmetrical Determination Thesis and the Principleof Atomism about Causal Powers. NPs play some determining role withrespect to PPs—let us concede—but not by themselves; whereas PPs havedetermining power with respect to other PPs by themselves. Thus the NPsof a thing that are determined by its PPs are worse off than metaphysicallydetermined higher-level PPs such as chemical or mental properties. For meta-physically determined higher-level PPs have a fairly full-blooded causal rolewith respect to PPs, whereas NPs do not. PPs have more determining powerthan NPs with respect to other PPs. The First Thought was hard to defendon its own, especially given that both PPs and NPs generate counterfactualand factual conditionals with respect to PPs. But given the AsymmetricalDetermination Thesis and the Principle of Atomism about Causal Powers,the First Thought can be vindicated.

§10. Coda: Property Rights

My approach has been to try to make progress with the general issue ofwhether some kinds of properties are more privileged than others by draw-ing on the idea of determination. The distinction between genuine and non-genuine properties does not cast light on the distinction between genuineand non-genuine determination. Illumination flows the other way. We canexplicate and empower the distinction between genuine and non-genuine

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properties by appeal to the idea that genuine and non-genuine propertiesdiffer in determining power. This means that we have some principle formetaphysical discrimination among properties. Metaphysical inegalitarian-ism can be justified. Only properties that can do something are genuine orreal. And the reality of properties can be measured by their determiningpower: the degree of reality of a property determines its degree of determin-ing power. This power often generates conditionals and necessities by whichwe can know their power and reality.

I argued that NPs fall short of PPs on the score of their determiningpower. And what they do achieve is parasitic on PPs. PPs, such as beingorange, have metaphysical primacy over NPs, such as not being blue. Thereis a relation of asymmetrical determination between PPs and NPs. Somethingthat is orange is thereby not blue; but it is not the case that something thatis not blue is thereby orange. And even if we consider complex conjunctiveNPs, they do not determine PPs by themselves in the way that PPs determineNPs by themselves. Lastly, I appealed to the Asymmetrical DeterminationThesis and the Principle of the Atomism of Causal Powers to show that PPshave a greater degree of determining power with respect to PPs than NPs.PPs do most of the work, while what NPs achieve is parasitic on PPs.

An austere and extreme view would be that NPs are not fit denizensof the universe, and should be cast out of it. But a more moderate viewwould distinguish first- and second-class citizens of the universe. This ismetaphysical discrimination whereby some properties have full rights andothers have derivative rights. NPs have powers, but they derive from PPs.Nevertheless, it is true that PPs need NPs for some aspects of their efficacy.We must concede NPs some metaphysical status.

NPs are like guests at a party who arrive without drink. Maybe they cancome in and enjoy the party, and have something to drink, but only becauseother guests brought drink with them. NPs are metaphysical free-riders inthe world party!

There are the properties that a thing has and those it lacks. There is noproperty that a thing has because of those it lacks, whereas there are manyproperties that it lacks because of those it has. At least in this sense, beinghas primacy over non-being.13

Notes1 What is degree of determining power? How could we measure it? Perhaps power is not

necessarily measured numerically. But there might be an ordinal ranking of powers where theeffects, or dispositional effects, of one property include that of a second. If so, the first exceedsthe second in power.

2 Locke seems to come near to this idea when he writes “[the terms] . . . solidity carriessomething more of positive in it, than impenetrability, which is negative, and is, perhaps, morea consequence of solidity, than solidity it self ” (Locke, Essay on Human Understanding, bookII.iv.1, Oxford: Clarendon, 1975.)


3 By “factual conditionals” I mean those conditionals where their antecedents obtain, bycontrast with counterfactual conditionals, where they do not. I assume that when both theantecedent and the consequent of a factual conditional obtains, that does not necessarily meanthat the whole conditional obtains.

4 I have heard the following kind of dialogue many times: “Would you like some tea orcoffee”, “Ooh yes please; I’d love a cup of tea”. Furthermore, even if someone just offers ustea, there are many kinds of tea: Assam, Darjeeling, Earl Grey and so on. So offering tea is adisjunctive offer just like offering tea or coffee, although its verbal expression may not have adisjunctive syntactic form.

5 Are there pairs of positive properties that are mutually exclusive and exhaustive? Onlywithin a domain, surely. For example, being odd and being even are exclusive and exhaustive inthe domain of integers. But if we lift the restriction to a domain, there are no such pairs. Forexample, everything that exists is concrete or abstract. But while ‘concrete’ can be positivelydefined in terms of spatio-temporality, ‘abstract’ can only be negatively defined.

6 For simplicity I assume that instantiations of properties are all or nothing and not amatter of degree.

7 In this sense, a necessary property may not be an essential property. Having atomic number79 or being prime might be essential to a particular substance or a particular number. But beingblue or not blue or being self-identical hold of all possible things.

8 There are ‘global’ notions of supervenience that say that if whole ‘worlds’ (rather thanthings in ‘worlds’) are similar in B respects then those ‘worlds’ must be similar in A respects;but we need not worry about this.

9 This contrast is not the contrast between ‘weak’ and ‘strong’ supervenience. Weak super-venience says that how it is with a thing at a time in a ‘world’ dictates how it things are withother things or at other times in that ‘world’; whereas strong supervenience dictates how thingsare in other ‘worlds’. But the contrast between covariation and Kim-supervenience is differentfrom the weak/strong contrast. Covariation and Kim-supervenience can both be expressed ineither a weak or a strong form.

10 Aristotelians say ‘yes’ while classicists say ‘no’.11 If there were an entire world that was completely full of orange things, and only orange

things, that are orange all the way through, and that never cease to be orange, then perhapsthat would be an orange world. But an empty world has no colour.

12 David Lewis put this argument to me.13 Earlier versions of this paper were read in the following order by Jim Edwards, Stephen

Yablo, David Lewis, Helen Beebee, Gonzalo Rodriguez-Pereyra, Kengo Miyazono, JonathanLowe, Jonathan Schaffer and Ross Cameron. I am very grateful for the interesting and helpfulobjections, questions, comments, criticism and advice that I received from them. The paper alsobenefited from discussion when it was presented as a talk at Keio University and at TokyoUniversity’s Hongo Metaphysics Club and at the dinners afterwards.

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Negative Properties

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