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Process Theory and the Concept of Substance

Ian J. Thompson

Physics Department, University of Surrey, Guildford GU2 5XH, U.K
Since the failure of both pure corpuscular and pure wave philosophies of nature, process theories assume that only events need to exist in order to have a physics. Starting from an ontology of actual events, a dispositional analysis is shown here to lead to a new idea of substance, that of a `distribution of potentiality or propensity'. This begins to provide a useful foundation for quantum physics. A model is presented to show how the existence of physical substances could be a reasonable consequence of a theory of processes.

Introduction

Aristotle, Descartes and Boyle all thought they had formed definite ideas about what it was to be a substance in the natural world. Their ideas were all different, however, so they cannot all have been correct. Aristotle's views held sway up to the beginning of modern science, at which point Boyle's corpuscular theory became more popular. His notion of an extended, impenetrable and eternal `material substance' was accepted by Locke and Newton, and as it become part of classical physics, it was thought to be clearly understood.

Modern physics however has rendered this certainty obsolete. Although quantum physics may predict the observable phenomena of nature exceedingly well, the idea of `natural substance' has become more mysterious, not less. Quantum physics postulates a wave function which seems to adequately describe natural probabilities, but no-one is clear what is described by this wave function. No-one knows what it is that exists with the form of this wave. Some interpreters of quantum mechanics have (not without justification) said that it is our knowledge that is described by the quantum wave function. Alternatively, seeking something more objective, we can have `processes' or `patterns of activity' in the various forms. In the Copenhagen Interpretation the question is not answered, as the unit of activity - the `quantum of action' - is assumed to have an intrinsic wholeness which cannot be analysed further. Achieving a full understanding of `substance' in the quantum world seems to have become an impossible dream.

In the quantum world it is not substances but events and interactions which have become much more `real', definite and understandable. In Whitehead's process theory, it is only events which are the `actual entities' in the physical world. Substances are relegated to being `chains' or `societies' of these actual entities, and thus seem to have a more nominal than real existence. Physicists such as H.P. Stapp (1977) have tried to apply these process ideas to give a more comprehensive interpretation of quantum physics. Stapp nevertheless has had to postulate additional `geodesics' which carry mass and energy between events.

In this paper I wish to show that if we were to start from a simple process world of events, and supplement this by some kind of causal analysis, we can be led to a concept of substance. This new derived concept, despite its novel pedigree from the theories of process and causation, will turn out to satisfy many if not all of the traditional concepts of `substance' as a `substratum which underlies time and change' (although its persistence will often be limited).

We must consider two cases. The actual events may either succeed each other continuously in time, or have non-zero time intervals between them. These two cases roughly characterise the difference between classical physics and quantum physics.

If the actual events succeed each other continuously in time, then one can identify a continuously-existing substance by that varying entity whose form at each time is just the actual event at that time. That substance would hence be actual and definite in the same way as the original events. It would persist continuously, and be like a Democritean Atom or Boylean Corpuscle. This is the idea taken up in classical physics, where the corpuscles or particles are conceived to be fully and continuously existing in full actuality.

If the actual events exist only intermittently, however, any substances will have to span the temporal gaps between them, and the problem of finding an enduring substance is more difficult. This case, in which only some events are actual and completely definite, is the one considered in more detail here.

Our aim is to derive a concept of substance independently of classical physics, so we can bypass some unwanted meanings that have accumulated from material corpuscularism. In this way, we can perhaps regain some of the insights of Aristotle, Aquinas, and Locke concerning substances. The independence from classical physics proves to be especially valuable in coming to understand quantum physics, as we can define what I believe is a coherent notion of a `quantum substance' which renders intelligible a number of the pecularities of quantum physics.

Traditional Views of Substances

There have been two (at least) extremal positions possible in philosophy with regard to any changeable enduring substance.

One position is exemplified by Spinoza and Leibniz, who defined substance as `that whose nature requires its separate existence'. On this view, substances are self-sufficient beings which contain within themselves the complete source of all their changes. Leibiz has for example that all natural changes of his monads come from within, as `an external cause can have no influence upon its inner being' (Leibniz, 1714, ¶ 11). The difficulty then, as Kant (1747, § 7) realised, is that on this account `it is not necessary for [a substance's] existence that it stand in relation to other things'. It is a puzzle, on this account, why substances even have positional relations that might enable the acting of one substance on another. The possibility of interactions of substances can only be regained by denying that substances are self-sufficient beings. In this paper, I want to deny that substances are fully actual and determinate with respect to external interactions. I want to look for some closer relation between substances and `powers' or `propensities', in order that substances may endure through changes in some of their properties (their `accidents') produced by interactions withother substances.

If substances were self-sufficient, there is always the difficult question of how their powers for interacting are supposed to be related to their `underlying' nature. It is not clear, futhermore, whether it is possible to properly conceive of any `naked substance' apart from all its powers. Locke explicitly had no clear idea of the relation between a substance and its powers, and it is debateable (see M.R. Ayers (1975) whether he distinguished any power-less substance. One view is that of Boscovich, Faraday and Harré, whereby a substance is at a single place at any given time, around which its powers are `fields of force'. All inertia still resides in the point substance, and around it the field of force extends away indefinitely. However, it is still not perfectly clear how these `point centres of mutual influence' are related to the extended fields.

