Introduction *

Shoemaker’s Account *

Swinburne’s Criticism *

Problems with Swinburne’s Criticism *

Problems with Shoemaker’s Account *

Causal Powers and Dispositions *

Redeeming Verificationism *

Requirement for the Qualitative *

Causally Relevant vs. Causally Operative *

Visualizing the Model *

The Illusion of Particles *

Objections to Our Account *

Conclusion *

Bibliography *

Properties have ordinarily been accounted for using two philosophical devices – the dispositional and the qualitative. Armstrong has claimed that properties can be expressed just in terms of their qualitative causal bases. Martin claims, instead, that properties are a "two-sided coin", and that they are really neither dispositional nor qualitative, but that they can be described only in part, by either one. In this paper, we will develop a purely dispositional account of properties. We claim that the qualitative is reducible to the dispositional. The qualitative, in our account, is only an illusion, which falls out of the fact that we are just as dispositional as the things that we take to be qualitative. We are naturally reluctant to consider ourselves as purely dispositional, since dispositionality has historically been taken to be a second-rate property of things or often not even a property of things at all.

That things may exist which are not properties – relations and higher order facts, for instance – is not our concern here. In addition to things like relations and higher order facts, which are higher order and therefore do not fall within the scope of our theory, we need to provide an account of the substance of which our properties are properties. We can see already that this will be neither dispositional nor qualitative, since it cannot be a property (otherwise it, too, would have to be a property of something).

In addition, we will suppose that there does not exist a non-physical aspect of the world. Many philosophers believe that mind, for example, can exist independently of a physical medium. For our purposes, we will suppose that anything can be expressed as the manifestations of a physical system. The mind, for example, would be considered as an artifact of an immensely complex biochemical system, which is nonetheless constrained by the same physical laws that govern more familiar, simpler, systems. That is to say, nothing is more than the sum of its physical parts.

We will begin our discussion with a consideration of papers by two philosophers whose opinions differ on the requirement for the qualitative. Sidney Shoemaker claims that all genuine properties are identical with their causal powers. In his reply to Shoemaker’s "Properties and Inductive Projectibility", R.G. Swinburne raises several arguments against Shoemaker’s account, but does not provide support for any another option.

In his papers "Causality and Properties" and "Properties and Inductive Projectibility", Sidney Shoemaker claims that all genuine properties are identical with their causal powers:

But what is a genuine property? Shoemaker raises the first criterion for genuine properties in the above excerpt – genuine properties must contribute determinately to the causal powers of their possessors. Consider, for instance, the sense of the property ‘grue’ such that any object, which is grue, will appear blue on the weekend and green on every other day. If we are asked, without seeing it, what colour an object with such a property will appear to be, then we need to inquire further whether what day of the week it is. The property of being grue does not alone contribute determinately to the appearance of the object.

Shoemaker’s second criterion is that genuine properties must be intrinsic. Take as examples, the property of being such that Jimmy Carter is president, and the property of being 50 feet south of a burning barn. These are relations, rather than properties of just one object. Suppose that a pencil had either property. Then it wouldn’t be possible, for instance, to look just at the pencil, and to tell if it had the property of being such that Jimmy Carter is president. Such properties are not intrinsic.

Now let’s return to the question of why all genuine properties are identical with their causal powers. Suppose that there were some property identical to, say, that of being spherical, except in some respect which has no causal powers for our world. Then we would have no good reason to believe that a particular object is spherical, because we could not, even in principle, distinguish an object with this property, from one, which is spherical.

In addition to claiming that all genuine properties are identical with their causal powers, Shoemaker rejects dispositions as properties of things. He contends instead that they are properties only of predicates:

Shoemaker seems to have identified dispositions with predicates, and not with properties, just because he doesn’t think that dispositions should apply to properties. That is, he doesn’t seem to have a very good argument to back up his statement – it sounds more like a ‘gut feeling’ than an argued point. The distinction he makes (that dispositions should not apply to properties) draws over into his previous statements, where he identifies a genuine property with its causal powers. Shoemaker believes that powers are the sort of thing that can be applied to properties, but that dispositions are not. We intend to show later that what we call ‘dispositions’ is identical with Shoemaker’s ‘causal powers’.

Following Shoemaker’s article is Swinburne’s article, "Properties, Causation, and Projectibility: Reply to Shoemaker". In his paper, Swinburne makes several charges against Shoemaker’s argument. Swinburne’s charges are as follows:

1. Shoemaker’s proof rests on verificationism. Shoemaker states that

 

I also deny that it is possible for two different properties to share all of the same causal potentialities. If that were possible, it would be impossible to know, or even have good reason for believing, that a single property is shared by two different things.

