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Particulars have their properties of necessity.

D.M. Armstrong

I assume here that particulars have properties, properties in the sparse sense, such things as mass, shape, size, velocity, as opposed to 'mere-Cambridge' properties, properties that are mere shadows of predicates. Suppose it is true that a particular a has property F. Is this truth contingent or is it necessary? It is common in the empiricist tradition to think that, with the possible exception of certain essential properties, this truth is a contingent one. Certainly, this is the way I have thought about the matter in the past. (Furthermore, I rejected essential properties except for the Lockean notion of properties that are essential relative to some concept in our minds.) Now, however, I wish to argue that for theories such as mine, and for some other theories as well, these truths are necessary.

Among those philosophers who accept properties in re, there are number of different theories about the nature of properties, and a number of different theories about the way properties stand to the particulars that are said to have them. Of particular interest to us here are first, the dispute between those who take properties to be particulars (tropes) and those who take properties to be universals; and second, the dispute between those who take particulars to be bundles of properties and those who take properties to be attributes of particulars. Since these disputes are largely independent of each other, this leads to four types of position: bundles of tropes, bundles of universals, tropes as attributes of particulars, universals as attributes of particulars. What I shall argue is that for each type of theory it is plausible, at least, to think that such predications are necessary. Famously, David Lewis always remained neutral between the positions just sketched. But I argue that he too should have embraced the view that these predications are necessary.

Bundle theories. We may begin with bundle theories, and it will not really be necessary to bother about the question whether the bundle is a bundle of universals or of tropes. For is it not clear that if a particular is just a bundle of properties, then it is a necessary truth that any particular property is a member of the bundle? We may not know just what properties a certain particular has, but for each such property it is necessary that the particular has that property because the property helps to constitute what that particular is. The situation seems to be just a particular case of class membership: a's being F, on this view, is a matter of F being a member of the class {F, G, H, … } where the members bear to each other a certain bundling relation. And the relation of a member of a class to its class is a necessary one.

A natural reaction to this little argument, one that I would have had myself in the past, is that it is nevertheless possible that the bundle as a whole might have existed except that it lacked F. And if this is true, does it not show that in some less superficial sense, F's membership of the bundle is contingent? In reply, I concede, somewhat grudgingly, that this shows that a sense can be given to 'it is contingent that a is F'. But the point to be insisted on is that it is not a sense that stands in any contradiction to 'it is necessary that a is F'. (I am indebted to John Heil for this way of putting the matter.) For, after all, a without F is something less than a, and therefore is not a. All that is true is that there is something genuinely contingent involved. I grant that the particular a is a contingent being. The proposition 'a exists' is contingent, hence a might not have existed. Furthermore, I grant there might have existed, at the same place and time, a counterpart of a, something that closely resembles a, although it is not a. If anyone chooses to call that contingency, so be it. But this is, as just argued, a 'contingency' compatible with necessity of the truth that a is F. It is a fundamental principle of modal theory, I suppose, that if a truth is necessary, then it cannot also be contingent (and vice-versa). I think the principle should be upheld. So I argue that this story about counterparts, a story that I accept, does no more than explain why, given a bundle theory, we might wrongly think that 'a is F' is contingent.

David Lewis. Lewis' theory of possibility is no more than a variation on this theme. He analyses the possibility that a particular in our world, such as the late Hubert Humphrey, might not have had some property that he actually does have in the following way: it is a matter of a counterpart of H.H. in another world than this one lacking that property, but otherwise closely resembling the original particular. Against Kripke's initially strong-seeming objection that we want the possibility to be a possibility for our Humphrey, Lewis contends, and with great force, that it is impossible that we can do any better than a counterpart, a counterpart that cannot, strictly, be identified with the actual Hubert Humphrey. But if so, then it is surely necessary that Humphrey has just the properties he has and no other. If it is impossible for him to be different, then that is a way of saying that he has his properties necessarily.

This means that Humphrey does not have his properties contingently. Again, Lewis' counterpart story can explain why we might be led to think or say that Humphrey has his properties contingently, but it cannot be an analysis of that contingency because there is no such contingency to give an account of! For it is, or it should be, of the essence of contingency that it is incompatible with necessity. And Lewis himself has given us the reason why it is necessary that Humphrey has the properties he actually has. It is because his counterparts cannot be him.