The second general position is the denial of `substance' altogether, and of any sense of continued identity, in favour of pure process. We then have a purely event or flux philosophy. Reasons for this repudiation have varied. Sometimes it has been the alleged unknowability of the real constitution of substances. At other times it has been a preference for `flux' or `creativity' as against the `Parmenidean influence' that is seen to pervade much of Western philosophy. Hume and Whitehead are perhaps the two most prominent figures here. As well, between the wars this century an ontology of `events' became widespread, especially because of a common interpretation of relativity theory and a positivistic approach to metaphysics. Russell's The Analysis of Matter (1927) is a good presentation of this position, wherein events are fixed in space and time. Paradoxically, they become then like fixed substances, and the understanding of event as `change' often fades.

After the Second World War, as Nicholas Rescher (1962) notes, there was a general reaction to such an extreme event-and-no-continuant ontology. Many writers now repudiate `events' in favour of substances and their relations. In the reaction, however, a very uncritical idea of `substance' was taken over, practically identical with `material object'. This has the result that there could be no very precise understanding of either the fact or the dynamics of real change.

With some philosophers, nevertheless, the realisation of the inadequacy of the event ontology came more moderately, and arguments were found for an ontology in which there are both events and continuants. Events could now be properly construed as real changes, by reference to the changes of the continuants involved. This was done as early as W.E. Johnson (1924), who was trying to counterbalance the middle Whitehead's Concept of Nature: it was Johnson who coined the term `continuant'. Without such a term, he remarks (1924, III, p. 127), it would be impossible to distinguish the case of two events A, B, say, causing two later events C & D, respectively, from their causing D & C, respectively. The necessity for substantial continuants was further supported by Reck (1958), who argued against an ontology of only events, and for a position closer to that of Johnson. However, neither Johnson nor Reck attacked the problem of giving a fully-fledged account of such continuants: they did not consider the problem, for example, of how a substance is related to its powers.

The present inquiry will therefore have as one of its starting points a process theory of discrete events, and will proceed with the help of Leclerc (1972). Since some notions of propensities are required in any useful science or philosophy of nature (see Thompson, 1988b), processes will be analysed on this basis. We are led to postulate a new notion of `propensity fields', to see whether such things can continuously endure through certain types of interactions, and then to see whether we can identify these propensity fields with the `substances' of classical philosophy. I will use however Johnson's (1924) term `continuant' to avoid a number of unwanted associations from the history of the term `substance'

The Analysis of Event Causation

The basic notion of how one event causes another event is rather a complex one, and I think that it can be usefully `unpacked' into a number of perhaps more basic notions. This analysis follows Leclerc (1972,chs. 25 & 26) in taking modal considerations seriously. It is summarised as follows.

Suppose an actual event A, say, causes an actual event B. This causation may be deterministic or indeterministic. Then the fact of that causation implies

  1. that the event B was possible,
  2. that there must have been a real and active power or propensity to make B happen rather than remain only possible,
  3. that the power or propensity must at least have been directed to the occurrence of B,
  4. that there was a set of possibilities for the change. This set may have members apart from the possibility for B, and its members form a `space-time' of possibilities for change, only one of which actually occurs,
  5. that these various possibilities are related to each other in some structure, and
  6. that there was a form of distribution of the power or propensity over the set of possibilities, since, in general, not all possibilities are equally likely.
For example, suppose event A is the emission of a electron from a negatively charged cathode, and event B is its hitting and exposing a grain on a photographic plate. Then
  1. it must have been possible for the electron to hit the photographic plate, and
  2. there was a electrostatic propensity to repel the electron, rather than let it stay where it was when emitted. The electron and the photographic plate had propensities to interact with each other, rather than simply pass through each other unchanged.
  3. The propensities of (2) are all propensities for the named occurrences (repulsions and interacting, respectively),
  4. if there are quantum effects in the electron's travelling, and these are objectively random, there are a large number of possibilities for the interaction B, as it can at least occur at different positions on and in the photographic plate, and at different times, and
  5. these different places are related by being in a four-dimensional `space-time', this being the combination of different positions in the three-dimensional volume of the plate with different (one dimensional) times. These places have metric distances from each other, and temporal intervals between them.
  6. These different places each have their own propensity (and hence probability) for being where B actually happens. The distribution is given according to the square-modulus the quantum mechanical wave function

On Active Propensities

These implications amount to a causal or dispositional analysis of the sequence of events. Some philosophers do not believe that such an analysis is necessary, desirable, or even possible, as they see the realistic notions of `power' and `propensity' used here as not sufficiently scientific or definite to be satisfactory. I have argued, however, in a previous paper (Thompson, 1988b) that some notions of `real dispositions' are necessary for activities in both science and elsewhere, and that, however much we may dislike these ideas, they need to be examined closely and used carefully. I argued that, for both theoretical and practical reasons, we do have to take certain modal considerations seriously, and find realistic foundations for them. The implications listed above are an attempt to analyse closely the structure of real dispositions in the physical world.