 

Here it seems clear that Shoemaker equates the possibility of our knowledge of a property with the possibility of the existence of that property. That is to say, he supposes that if we cannot experience a property, then it cannot exist.

 

2. Shoemaker’s account results in a ‘vicious regression’. In his article, Swinburne points out that

Properties are something more than their causal powers. Properties possess a directness, which their causal powers do not. Swinburne says that, "What we see no doubt we see because we are caused to see, but what we see is not that we are caused to see." That is, the sky not only has the causal power of making a person see blueness, but it also has the property of being blue. Swinburne holds that these two are distinct, and both present.

Shoemaker denies Swinburne’s charges of verificationism. Shoemaker claims that

We know that there can be no property indistinguishable (that is, indistinguishable through observation of its causal powers) from, but not identical to, say, that of being spherical, because if there were such a property, then we would have no reason to call anything spherical. But we do call some things spherical (spheres, for instance), and we do know that they are spherical, so such properties cannot exist.

Swinburne claims also that Shoemaker’s account results in a "vicious infinite regress". Martin seems to hold a similar view on this matter, claiming that "It is like a promissory note that may be actual enough but if it is for only another promissory note which is…, then that is entirely too promissory.". Swinburne and Martin both hold that, if all properties are capable only of changing other properties, then such changes will never result in a "realization" of a manifestation.

What Swinburne in particular seems to forget is that among the chain of changes in properties brought about by a manifestation will be, in cases in which we can experience the manifestation, some change in the properties of the mind which we would identify with recognition of the manifestation. It is important to note that the verificationism here is not ours, but Swinburne’s – in his example, he considers only the effects that he supposes Shoemaker’s account would have on our ability to experience manifestations. Our rebuttal, correspondingly, addresses those concerns.

We should consider more in depth why it isn’t a problem to have an entirely "promissory" account of things. Suppose that we have an observer, and that in front of the observer sits a red ball. Let’s consider a possible line that the ‘vicious regression’ could take. Because the ball has the property of being red, it is the case that if light with the property of being white were incident on the ball, then only light with the property of being red would be reflected from it’s surface. Because only light with the property of being red is reflected from the ball’s surface, it is the case that if that light were incident on the observer’s eye, then it would cause chemical changes in the retina, which have the property of causing an experience as of seeing a red ball, in the observer’s mind. Because those chemical changes have the property of causing an experience as of seeing a red ball, in the observer’s mind, it is the case that those chemical changes have the property that their occurrence causes, in the brain of the observer (which is, after all, just a very complex biochemical system) the occurrence of other chemical changes, which have the property of causing in the whole of the brain, a series of changes which we associate with the perception of the red ball.

None of the three of us is a neuroscientist, so we will not consider this regression any more exhaustively than we have. In fact, it should be possible in principle to associate some of the steps we’ve taken here with hundreds, or thousands, of smaller steps. To include those steps, or to continue this regression further, would be pedantic. The reader should be able to see, at this point, that the regression need not terminate in order to cause a sense experience in an observer.

The reader should also be able to see that we have ignored, for instance, the rays of incident light which are absorbed into the ball, since they didn’t lead to a perception of red by the observer (this was done to make the example clearer). In fact, those rays, and the uncountable other steps which we have ignored, form part of what Martin calls the ‘power net’, which is the collection of all such interactions between properties.

The major problem which Swinburne seems to be plagued by is the mistaken consideration of the observer as being outside the system he is observing. Somehow the observer records information about the system (for example, that there is a red ball in front of him) without being affected by the system, which immediately seems absurd. What Swinburne seems to looking for is an account in which a chain of changes in causal powers is initiated by, for example, the red ball, and terminates in something qualitative. The observer somehow ‘sees’ this without the need for a change in his causal powers (for instance, changes in the causal powers of his brain). By considering that the observer is no less a part of the system than the red ball is, we have eliminated the need for the chain of changes in causal powers to terminate in something qualitative. In fact, it need not terminate at all.

Martin’s objection (that Shoemaker’s account is entirely too promissory), however, is of much broader scope, and will be discussed later in this paper.