Subject/attribute with tropes. It is not quite so obvious that subject/attribute analyses of particulars must yield the necessity of predications. This is because a subject/attribute analysis creates a certain 'distance' between a particular and its properties, a distance not present in bundle theories. On the subject/attribute view the particularity of a particular is not exhausted by the bundling together of its properties. But if so, cannot we introduce the notion of the 'bare' or 'thin' particular which has its properties contingently? Mere bundling is essentially a bundling of certain items. Bundling is therefore like the class operator, just what is bundled is of the essence of the resulting entity. But given a subject/attribute analysis, the subject, the particular, seems to stand in some way or degree outside its properties. So may not the connection between subject and its attributes be contingent?

If these attributes are tropes then we have the sort of subject-attribute theory of particulars that is favoured by C.B. Martin and John Heil. They substitute tropes for universals. They hold, further, in Martin's phrase, that tropes are non-transferable. By this is meant that it is part of the being, part of the identity-condition, of a trope that it is a property of the particular that it an attribute of. A minor dispute in trope theory may illustrate the view. Consider two exactly resembling tropes that are attributes of different particulars. Is there a possible world in which the two tropes are swapped around between the two particulars? I used to argue that trope theory is forced to accept this as a possibility, but then, I said further, it is doubtful that it really is a genuine possibility. This 'swapping problem' was, of course, at best a minor difficulty for a trope theory. And if tropes are non-transferable, as Martin and Heil claim they are, then the difficulty vanishes. There is no such possibility. But with non-transferability comes necessity. Given this particular and this trope then the trope must of necessity attach to this particular. The particular and the trope are presumably contingent existences, but once they exist their place in the world is fixed. On this view the true predication of a trope is, or should be, a necessary truth.

However, it is not very clear how the essential premiss that tropes are non-transferable is established. How is the alternative hypothesis that tropes attach contingently to their particulars refuted? Suppose that one distinguishes between the identity-condition and the identification-condition of a trope. And suppose that then one grants that the identification-condition of a trope is tied to a specification of the particular particular that the trope is an attribute of. How is it to be further shown that being an attribute of this particular is of the essence of this trope?

It might be replied to this that the trope must have some identity-condition and what condition is available except its being the trope of this particular? But could there not be an intelligible conception of a trope that is, as it were, its own identity-condition without reference to the particular it happens to qualify? (On pain of regress, apparently a vicious one, there must either be such tautological identity-conditions, Gertrude Stein identity-conditions as one might call them after her remark that a rose is a rose is a rose - or else a virtuous circle of identity-conditions.) I am not clear just how Martin and Heil can rule out tautological identity-conditions for tropes.

But staying with non-transferability, we see that it as it were glues tropes to their particulars. Notice that this means that states of affairs (a particular's having a property) are obtained at no further ontological cost. States of affairs are important to have, particularly, I think, as the relata for singular causal connections. (You need particulars for causation, yet at the same time it is some and only some of the properties of a particular that are involved in the causal transaction. It is the mass and velocity of the billiard ball that are relevant to its making the second ball move, not its colour or smell. So it is the ball's having certain properties - a state of affairs - that is the first term in the singular causal relation.) As we shall see, all subject/attribute theories deliver us states of affairs, whether the attributes be tropes or universals.

Subject/attribute with universals. Is this account of the predicative tie compatible with making it contingent? I now think that this conception of particulars makes the tie a necessary one. Some background is necessary. Under the influence of Donald Baxter of the University of Connecticut I have come to a new view of the 'relation' between a particular and a universal that instantiates it. Baxter starts from a variant of the problem of the 'fundamental tie' that we have just seen in the case of the Martin/Heil view. In their view the tie holds between particulars and their properties, with the properties conceived as tropes. But Baxter starts by asking how we are to understand the link between particulars and properties conceived of as universals.

If you accept universals and have particulars instantiating them, then you will have to recognize facts or states of affairs, such as a's being F. A and F form a unity of some sort with a and F as parts. A and F are linked in some special way, they form a fact or state of affairs. But what is this link? Baxter's suggestion is this: what we have here is a partial identity of the particular and the universal (Baxter, 2001).

As I now see it, this partial identity is constituted by the fact that the property-universals are actually parts of the particular, at least if we confine ourselves to non-relational properties. (A term that I find convenient for these special parts is 'constituents' although I don't think of this bit of terminology as solving any ontological problems.) In the past I half-recognized this point, but I distinguished between the thin particular, which was the particularity of a particular abstracted from its properties, and the thick particular that included these properties. This left the properties outside and merely contingently connected to the thin particular, leaving the fundamental tie between thin particular and its universals a very puzzling matter. Baxter's call was for a more thorough interpenetration of particular and universal.