By `power' of course is not meant `energy flow per unit time', but a general `capability' or `dispositional property' to act in a certain manner, as in Harré (1970a) or Ducasse (1964). The notion of `power or propensity' here has a long pre-scientific history as the specific `potential', `active force', `motive power', `drive', `impetus', `spring of activity', or `dynamicism' for change. For the purposes of analysing events on a causal basis, however, from these ideas I take simply `that which is necessary to make any change in fact occur'

In traditional philosophy, the concept of `power' or `propensity' has had a varied history. It appears mostly in the works of Aristotle, Locke (1706, Bk. II, ch. XXI), Leibniz, and the proponents of `dynamic matter' such as Boscovich (1763), Priestley (1777), and Faraday (see Levere, 1968). In this century, it has been advocated by Bergson, Ushenko (1946) and Harré (1970a), but not all of these accounts are equally satisfactory for the present purposes. When Whitehead uses `real potentiality', for example, he emphasises the `possibility' aspect, and ignores the `power or propensity' component. In Whitehead's event philosophy, as Ushenko and Leclerc pointed out, there is no concept of active power, yet some such notion, one would think, would have a central role in any adequate theory of process.

In the sense that we require, `power' and `propensity' must mean more than `passive capacities' for being formed (as in the Thomist schools). We need to include the active powers that are in an agent that could actually initiate such forming. Any passive capacities or `liabilities' can be regarded as special cases of a more general sense. They could be regarded as `weaker powers', for example, compared with those of an active agent.

One criticism of the use of powers and propensities is that they are used in a very general sense to refer to any capacity for any change, and that this sense is so general that its theoretical and empirical content for any explanation is low. It becomes too easy, the critics say, to postulate many distinct ad hoc powers which have no specific mutual relations: one for each change possible. Just how many distinct capabilities does a complex biological organism have, considering the great many situations in which it may be found, and the great many internal states that are possible for it? And how many powers does opium have, along with its `dormative virtue'?

This criticism is justified, but that does not mean that there are no such things as powers or propensities. The world would be a very peculiar place if people and objects had no capacities or propensities apart from what they actually did. In the history of the sciences of matter, admittedly, the notion of `power' tended to be abolished in favour of matter as corpuscular and purely actual. However elegant the motives and results of this tendency may have been, it is nevertheless inadequate both empirically and theoretically. Scientists from Newton on soon found themselves compelled to postulate powers of attraction and repulsion, and Faraday found that for electric and magnetic effects more complicated notions of forces and potentials are required. The task of science should be to reduce the number of different types of propensities needed to explain experimental phenomena, but for reasons given in Thompson (1988b), this number will never be reduced to zero.

Propensity Fields

Places in Space and Time

In section 3 we saw that for an actual event A to cause an actual event B, there was a set of possibilities for the change. This set may have members apart from the possibility for B, and its members form a `space-time' of possibilities for change, only one of which actually occurs. We can now identify (following Leclerc, 1972) places in space-time as just these `possibilities for actuality'. We can then say that the event is at a place when that possibility is being realised, and that this results in that place being `filled'. Since what is actual is at least possible, the set of filled places is a changing subset of the set of all places possible in the world.

These places are being regarded as `wheres' and `whens'. That is, in the terminology of modern physics, places are places in space-time, not just in space. This is especially important if these places are to be the possibilities for events, for two events at different times, even though perhaps at the same spatial location, are always distinct: they realise different possibilities. This consideration is independent of any requirements of relativity theory, as it can be used with both Newtonian and Einsteinian space and time.

The account of time implied here is that in which only the past is actual and definite, and the present is the process of `becoming' or `coming to be' of this definite past. This view was held by Whitehead (1929) and by C.D. Broad (1923). How this theory of time overcomes the objections of McTaggart has been outlined by Broad (see also Thompson, 1988a).

If the events being considered are ordinary physical events such as interactions, collisions, etc., in our everyday three-dimensional space and time, then places (as `possibilities for these events') can be identified with distinct regions of spacetime. The relational structure of implication no. 5 can be identified with the metric tensor that gathers regions into subsets of some larger space-time continuum. The theory of spacetime being developed here is closely related to Whitehead's notion of a `extensive continuum', which is the `coordination of all possible standpoints' (emphasis added). The discussion of whether this is an `absolute' or `relative' view of spacetime is beyond the scope of the present paper.

The events however need not be in our usual space and time: the analysis is quite general. Quantum mechanics postulates, for example, that particles with intrinsic spin have this spin `oriented' in a `spin space' distinct from our three dimensional space, and not simply embedded in it. Moreover, intrinsic spins have only a discrete range of possibilities. According to the process analysis of this paper, this is equivalent to saying that the spin can only range over a discrete set of `positions' or `places'. These places would be related to each other, in this case, as integers, or half-integral numbers.

On Real Possibilities

It is essential to remember that `places' are realistic possibilities, and are not merely abstract or de dicto possibilities such as those which arise when we might think or form propositions about what is possibly the case. Rather, we want here to have possibilites for physical events: possibilities which are relevant to what actually occurs. A great many de dicto possibilities are perfectly capable of being rationally entertained, but are nevertheless never possibilities for actualisation, either because they are not within the scope of physical laws, or because they are ruled out by the path that history has taken up to the present.

The `possibilities for events' are not de re possibilities either. For de re possibilities involve particular objects, and here, the `possibilities for an event B' are distinguishable even if no such event occurs or exists in any way. They are certainly not `possible events', or any kind of events which in some way `subsist' without actually existing. As Quine (1961, p. 4) indicates, there are decided problems with the the notion of `possible entities'. Taken together, they seem to be part of an `over-populated universe'. ``Take, for instance, the possible fat man in the doorway; and, again, the possible bald man in that doorway. Are they the same possible man, or two possible men? How can we decide? How many possible men are there in that doorway?''.