Swinburne’s objection that, "What we see no doubt we see because we are caused to see, but what we see is not that we are caused to see," derives from his assumption that the causal chain must end in something qualitative. It seems as though Swinburne associates our qualitative terminator with that which we see, and associates the remainder of the causal chain with the statement ‘that we are caused to see’. Then his dissection of properties into the causal part and ‘something else’, is due to the assumption we have outlined (that the observer sits outside the system). The ‘something else’ becomes unnecessary when we make the observer a part of the system.

Whereas we, in agreement with Martin, would say that ‘x is dispositional’ is a predicate, which can be applied to the properties, x, of things, Shoemaker claims that this predicate can be applied only to other predicates. That is, Shoemaker holds that dispositions are nothing more than predicates (because properties of a thing cannot be considered dispositional).

But the elementary particles, which may include electrons, seem to have properties without also having structure. Certainly if those things which we currently recognize as elementary particles, turn out not to be elementary, then they will be composed of something else, which may in turn be an elementary particle. It seems absurd to think that this sort of reduction, to more elementary pieces, could continue forever. At some point we will have to identify something as elementary, which is to say that it cannot further be broken into other components. That something will have properties, without also having structure. It is not possible that the properties of the things, which are elementary in this way, should be explained away by means of their structure. Shoemaker is left without a structural basis for the behaviour of elementary particles. What, then, is the basis for their behaviour?

Suppose that we take a ‘snapshot’ of the world at some instant in time. Suppose the picture records all the properties manifested by everything in the world, at that moment in time, and not just their sensible properties. Roughly speaking, then, the things, which are recorded in the picture, are the qualitative properties of the world in the moment at which we took the picture. Some things, such as mass, could not be identified in the picture. Very few people claim that they can identify any sort of structural basis for mass, and certainly those who do claim it haven’t adequately been able to back up their claims. Most physicists will tell you that the only way to determine something’s mass is to apply a force to it, and observe its acceleration. Using Newton’s first law, we can find the mass of the object, given the applied force, and the resulting acceleration. Mass is nothing more than a relation between force and acceleration, and can’t be found in our snapshot. In order to determine the mass of an object in the picture, we require the passage of time, so that we can measure its acceleration in response to a known force.

We are, of course, indulging in a bit of verificationism. We believe, though, that in this case it is harmless. Our snapshot has captured every manifested property at one instant in time, and not just those that a particular person might observe. We could determine, from the picture, even the finest structure, at that point in time, of anything in the world. The identity between the things that we can see in the picture, and the qualitative properties of the world at some point in time, is a rough one. We include it here only as an analogy by which the reader might gain a better understanding of what we have taken to be qualitative properties, and to demonstrate the absurdity of qualitative properties without a basis in structure.

We are left with some properties that cannot be found in the structure (and so they also are not found in our picture). We call these properties dispositional properties, because they are related more to what a thing would do if acted on in a certain way, than to its structure. Those properties that are found in the snapshot, we call qualitative properties, since they are based strongly in the qualities of a thing.

We have previously established that Shoemaker has no structural basis for the properties of elementary particles. It seems reasonable to assume, then, that any properties that they do have, must be dispositional ones. Since Shoemaker denies the existence of dispositional properties (he says that the predicate ‘x is dispositional’ can be applied only to other predicates, and not to properties), then he has no causal basis at all for the properties of the elementary particles. We can get Shoemaker out of this mess, if we build an identity between causal powers and dispositions.

What Shoemaker calls ‘causal powers’ seems to coincide with what we would call ‘dispositional properties’. What does Shoemaker mean by ‘causal powers’? Can we equate this with ‘dispositional properties’ without losing Shoemaker’s identity between properties and their causal powers?

One objection to such an identity might come from a perceived directedness in the causal powers of a thing. For example, suppose that we dissolve a small amount of salt into water. We might first suppose that the water has the causal power of being able to dissolve salt, whereas the salt simply is dissolved. It is easy enough to demonstrate that this cannot be correct, and that the salt should play as important a role in its dissolving, as the water does.

Suppose that instead of trying to dissolve a small amount of salt, we try to dissolve a small piece of granite. Obviously, the granite will not dissolve in water the same way salt did. In the same way, we might instead have replaced the water with air, and we would find that the salt would not dissolve in air. Clearly, the properties of both the salt and the water play equal parts in the dissolving of salt into water. We say that the dissolving of salt into water is a mutual manifestation of the properties of water and salt. The process of dissolving one thing into another is not a process that occurs between an active and a passive reagent. We believe that any manifestation of a causal power will be a mutual manifestation between partners. After all, how would it be possible that one thing would have some effect on another, without regard to the properties of the second? The result of striking a glass depends on how fragile the glass is; the result of applying a force to some object depends on the mass of the object. Indeed, it seems impossible that we could make a statement of the sort, ‘x has such-and-such an effect on any object y, regardless of the properties of y,’ for any x.