What has to be done, I thought, is to re-think the notion of the thin particular. This can be achieved by conceiving the particular as a one running through the many properties, a 'one in the many', a uniting factor or principle in virtue of which they are all properties of the same particular. This comes closer to the bundle theory, but I don't think it is a bundle theory. The factor of particularity, though inseparable from the universals it unites, is not analysed away as it is in bundle theories. (It is worth noticing that this account of particulars seems to be as much available to those trope theorists who accept a substance/attribute account as it is available to upholders of universals. They could, and I think should, think of ordinary particulars as ones that run through many tropes in virtue of which the tropes are all properties of the one particular.)

But bringing the universals thoroughly within their particulars meant disagreeing with Baxter at a vital point. He continued to hold that it is a contingent matter what particulars instantiate what universal. But it seems to me that if a universal is partially identical with its particulars then it will be necessary that the particular instantiates that universal. A particular that did not instantiate that universal would not be that particular. So I now think that where F is a universal and a has F, it is a necessary truth that a has property F.

Like Lewis, a simulacrum of contingency can still be offered. Particulars are contingent beings. So a particular might not have existed and instead, in its vacated place, there could have been a particular very like the really existing particular. And if one further holds, as I hold, that universals are also contingent beings, then any universal might not have existed, but instead a universal very like the really existing universal might have existed. But this does not make predications contingent. What we have instead, I suggest, is a necessary connection between contingent entities, the particular and the universal. Just as in the case of non-transferability of tropes, given particulars and given universals, states of affairs are then nothing over and above the particulars and universals that 'participate' in each other. The particulars are contingent beings, and, as I have just said, I'd argue that that the properties are also contingent beings, and so, therefore, the states of affairs involved are also contingent beings. But the link between particular and property is necessary.

Perhaps the young Socrates in Plato's Parmenides got it right first go when Parmenides asked him how particulars stand to Forms. Socrates' first suggestion was participation. Perhaps he should have stopped there! On the other hand, in the dialogue the Forms appear to be transcendent entities, which seems to rule out genuine participation. Participation goes better with a down-to-earth account of universals, an Aristotelian or perhaps 'Aristotelian' view, the sort of view that I favour. The universal is a one that runs through its particulars just as the particular is a one that runs through its universals.

Relations. So far I have confined the discussion to the intrinsic or non-relational properties of particulars. But what of the relational properties of things? Are they to be given the same treatment as non-relational properties? I think not the same treatment, but it will be better at this point to switch the discussion to relations rather than relational properties. A fairly traditional way of classifying relations in metaphysics, going back to Hume at least, is into internal and external relations, where internal relations are those necessitated by their terms. For instance, given two objects of different sizes, with a bigger than b, then this relation bigger than holding between a and b is internal. (I'm making the assumption here, a plausible one I think, that size is a non-relational property of objects.) This bigger than relation seems to supervene on the two objects having the size they have, and I'd argue that ontologically there is nothing there except the objects with their sizes. Contrast this with the two objects being a mile apart, an external relation. The moral that I would draw from this is that, although true predications of internal relations are necessary, we need not pay them a great deal of attention. In particular, we do not need to recognize states of affairs over and above any states of affairs that may be involved in the terms. External relations, however, do, I think, yield states of affairs.

Concentrating on external relations, then, how do they stand to their terms? If we have given an account of property-universals - monadic universals - as lying within their particulars, then it will be natural, if we can, to give an account of the instantiation of relation universals - polyadic universals - as lying within their particulars. And, pace Baxter again, this partial identity will, I maintain, have as a consequence that each instantiation of a polyadic universal is a necessity. There will, of course, be the possibility of simulacra of these universals that do not instantiate just these particulars, but they can be no better than counterparts. In the past I would have said that internal relations are necessary but external relations are contingent. Now I say that both are necessary but that internal relations do not, and external relations do, involve states of affairs. The external relations will be universals that are constituents of these polyadic states of affairs.

But how are we to bring external relations within their instantiating particulars? It may seem a rather opaque idea (even by the standards of this paper, some may consider). My present idea is to provide more clarity by exploiting the link between external relations and what I call structural properties. The latter are monadic, but they attach to a particular in virtue of the way that the proper parts of that particular are related to each other. For a simple example think of a blade and a handle fitted together to make a knife. Having a blade and a handle standing to each other in this way is a structural property of an object, the object that is the mereological sum of this blade and this handle.

Now consider any dyadic external relation, for an example being two miles apart. In every concrete situation where this relation holds there will be two particulars, a and b, that are two miles apart. But now consider the particular a + b, the mereological sum of the two particulars. This particular will have a structural property, a monadic property: having at least two parts separated by two miles. The suggestion then is that it is this monadic structural property that is a special sort of part of the special sort of particular that has this structural property. Provided that the mereological sum of the terms can always be regarded as a particular, even if a particular of otherwise little practical interest or importance, then it seems that this solution can be extended to cover all external relations.