There are severe problems for the application of identity-criteria to `possible entities', but not to the `possibilities for entities' discussed above. A `possibility for a fat man in the doorway', for example, is just any one of a number of regions in the doorway at some particular time, and these are identified and individuated by the usual spatio-temporal relations in an unambiguous fashion. The doorway may well contain a possibility for a fat man and/or a possibility for a bald man, but that does not require that we identify and individuate these `subsisting' men. We only need to identify the places which would be occupied if such men were to exist.

The important thing is to take possibilities seriously, and not to confuse them with actuality. From the mathematical point of view, for example, possibilities and actualities could be all grouped together in a one-level universe of Fregean `objects'. In mathematics, however, no distinctions are made between actualities and possibilities. From the point of view of extensional semantics, possibilities are just as much `objects' as actualities. This does not mean that, properly considered, actualities cannot be the realisation of possibilities. As Whitehead put it (1929, p. 61),

It cannot be too clearly understood that some chief notions of European thought were framed under the influence of a misapprehension, only partially corrected by the scientific progress of the last century. This mistake consists in the confusion of mere potentiality with actuality.

Field Distributions in Spacetime

If an actual event A causes an actual event B, then the fact of that causation implies that there was a form of distribution of the power or propensity over the set of possibilities, since, in general, not all possibilities are equally likely. The possibility which is eventually realised cannot just be the one with the greatest propensity, otherwise the competing alternatives with lesser propensities would not have been real possibilities in the first place. Allowing for a distribution of propensities means therefore allowing for a range of possibilities, each of which has some (i.e. non-zero) chance of occurring.

This was the sixth component of the analysis of section 3. We can now make this idea more concrete, by using the identification of these possibilities as places in spacetime. Since the `form of distribution of the power or propensity over the set of possibilities' now is seen to be a `form or distribution over regions of spacetime', it can best be represented as a field.

It could be that powers and propensities have themselves some numerical measure, by means of positive real numbers representing probabilities for example. This field would then, in mathematical terms, be a positive scalar function over a subset of the four-dimensional continuum R4. In general, however, we do not have a priori reasons to choose that (or any) measure for the propensities themselves. More complicated measures may have to used, provided that some probability distribution can be derived for where the subsequent events are likely to occur. The Schrödinger equation in quantum mechanics, for example, uses a complex valued measure to describe the propensity distribution, and Dirac found it necessary to generalise this to a four-component complex-valued function, in order to describe both electron spins and anti-electrons in the same formalism. Whatever measure or descriptions of propensities may prove necessary, the notion of a field can be used to give the degree of propensity that is operative at each place in a spatiotemporal field.

Philosophically, what is important is that a particular propensity field can extend over many places, with different degrees of propensity at these different places, and not by itself single out any particular place in that region. The propensity field therefore extends over all places at which events `might have occurred', given the actual history of the world up to that point. Of course, one particular place will become selected once an event occurs, but this selection may well be objectively random in the sense that repetitions of this same history and of this same propensity distribution may result in the occurrence of different events.

To recapitulate on the schema for causation that has been developed: we start considering the causal process with an event A, say, at some place pA in space and time. The propensities (which are responsible for making occur a successor event to A) therefore extend and endure through the spacetime continuum away from the place pA over places where successor events may occur. The exact spatio-temporal form of this field is given by a general field equation from a theory of physics, along with the boundary conditions that the field must be contiguous with the event at place pA.

Once the propensity field has been formed, it endures until its realisation produces a new actual event B, say, at some place pB. If and when that realisation occurs, there are produced further propensity fields which extend from the place pB and thus endure into the regions of spacetime to the future of B. The whole process is thus started over again. It is possible to say that the first propensity field becomes another, because the act that is the realisation of the first field is simultaneously the act of forming the second, and because there is a spatio-temporal continuity between the initial and the final propensity distributions.

The acts of `realising' which have been discussed so far are somewhat simple, being the acting of just a simple homogeneous propensity field. It is much more likely that most events or acts are interactions, or the acting of one propensity field on another. As Leclerc (1972, ch. 23) points out, `actings on' always involve a reciprocal capacity to `receive' in that which is acted upon, so that aspects of capability or propensity are required in both the agent and in the patient. That most events are interactions is also supported by quantum physics, where events which are the spontaneous action of a single particle are comparatively rare, because events such as spontaneous decays are not the most common type.

If an interaction between two propensity fields is to result in an actual event at a particular place, it will be necessary for the two propensity fields to overlap in at least that region. It may be concluded that two propensity fields may only interact if they overlap in spacetime, and that, if they do interact to produce an actual event, then both the fields are reduced in spatial extent at the time of the event. The likellihood for specific interaction events occurring will again depend on the form or distribution of the measures of the two propensity fields, and it is likely that the probability of interaction will depend on something like the product of the two fields. Exactly how this works is of course for physics to determine.

Continuants (Substances) Which Endure Through Change?

We now come to the question of whether a concept of `substance', as at least `continuant', can be constructed using the above analysis of process and dispositions.