The partners in a mutual manifestation need not number just two. There is no limit on the number of things which might need to come together in order to result in a particular manifestation. The causal powers of a thing correspond with its capabilities of being a part of a set of partners for a mutual manifestation with other things in the same set. Those capabilities also correspond to the thing’s dispositional properties! We do not claim a one-to-one correspondence. It is obvious that one disposition might correspond with a number of causal powers. Rather, what we claim is that the ground that is covered by causal powers, is the very same ground that is covered by dispositions. We claim an identity between the set of causal powers of a thing, and the set of dispositional properties of the same thing. We do not claim a necessary identity between any particular causal power of a thing, and one dispositional property of the thing.

Shoemaker claims that his argument is not verificationist because it starts with the fact that we can know the difference between two distinct properties, and infers from this that any account in which we might not know the difference between two distinct properties, is absurd. Is it true that we can always tell the difference between distinct properties? Imagine, for example, a white piece of paper, and a white Styrofoam cup. The two share the property of whiteness. Why do we say that they are both white? We say that they are both white because they both have the power to cause a sensation of whiteness in an observer, under particular lighting conditions. In plain English: we say that a thing is white if we perceive it as having the same colour as all the other white things, under particular lighting conditions. Every property that we can imagine originates from some perception – the property of whiteness, as well as properties such as being hot or being cold, being loud or quiet, of smelling like roses, or of tasting like ice cream. Even properties based more loosely on our everyday experience, such as the property of having positive electric charge, are based on observed interactions between one thing and another. We would not say that something had an electric charge unless, for example, we observed the expected changes in some sort of measuring device, when it was placed in the region of the electric charge. The verificationism in Shoemaker’s account stems not so much from his own arguments, as from our methods of discovering if something has such-and-such a property.

We can strengthen the verificationism on which Shoemaker relies, by asking not that two distinct properties be distinguishable just to ourselves, but that their possible effects on things in general should be different. We are prepared to claim that if two properties are identical in their causal powers (that is, if they are identical in their ability to change any state of affairs), then they are the same property.

Suppose that a thing has a set of properties P which have causal powers for our world, and another set Q of properties that do not have causal powers for our world. We can claim identically that the thing has just the properties in the set P, without losing any information at all about that thing’s effects on our world. This is also Shoemaker’s claim.

By most accounts, properties can be divided into two categories: dispositional and qualitative. Several attempts have been made to account for the world in a completely qualitative way. But there is a conspicuous lack of purely dispositional accounts of properties. Why do so many philosophers (including Shoemaker) come to the conclusion that the qualitative is necessary?

Mostly, it seems that philosophers have been unable to avoid using qualitative properties to account for substance. Most accounts seem to be built around the idea that qualitative properties are somehow more ‘real’ than dispositional properties. Often, purely dispositional accounts come down to a view that space-time is substance – that it is the haver of properties, not itself had as a property – and that the world around us consists entirely in changes of the dispositional characteristics of space-time.

An analogy is drawn between this space-time, and a marquis board. Perhaps a more flexible analogy would be with a television set. Although the light at various points on the screen can change colour and intensity, many times in one second, to give the illusion of motion, we wouldn’t say that there is actual motion taking place. Or would we? Is it necessarily wrong to claim that there is ‘real’ motion on a television screen, or equivalently that there is not ‘real’ motion in the world around us? In his best-selling book, Illusions, Richard Bach outlines a conversation between himself, and a fellow named Donald Shimoda:

Bach isn’t actually trying to make the same point we are. But in this and others among his books, he has nonetheless locked onto the fact that we need not be concerned, if it turns out that everything around us is as illusory as a world consisting entirely of a television screen. It seems as though most of the criticism of that sort of view has come from a ‘gut reaction’ that the world simply must be made up of something more than illusion.

Before we move onward, we will establish a couple of definitions, to help make sense of what follows. We will provide a definition for the terms property, predicate, and qualitative property. The first thing to realize is that a property is the sort of thing that can belong to something else. A property is considerably more ‘real’ than a predicate, which is just a grammatical tool. A predicate is an expression, with ‘blanks’ substituted in place of references to certain particulars. One such predicate would be the phrase ‘x is four feet tall,’ where the variable x is replaced by real things as needed. We might say, for instance, that ‘Jack is four feet tall.’ A property is more than just a grammatical tool. To say that an apple has the property of redness, for example, is more than to say that the predicate ‘x is red’ is true of the apple. When we ascribe a property to something, we are saying that there is a quality that belongs to that thing.