One interesting thing about this suggestion is that it reduces all instantiations of universals by particulars to the monadic case. Taken ontologically, the form of all instantiations is x is P. We are now accustomed to write R (a, b). But, for the case of external relations, the true form according to this new theory is x is S, where x is the mereological sum of the terms of the relation (a + b), and S is a structural property of this particular. External relations become, as it were, the cross-bracings of certain non-simple objects. By contrast, the true ontological form of R(a, b) where R is internal is no more than Fa + Gb, a mere mereological sum. You have no doubt observed, as Don Baxter observed to me, that the words 'internal' and 'external' have become pretty unsatisfactory. It might be better to reverse them! But for the present, at least, I pour the new wine into the old bottles.

Let me note once again that states of affairs are contingent existences, and so are their constituent universals and particulars. But once given those universals and those particulars, then the states of affairs are necessary, they are fixed. (And equally, given the states of affairs, the constituent universals and particulars are fixed.) These contingent existences might not have existed, and other closely resembling states of affairs existed instead. It is interesting to notice that this situation does not contravene the Humean interdiction of necessary connection between distinct existences, at any rate if 'distinct' here is read as 'wholly distinct'. The particulars and universals involved in states of affairs are not wholly distinct because they are partially identical.

Relational properties. We should now clear up the status of the relational properties of particulars. For the purposes of ontology they do not seem to be a very important category. For suppose that we are given all particulars and their non-relational properties, and are also given all the external relations between particulars. Then, it would seem, not only do all internal relations supervene, but so do all relational properties. This holds both for what have been called pure relational properties - being a mother - and impure properties - being the mother of Alexander.

Higher-order relations. If the theory advanced about the nature of instantiation is correct, then it will presumably apply to higher-order instantiations. In particular, it ought to apply to those links between universals that I identify as laws of nature. These, as I now think, are best represented as causal or quasi-causal links between what I call states-of-affairs types. Thus, very schematically, I now see the simplest sort law (perhaps too simple for any actual instances) as having the form something being F causes that same something to be G, with F and G universals. Causing, or determining something to be the case, is in my view a relation that we are actually given in experience in favourable cases such as pressure on our bodies and the operation of our own will. That, of course, is just causality in the particular case. But I suggest that it is a plausible hypothesis that the relation that we experience at the level of particulars may also hold between states-of-affairs types. Ordinary language suggests this: we say, for instance, that arsenic causes death, which on the surface is a linking of types (universals). It is perhaps only our long unhappy love affair with Humeanism that insists on putting this into the form of a universally quantified proposition.

It will be seen that if the same sort of relation that is experienced to hold in the singular case can also hold in the case of states-of-affairs types then the inference to the regularity of the causal sequence becomes rather perspicuous (though informal).

My new account of external relations sees them all as the instantiation of a structural property by one object only, the object formed by the mereological sum of their terms. This account seems to be available for higher-order connections. The nomic relation or relations will become a monadic but structural property of a certain object. This object will be the mereological sum of the states-of-affairs types that are nomically connected.

There is a lot of complication to be added here. We need to deal with laws that are merely defeasible, laws that are probabilistic only, and to expand the account to include the all-important case of functional laws. But I am here interested only in the modal status of laws. I used to argue, as did Michael Tooley and Fred Dretske, that these connections between universals were contingent only. It sounded like a decent empiricist theory. But if the instantiation of a monadic universal holds of necessity and if this extends to polyadic universals, then it should extend to relations between universals. The states-of-affairs types can be taken as higher-order particulars, and the mereological sum of two or more such higher-order particulars will also be a higher-order particular. If a causal relation holds between the mereological parts of this special higher-order particular, then that relation can be taken to be a structural property of that particular, and so a special sort of part of the particular.

The higher-order particulars and states of affairs will be contingent existences as will the particulars and the universals that are their constituents. But given just these constituents, the way they stand to each other will be necessary. That has the consequence that the very same universals must stand in these higher-order states of affairs. All that could stand in different higher-order states of affairs - different laws on the suggested account of laws - are counterpart universals. So laws are necessary not contingent.


Armstrong, D.M., 1997. A World of States of Affairs. Cambridge: Cambridge University Press.
______ 2004. "How do Particulars stand to Universals?" Oxford Studies in Metaphysics, Vol.1, ed. Dean Zimmerman, 139-154.

Baxter, Donald L.M., 2001. "Instantiation as Partial Identity". Australasian Journal of Philosophy, 79, 449-464.