A continuant has been defined by Johnson (1924, III p. xx) to be `that which continues to exist throughout some limited or unlimited period of time, during which its inner states or its outer connections may be altering or remain unaltered'. Johnson used the term `continuant' as against `substance', for the term `substance' is impaired by the fact that, in the history of philosophy, many diverse senses have been assigned to it, senses which give associations which are not wanted here. For example, though continuants can endure through change, they need only endure for at least a while, and not necessarily everlastingly, as many suppose that substances are required to do. (Leibniz, for example, argues from everlasting substances to immortality.) Further, since Locke at least, it has become obscure exactly how a substance is supposed to be related to its powers, qualities and properties, etc. `Substance' has come to be regarded as an `I know not what' which in some obscure manner `underlies' and `supports' its attributes.

Ducasse (1964) has proposed `substant' for a new association-free term, but in some ways `continuant' is still preferable. This is because substants do more than just continue: Ducasse lists another five general features of substants, another five things which they are capable of doing:

  • acting (as an `enactor')
  • being in a state (as a `tenant')
  • affecting another substant (as an `agent')
  • being affected by another (as a `patient'),
  • changing into something completely different (as a `mutant'), as well as
  • enduring changes (as a `continuant').
As all these details presuppose a detailed analysis of the concept we are constructing, I will use the term `continuant' to refer to any particular individual being in the world which can continue to exist at least for a while, and can effect and undergo some change while remaining the same being (`same' in some sense to be elucidated).

Unchanging Continuants

We will first consider what particular things can endure through time, even if they are not permitted to change at all in that time. Since actual events are at definite places in spacetime (once they exist), the longest they may be said to endure is for the temporal aspect of their space-time region. If our initial events are separated by finite time intervals, then the events themselves do not endure from one event to the next. The only particulars that so far are certainly known to endure are the propensity fields themselves. They endure because their source and realisation events are separated in time, and, because the second event could have occurred earlier, the propensity for its occurring is distributed over all the intervening possible times. Considered as a particular thing, the whole propensity field therefore endures over the finite time interval between the events.

Admittedly, this endurance of propensity fields is not entirely conventional, for they extend `with one span' over temporal as well as spatial intervals, rather than being a real succession of spatial fields at successive times. It of course appears to us as if they move successively and continuously through different spatial regions between the events, but this does not mean that there is a continuous succession of actual entities, as we are really only looking at potentiality or propensity fields. It is a grave mistake to think that because something can occur at any time between two actual events, then something actually is occurring at those times: we must not confuse actualities and possibilities!

Since single propensity fields do endure, at least for a while, they can be regarded as the most basic continuants in that they never change so long as they continue to exist, and hence must remain the same even under the most technical and exacting sense of identity. Therefore we define unchanging continuant as a `separable propensity field.' They are unchanging, because they endure unchanging for their short while between two successive actual events. They can be viewed as `brittle' or `precarious' continuants, in that they cannot change in any way without becoming different continuant(s), yet while they do endure, they stay exactly the same, even staying at the same places in space-time.

Note that

  1. although they are unchanging continuants, they do not prohibit natural change: only when they do lead to changes, they must mutate into something different,
  2. they may still appear to change for us, if we change, for example, by moving our place of view during the time between two actual events for the continuant being observed, and
  3. unchanging continuants in nature will typically only last for some small fraction of a second, the time between successive molecular collisions in typical solids, liquids, and gases.
The powers of any entity are what it is capable of doing and how it is capable of interacting. The ascription of powers is typically, adapting a definition of Harré and Madden (1975) (see also Harré 1970a), of the
``Object S has the dispositional power P to do action A''
if and only if
``if S is in some circumstance C, then there will be a non-zero likelihood of S doing A, in virtue of the constitution of S''.
In general, C will depend on P and the kind of the action A.
Here, the `circumstance C' is usually defined by multiple spatial relations to other objects, and the `action A' can either be a change in S itself or an interaction with other objects. The phrase `in virtue of the constitution of S' is designed to exclude `changes' to certain properties of S that are changes in purely external relations that may come about completely independently of whatever S is actually like.

The powers of a propensity field are given entirely by the spatiotemporal distribution of propensity within the field, along with the measure or description of the nature of the propensities at each place in the field. For, given the form of the field and the descriptions of its propensities, then one can predict exactly how the field is likely to interact with other fields in any given situation. This is because the `circumstances' are just the degrees of overlapping with other fields, and the actions that are possible in those circumstances are just those events to which the propensities are directed.

Matter and Form

We are now in the position of being able to identify the matter and form of the continuants defined above. Since an `unchanging continuant' has been defined as a single potentiality field, the powers of that continuant, what it is capable of doing, must be completely given by the extensive form of that field. This form for any continuant may therefore be called its substantial form, and for an unchanging continuant is again strictly unchanging. A continuant retains exactly the same powers as long as it lasts.

This substantial form can be regarded as a predicate qualifying `propensity-as-such', as it is propensity (as such) which has that form. Propensity, therefore, can be regarded as the underlying `substance' or `matter' of all enduring continuants, which are therefore `forms of propensity'. `Propensity' is thus the logical subject - `that which is not predicated of something else' - and the substantial form is a predicate qualifying this subject. Traditionally, following Aristotle, this underlying subject is called the matter out of which natural things are constituted. I will not be using this term, as today it leads too readily to the concept of `material substance' of Boyle, Locke and Newton. As I wish to have a concept of substance which is to some extent independent of classical physics, the term `matter' will not be used.