Properties can be divided into two categories: the dispositional, and the qualitative. The term qualitative property has ordinarily been used to describe properties which are somehow more concrete than dispositional properties, which (it has been said, and also argued against) tell us what might happen if we acted on something in a particular way. A dispositional property, for example, might tell us what would happen if we struck a glass. A qualitative property would tell us the shape of the glass, its size, etc.

We might then ask, how are qualitative properties more ‘real’, or more ‘concrete’ than dispositional ones? We would expect, first of all, that a real property would carry with it some information about the behaviour that we would expect from the thing that has the property. This is equivalent to Shoemaker’s requirement that genuine properties make a determinate contribution to the causal powers of a thing.

How does the fact that Jack is four feet tall, contribute to his causal powers? Well, if Jack tried to pass under a three-foot high bridge, without ducking, then he wouldn’t make it. This seems more dispositional than qualitative. It seems like there should be something else, which clearly is not dispositional, by which the property of being four feet tall contributes to a thing’s causal powers. But every time we come up with something else, it seems like it can be described as a dispositional property.

It seems as though there are no qualitative properties – just qualitative predicates ascribing certain dispositional properties to things. That ‘x is four feet tall’, tells us certain things about what would happen if x passed under a three foot high bridge (without ducking), or about what the measurement would be if we placed a ruler against x. To say that x is four feet tall, is to say nothing more than that all of these dispositional properties belong to it. Qualitative properties make no direct contribution to the causal powers of a thing. Applying Shoemaker’s requirement that a genuine property must contribute determinately to the causal powers of a thing, we can see at this point that qualitative properties are not genuine properties.

This is a good start toward a dispositional account of properties. But there are four properties remaining, which may seem somewhat different from the other properties that we have considered here – they are the properties of spatial and temporal location and extent. These four properties make up the fabric of space-time, which we take to be the haver of all properties, not itself had as a property. What is needed is a purely dispositional account of space-time.

We have established that properties must be causally operative. Space, however, seems to be causally relevant but not causally operative. Right away, one might ask, "But what about things like gravitation, which are dependent on the distance between two masses?" The answer to this question comes from General Relativity, which considers space somehow to be curved in the vicinity of any mass. Consider a particle in a gravitational well:

The diagram shows two objects with different masses. The larger one is surrounded by what is known as a gravitational well. The smaller one causes its own well, too, but for simplicity we assume here that the gravitational well caused by the smaller mass is insignificant compared with the well caused by the larger mass.

A popular demonstration which shows how the idea of a gravitational well works, is to stretch a sheet of plastic over a garbage can, and then tie it around the outside of the can. Then place a ball in the middle of the plastic. The plastic will stretch downward a little bit, and will create a sort of a ‘well’ in the plastic sheet. Now place a smaller ball on the sheet near the outside. Of course, it will accelerate inward and eventually it will hit the larger ball. We can even cause the smaller ball to orbit the larger ball, this way, if we give it an initial velocity along the edge of the garbage can.

Wells in space-time work a little differently, but this demonstration will help us get our idea across. Think for a moment about what caused the smaller ball to roll toward the larger ball. Did the smaller ball ‘know’ where the larger ball was? No – the ball can take its cues only from that with which it is in direct contact. The ball would undergo exactly the same acceleration, at that point in time, if the sheet looked like this:

This is because the smaller ball is affected not by the distance to the larger ball (or even by its presence), but by the slope of the sheet beneath it. We say that the larger ball is causally relevant, because its presence is certainly related to the motion of the smaller ball. But we cannot say that it is causally operative, because in fact it is the slope of the plastic sheet, and not the presence of the larger ball, which causes the smaller ball to accelerate. Were we to remove the larger ball, and then tip the garbage can slightly to one side, we would get the same effect as if we had left the larger ball in place.

Similarly, we say that one mass is causally relevant in the acceleration of a nearby mass due to gravitation, but not causally operative, because it is the curvature of space-time, and not the presence of the former mass, which causes the latter to accelerate. Neither is the distance between the masses causally operative, although it is causally relevant, too, for the same reasons.