In the Thomist traditions, there is an ultimate subject defined as the `pure capacity to receive determination', and called `pure potency', `primary potency', or even `prime matter'. It is thus rather more abstract than the propensities of this paper, which are always propensities for specific events and are thus to some extent already determinate even if not localised in space or time. The Thomist concept of `pure potency' or `pure capacity to receive determination' takes only the `possibility' component of the logical analysis of section 3, and is therefore a somewhat limited abstraction. Perhaps it is even a self-contradictory one, for is not to call it `pure potency' to give it some determination? There have been doubts whether such a concept is intelligible, but fortunately it is not needed for the present enterprise. We need only the concept of `propensity' or `power', as we only want to have a concept of the logical subject or substance of particular things.

Individuals

Since an unchanging continuant has constant powers so long as it lasts, it is that respect similar to the `Parmenidean Individuals' of Rom Harré (1970b). According to Harré, `Parmenidean individuals' are the ultimate individuals in nature at whatever level of microscopic analysis that may turn out to be, so the scientist does not have recourse to the internal arrangement of its parts to explain the powers of such an individual. It used to be thought, for example, that atoms were Parmenidean individuals, then (later) protons and electrons. The most likely present-day candidates are quarks, leptons and field quanta such as gluons and photons. The arrangement of their parts is not needed, because they are the ultimate individuals, and their internal constitution is not separate from their powers. Since they have no separable constituents, their nature must be identical with the particular form of all their powers. That is, to completely specify the powers of a Parmenidean individual is to completely specify its nature, its real constitution, and vice versa. This is in contrast to what Harré calls an `Aristotelean individual', which is a complex individual whose powers are explained by means of the dispositions (i.e. powers and arrangements) of its parts. Harré's Parmenidean individuals, however, endure indefinitely, and ``cannot be altered, ... being the bearers of numerical identity [they] cannot be transformed'', whereas the `continuants', as being conceived in the present inquiry, do not necessarily last indefinitely, only at least for a while.

The process derivation of `continuants' has the feature that in it we can see more clearly how the nature of a continuant (as a propensity field) can be identical with the `particular form of all its powers'. This is because, as was seen just above, all the powers of a propensity field are given by its `substantial form': the form of the field as an extensive distribution of propensity. This is in broad agreement with Ducasse's account (1964) of how a substant is related to its capacities. He argues that

contrary to what the etymology of `substant' may suggest, the relation between a substant and its capacities it `has' is not analogous to the relation between, for example, a table and the objects it `stands under' and `supports'. Rather, the relation between a substant and its capacities is analogous to that which obtains between, for instance ... an automobile and its parts; or a living body and its organs; or more generally between any whole and its parts.
Now, on the present account, a propensity field is a single whole particular thing, and has various possibilities for actualising contained within its extent because it extends and endures (by definition) over all the places possible. One can regard the relation between a propensity field and the places possible within it, or equivalently between a continuant and the interactions possible for it, as therefore just the relation between a unitary whole and the parts into which it may possibly (not actually!) be divided. One important consequence of this account of the continuant as a `whole' with respect to its powers as `parts' means that continuants cannot ever be properly conceived apart from their powers. Thus there never exists any separable, pure or `naked' substance.

The only qualification I would give to Ducasse's account is to note that the actings of a continuant are most often interactions with other continuants, so that an account of a continuant's powers - what it is capable of doing and how it is capable of interacting - must make some reference to the condition of the other continuants with which it reciprocally interacts, and not depend only upon its own substantial form.

Changeable Continuants

So far I have defined only particular unchanging continuants, as particular propensity fields. What about changeable continuants: continuants which can endure through certain changes to themselves but keeping the same powers and properties etc.? Since under a strict sense of identity, nothing can itself change or move in any way, and still remain the same particular, it will be necessary to relax this strictest sense of identity if a sense of `continued identity' is to be obtained. We want now a sense under which one continuant can undergo interactions and shift around, and not only remain unchanging between some pair of events.

Perhaps the most obvious relaxation is to allow the same substantial form over different places, so that the same continuant can at least move, as a whole, to extend over a different region of space and time. There is hence a sense of continued identity which treats two `unchanging continuants' as in fact the adjacent and successive stages of the same `changeable continuant' when

  1. there is some event over which the two `unchanging continuants', as propensity fields, are extensively continuous with each other. This event would then be the product of the earlier continuant and the cause of the later one.
  2. these two continuants have the same `substantial form' even though they do not extend over the same sets of places.
That is, for a changeable continuant to have continued identity, there must be a spatio-temporal continuity of the same substantial form.

A changeable, enduring continuant therefore retains the same substantial form and the full possession of all its powers through any changes or interactions it may pass, so long as it lasts. The above conditions do not imply that even a changeable continuant must last forever: there can be sufficiently radical events in which no outcoming continuant has all the powers that once constituted one of the ingoing continuants. There can be changes in which not all the powers of a continuant are preserved through the change. Such changes could be called `substantial changes' because some continuant did not survive. Changes in which a wholly new continuant is formed can also be called substantial changes. Generation and decay events would be examples of substantial change, provided that what was generated or decayed was a single continuant, not merely an aggregate or arrangement of continuants. An example is the decay of a neutron, which in free space after about 12 minutes decays into separate proton, electron and neutrino fields, where none of the outgoing continuants has all the powers that the neutron once had [1] Most of the other interactions of the neutron such as collisions and refractions etc. do preserve that continuant, as there is a continuity of its substantial form and of its powers.

On Real Essences

Since the `substantial form' of a continuant is that on which all its powers depend, it may be called the `real essence' of that continuant. The `real essence' is defined by Locke (1706, Bk. 3, ch. 3, § 15) as `the internal, but generally (in substances) unknown, constitution, whereon their discoverable qualities [2] depend'. They may often have been unknown, but that does not mean that they are unknowable. I argue that the `real essences' of continuants, the `substantial forms' of continuants as propensity fields, are in principle quite knowable, especially as many fields can be very easily described mathematically. As Copi (1954) has pointed out, `it must be admitted that the doctrine of the unknowability of real essences was not an unreasonable doctrine to draw from the relatively undeveloped state of science in Locke's day', drawing attention to Locke's description of the then sorry state of chemistry (Locke, 1706, Bk. 3, ch. 6, § 8). It is, however, the real essences of things which science seeks to discover, and the sciences have made considerable progress since Locke's day.

It should always be remembered that these `real essences' are always the real essences of particular things. While we can intellectually distinguish the idea of the essence or form of a particular from the idea of that particular thing, that does not mean that the essence or form actually exists apart from that particular object in the world. The real essence is present only so long as the object continues to exist. They are not the `essences' of the medieval neo-Aristoteleanism heavily tinged with neo-Platonism, of which a certain number were supposed, `according to which all natural things are made and wherein they do exactly every one of them partake, and so become this or that species', as (Locke, 1706, Bk. 3, ch. 6, § 30) described the notion. The idea in the present enquiry is not of any such `natural essences' apart from particulars, but of the (essential) natures of particulars. We want to describe the nature which includes what a particular thing is, the principle of any changes it may go through, and that by which it may be intelligible to us.

Quantum Substances?

One feature of the present account of substances is that they are not necessarily located in small volumes of space, as, for example, the corpuscles or `particles' of classical physics would be. The propensity fields that have been defined do not even have any special `centre' distinguishable from all the other places in the field. They have no centre which could be regarded as the `true substance', so that the surrounding field could be regarded as just the `sphere of influence' of the central substance. This was Boscovich's conception, and it slowly percolated into physics, resulting in the `dynamic matter' of the mid-nineteenth century. This view is best summarised by the aphorism ``No matter without force, no force without matter''. Our propensity fields, though, have no special continuing centre: the only `point source' which could perhaps be identified is the source event, which must have a definite location in space and time. The field is therefore only localised very briefly, if at all, at times just after this source event. The `continuants' we define are thus occasionally, but never necessarily, strongly localised. For most of the time they have significant spatial extensions.

Substances with this nature are particularly relevant to modern quantum physics, wherein it is found that the concept of a corpuscle with definite `extension, hardness, impenetrability, mobility, and inertia of parts' (from the beginning of Bk. III of Newton's Principia) is markedly inadequate, yet for which no philosophically adequate replacement has been hit upon. Despite the influence of a positivistic approach to metaphysics, which did not encourage people to look for new concepts, there have been a number of developments since 1926 in the interpretation of quantum physics that lead to concepts of propensities, etc., though with varying degrees of clarity.

For example, in 1926 Born realised that the quantum theory did not predict the precise state after a collision, but only the `possibility of a definite state'. The wave fields were not actual fields, but only determine the probability of the presence of quanta. As Jammer (1966, p. 286) relates,

Laws of nature, as Born and Heisenberg contended from [then] on, determined not the occurrence of an event, but the probability of the occurrence. For Heisenberg, as he later explained it [3] such probability wave are ``a quantitative formulation of the concept of `dynamis', possibility, or in the later Latin version, `potentia', in Aristotle's philosophy. The concept of events not determined in a peremptory manner, but that the possibility or `tendency' for an event to take place has a kind of reality - a certain intermediate layer of reality, halfway between the massive reality of matter and the intellectual reality of the idea or the image - this concept plays a decisive role in Aristotle's philosophy. In modern quantum theory this concept takes on a new form; it is formulated quantitatively as probability and subjected to mathematically expressible laws of nature.''
Unfortunately Heisenberg does not develop this interpretation much beyond the sort of generality of the above statements, and the concept of `potentiality' remains awkwardly isolated from much of his other thought on this subject [4] The reconsiderations suggested by quantum physics have over the last sixty years for the most part come fitfully and in scattered parts of which few physicists or philosophers were fully aware in a critical sense. Heisenberg, for example, notes (1958, p. 156) that what a typical physicist of today tends to think is rather close to Aristotelean `potentia', even if unwittingly. The meanings of words such as `particle' have moreover gradually changed in these sixty years. Kaempffer (1965), for instance, after pointing out the `erosion of naive pictures of particles', goes on to suggest that the word `particle' stand for a "quantum mechanical state [a wave field], characterised by a set of quantum numbers, which is associated, in principle, with an identifiable event such as the momentum transfer in a `collision'". This conception of a wave field associated with a definite event has come a long way from the corpusclar theory, and is remarkably similar to the present account of a continuant as a propensity field which extends over the various places possible for actualising events.