It seems as though spatial location and extent are not causally operative, although they may be causally relevant. General Relativity makes the claim that space and time are interchangeable. We will assume for the remainder of this paper (in accord with General Relativity) that time works in much the same way that space does, and therefore that the whole of space-time is causally relevant, but not causally operative. If space-time is not causally operative, then it certainly cannot be a property – recall that a property must be causally operative for our world, so that we can distinguish its presence from its absence.

Suppose, then, that the dispositional composition of the world arises from dispositions of space, rather than from the dispositions of things in space. Suppose, as we have said a number of times already, that space is the haver of properties, not itself had as a property. How could space have properties, without being had as a property? How can we visualize this model of space-time?

Consider of a straight piece of string. The string has certain properties. Perhaps it is a fuzzy, white piece of string, and perhaps if we set it in a small flame, it will catch fire. These are all properties that we might expect of a piece of string. Now tie a bow in the string. The string retains its original properties, but just by arranging it differently, we have bestowed upon it some other properties. These extra properties we might confuse as being properties of the bow, because when we made the string into a string tied in a bow, it gained those properties. What we have to remember is that those properties are properties of the string. The bow is illusory, and cannot exist independently of the string. Nor can it have properties.

An infinitely thin string can be thought of as a one-dimensional object curved in a higher-dimensional way (be it two dimensions, or three, or more). We can imagine that space might be thought of as a three-dimensional object, curved in a higher-dimensional way, too. This is key to General Relativity. We might imagine that it is space-time’s curvature (its folds, knots, and other distortions), in higher dimensions, that results in its properties. The properties might appear to be properties of a particle in the space-time, in much the same way as we saw that the bow seemed to take on its own properties distinct from the properties of the string. But again, what we’ve got to remember is that the curvature cannot exist independently of space-time itself, and so the properties are really properties of space-time, and the particles themselves are illusory.

"But what about protons, and neutrons? What about up quarks, and down quarks?" Modern physics continues to pry apart any particle that has been considered elementary. Atoms, once thought elementary, gave way to protons and electrons. In time the existence of the neutron was also recognized. We now know that protons and neutrons are made up of various types of quarks. Many other exotic particles have been uncovered in particle colliders around the world, and the family of elementary particles continues to grow. But one thing is for sure: every time a new particle is postulated, the fundamental constituents of the world become a little smaller. The atom becomes a very small nucleus, surrounded by a cloud of electrons. The nucleus becomes a jumble of tiny protons and neutrons, which in turn are found to be made up of exceedingly small quarks. The electron becomes an animal that can’t particularly be located in its orbit around the nucleus, but which rather is assigned a probability density that determines where it might be found. We find ourselves increasingly in a world made up of different sorts of points, with their associated fields. It is the fields that do all of the interacting – points can never collide, or interact in any way except through their fields. What would it mean for two points to come into direct contact, anyway? The fields represent a myriad of properties which can belong to elementary particles – charge, mass, charm, strangeness, and others.

Why do we keep the points in our ontology, then? The answer is in the world with which we regularly interact. Particles are an unnecessary extrapolation from our daily experience with cue balls, and cannonballs, and bricks. Particles are an artifact of the macroscopic history of physics, which can be traced back to a time when scientists were still trying to figure out just what path projectiles follow.

We leave the world just with fields. In the place of particles, we leave a space-time which itself is the holder of the properties which previously were ascribed to points or to suitably point-like particles. We suggest that the world around us, and indeed we ourselves are nothing more than folds, knots, and other distortions in space-time, interacting in complex ways, which include our interaction with the world around us.

The objector might argue that any complete definition of the topology of a space requires that we posit points in the space – often a continuum of points. The objector will also require relations between the points (i.e. distance). Euclidean space, for instance, is entirely defined by a set of relations (i.e. a metric) which determine the distance between points in the space.

Suppose that a space is equivalent to the set of points in the space, and the set of relations of distance between those points. The points seem to be qualitative things, and it seems then that the space itself should be a qualitative thing, or a combination of qualitative and dispositional things. But we’ve already shown that space is not a property at all – space is the haver of properties, not itself had as a property – and therefore it is neither qualitative nor dispositional. Space, then, ought not to be equivalent to the set of its points, and the set of relations of distance between its points.

We draw the following conclusions:

• Properties must be causally operative, and therefore reducible to dispositions.
• Space-time is not causally operative, and therefore must not be a property.
• Space is neither dispositional nor qualitative – it is the haver of dispositional properties, not itself had as a property.

We have herein proposed an account of how things are, composed of the dispositional properties of space (perhaps curvature), and of space itself. Our account requires no particles and no distances. In fact, we require no qualitative nature at all.