The conjunction of an extensive field with some actualising event also corresponds, I believe, to what Niels Bohr has called [5] the basic `quantum phenomenon', being an `undivided' and `closed' occurrence. It is `undivided' because between the source and realising events is a single extensive propensity field, and not any intervening actual events which could constitute some kind of unknown connection. It is `closed' because once a place in a propensity field has become realised, the field no longer exists: its history is closed. Bohr's `complementarity' of the wave and particle aspects of the quantum phenomenom arises because although a propensity field can be regarded as propagating through space and time like an oscillating wave and as obeying a wave equation, it is in fact a single field which can produce only one actual event. This event must be at one definite place, just as a strongly-localised particle would produce. If we were not aware of the notion of a `distribution of propensity for a definite event', we would be confused because sometimes the continuant behaves like a wave, and sometimes like a particle.

The point in fact is that the continuant-field does not have a fixed spatial size. Sometimes it behaves more like a spread-out wave, and when (at other times) it interacts it behaves like a localised particle. In fact, propensity fields can have practically any extensive shape over the places that are possible for it, subject only to some field equation. This allows them to propagate in interesting manners around obstacles which would stop any classical atoms. They can even tunnel through barriers, as the probability for a definite interaction may be reduced but non-zero. In this way it becomes reasonable to expect the diffraction, interference and tunnelling effects we know in quantum physics.

It would appear overall, then, that the present conception of substance is able at least qualitatively to account for several of the features of nature that have been captured by quantum physics, and which are mysterious or impossible in classical physics. We can see how there might arise a `wave-particle complementarity', indeterminacies, objective probabilities, diffraction, interference and tunnelling effects.

Propensitons

The above concept of `continuant' is very similar to Nicholas Maxwell's notion (1982,1985) of smearon or propensiton:
``Smearons'', as understood here, are hypothetical fundamental physical entities, having characteristics somewhat like the ``wave packets'' of orthodox QM in being smeared out in space like a wave function, but being unlike orthodox wave packets in having physically real nonlocal characteristics that in general exist in space and evolve in time independently of methods of preparation and measurement. What is smeared out in space is the propensity of one smearon to interact in a probabilistic, quasiparticle-like way with another smearon, should the appropriate physical (smearon) conditions to do so arise. The state vectors of QM are to be interpreted as characterising the actual physical states of smearons. The physical states of smearons evolve deterministically, in accordance with Schrödinger's time dependent equation (for elementary QM) as long as no probabilistic particle-like interactions between smearons occur. Probabilistic particle-like interactions between smearons involve changes of state which violate Schrödinger's time dependent equation even though no measurement is made. If appropriate physical conditions arise for an unlocalized smearon, in a state F, to interact in a probabilistic way with just one of many other highly localized smearons, then, roughly speaking, the probability that the unlocalized smearon interacts with the smearon localized in dV is given by |F|2dV. (this being a microrealistic reformulation of Born's original (1926) probabilistic interpretation of wave mechanics, which appealed explicitly to measurement). Smearon QM is thus a theory that is, in the first instance, exclusively about how smearons physically evolve and interact with one another in space and time independently of preparation and measurement. Measurements are probabilistic interactions between smearons which just happen to be recorded by physicists. Stable macro objects are the outcome of many probabilistic interactions between smearons. (Maxwell, 1982, p. 609)
The causal analysis of the previous sections can therefore be used to provide a philosophical justification and elaboration of the idea of smearons or propensitons, provided it is further assumed that propensitons only localise themselves intermittently.

Conclusion

In this paper, I hope to have shown that a useful concept of substance can be constructed from theories of process and causation, provided we go further along the path started by Whitehead, and take seriously questions of both possibility and propensity. The reinstated concept of `continuants' means that it is not `continuants which have powers', but that is `continuants which are powers'. More precisely, they are fields of powers, where fields are spatio-temporal forms or distributions.

This close connection between substances and powers was seen long ago by Locke, who wrote that `powers make a great part of our complex ideas of substance'. He also gave the even stronger characterisation of power as `a principal ingredient in our complex ideas of substance'. Locke might perhaps have gone on to view a substance as a `complex of powers', but he was severely constrained as he wanted to agree with the corpuscular philosophy of his day. In that approach all substance was `material' substance, and was purely actual with no trace of inherent power. However, despite these and other trends in philosophy and science to denigrate the role of powers and propensities in explanations and ontologies, it now turns out that powers have an essential role in helping us to see what it is which persists in the natural world.

Notes

  1. Though whether neutrons are single continuants or aggregates is strictly an empirical result from the physics of elementary particles.
  2. By using the term `quality', Locke is following the corpuscular philosophy of his day. His `qualities' are not static properties, but are in fact a certain kind of power. As he says (Bk. 2, ch. 8, § 8), `the power to produce any idea in our mind, I call the quality of the subject wherein the power is'.
  3. W. Heisenberg, `Planck's discovery and the philosophical problems of atomic physics' (1961, pp. 3 - 20).
  4. Heisenberg, for example, brings into his thought on quantum physics the Kantian phenomena/noumena distinction, as well as some of Bohr's ideas on `complementarity' in experimental arrangements.
  5. For a good exposition of Bohr's views, see Petersen (1968).

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Author: I.J. Thompson (except as stated)

Email: IJT@generativescience.org