Next: 7. Potentiality Up: 6. Actuality Previous: 6.2 Finite or Infinite?
We discussed above the nature of continuity, and in the next chapter it will be seen how extensiveness can be continuous. `Pure actuality' has been defined to be finite in itself and in aggregrates. Using the Finiteness Postulate of the previous section, actuality is further intended to exclude all divisibility, including divisibility of extent. This follows as `divisibility', strictly speaking, means `possibility for dividing', and the definition of actuality means that possibilities cannot be attributed to pure actualities.
because they can themselves change, and hence are not fully determinate. The primary definition above of pure and full actuality singles out those things which are in no way themselves constituted by potentiality or possibility. Any potentiality they may have or which they may influence is only for other entities, in order that the realisation or non-realisation of that potentiality has no effect on the original actual particular. In this way, actual particulars are fully determinate, and will always be so, so long as they exist. The only way of there to be change is for an actuality to cease and a new actuality produced. But then, one actuality is being replaced by another. It is not the case that an actual entity continues or endures through the change, as substances and everyday objects usually do.
This means that substances and objects, as those particulars which can continue and endure even though they change certain of their properties, are not actual in the primary and full sense. This is because they must have potentialities or capacities for themselves becoming different yet remaining the same particular thing. They can only be called `actual' in the second sense of being present, or the third sense of being active, without being fully actual and determinate in every respect. How in fact we should conceive substances, etc., will be considered in chapter 9.
As was discussed in chapter 3 above, however, this identification of matter and actuality makes it difficult to describe intelligibly the dispositions of particles to interact with each other. It also makes quantum phenomena seem utterly mysterious. For these reasons, we must reject both the identification of matter and actuality, and the identification of actuality and infinity. We cannot allow the material corpuscles of Newtonian physics to be actual in the primary sense. For either they have no dispositions for interacting, in which case they are empirically inadequate, or they do have dispositions for interacting, in which case they are no longer purely actual.
If we accept the Finiteness Postulate of the previous section, then that would be a further reason for rejecting their actuality (whether or not they had dispositions), for Newton and Boyle imagined their corpuscles to actually fill a finite and continuous volume of space. When space is composed of an infinite number of points, there would be an similar number of points where the corpuscle actually existed. Infinities of actual things must be ruled out by the Finiteness Postulate.
Nothing intrinsically and forever fixed in space and time can be considered as `particulars in our changing world' to start with, let alone as the actual particulars in that world. This is because such thin gs are fixed at all times `from eternity to eternity', and it is impossible for there to be any real changing in or of these things themselves.
As explained in chapter 2, I am seeking to give accounts of the real nature of such things as dispositions, possibilities and potentialities etc. as part of the objective situation. To have an ontology in which all particulars are fully determinate for all time allows only a nominal definition of dispositions and possibilities, as necessarily related to either purely hypothetical counterfactuals, or to human ignorance. I am not denying the logical possibility or even the consistency of the philosophy based on the `block' view of spacetime. It should not however be the only alternative that might be compatible with logic or physics (despite its popularity among certain scientists and philosophers of science, e.g. from Minkowski to Grünbaum). There will be further discussion in chapter 8. I hope to show, by means of this book, that the quasi-static view of spacetime, though conceptually simpler, is not the most suitable approach.
It is sometimes considered that only the present states of objects are actual, as their future states are yet to occur and their past states are no longer operative. This avoids the objections to the previous two objections. For such actualities do not have to change yet remain the same actuality, but now new actualities are being formed successively at every moment in time. And we are not considering all future and past states to be actual in the same way as the present states, so it does appear that real changes are occurring.
The difficulty with this suggestion, however, is that there would now be an actual infinity of such actualities, even over a finite duration of time. From the point of view of classical Newtonian physics, this is certainly allowable, but, as explained earlier in this chapter, an actual, fully-determinate infinity is certainly a borderline notion, and I argued for its ultimate untenability. A consequence of the Finiteness Postulate given earlier is that actualities cannot, taken together, form transfinite sets. Only possibilities can do so. In the context of the present investigation, therefore, we must reject the identification of actualities with the momentary-present states of objects.
Processes which take place over an extended duration cannot be fully actual, because, by numerically dividing the overall duration, they can hence can be divided up into a sequential aggregate of sub-processes which actually succeed each other. However, anything purely actual must exclude all divisibility, as divisibility means possibility for division. Purely actual things must be simple, unextended and indivisible.
The arguments above exclude the actuality of extended processes, but what about the actuality of those events which are in fact durationless and indivisible, and hence in a sense ultimate? Those indivisible events would be those which just happen somewhere and at some time, without duration or extension being part of their nature. Exactly how we can conceive durationless events will be considered later, in chapter 10, but in the meantime the question is whether or not `actuality' can be identified with these ultimate events.
If events are actual, then the event, as what happens, must be related to the actuality, and hence to the becoming and the perishing of that actuality. Although it is quite reasonable for us to distinguish an extended process from its (act of) becoming, it is senseless to do so for a durationless event. Surely such an event is its becoming. An event is not one thing and its happening another, as Chappell  points out. Happening adds nothing to an event, for to be an event, to happen, to be an act (e.g. of becoming) are all one and the same.
Thus if `actuality' is identified with `durationless event', both of these must be further identified with their act of becoming, and, by a completely analogous argument, all three must be identified with their act of perishing. But if the becoming is found to be identical with the perishing, how could we say becoming, then perishing'' any more than perishing, then becoming''? In the later case, the event would not be actual at all. We conclude, therefore, that since it is found that supposing `actual, durationless events' does not lead to sufficiently unambiguous consequences, and in fact leads to opposing consequences, `actuality' cannot intelligibly be identified with `durationless event'. Thus neither processes with duration, nor ultimate events without duration can be themselves actual in the primary sense.
`Strands of history' cannot be actual, because if (a) a strand is a collection of past states, then no collection can be a simple particular, and a changing collection can never be an actual particular. If (b) a strand is a single, growing entity, then it must itself be continually changing, and its actuality is ruled out by the arguments give above against substances and other changable objects.
In opposition to such a proposal, however, I wish to reassert the Finiteness Postulate concerning what actually exists. I wish also to follow Whitehead and Leclerc and to distinguish a particular from its place. In chapter 8, an appropriate conception of space and time will be explained. It will be based on the notions of `possibilities' and `extensive relations', in order to avoid having space or spacetime as any separate existent. There should be no need to give space or time or spacetime an actuality alongside the particulars that occur in space and time. We can then also avoid the Newtonian tradition of space as an absolute entity that actually exists in some sense, independently of any possible particulars.
Stages between two changes in a continuing object could perhaps be purely actual, provided that the stage was immutable so long as it existed, and that the existence had at least a finite duration. It has to have a least a finite duration, otherwise its becoming and its perishing would be awkwardly identical. It does not seem to make much sense to talk of the becoming and the perishing of a point event, yet any actuality must have a becoming at some time, when it first existed, and may well have a perishing, when it last exists.
An actual stage can have a finite duration, and still be actual, as long as that duration is not actually divided in this case. On this account, actuality comes into existence from some cause, then it endures unchanged for some duration, then, from some external cause (not from its own nature), that actual stage perishes to be replaced by something else.
Although this account of what is actual appears in itself to be consistent, there are other reasons why it is no longer as plausible as it once was. For, according to this account, there is a basic notion of `rest'. A continuing object `rests' immutably in some state for some finite duration, and (anticipating the definition of `place' to be given in chapter 8) therefore rests in a single place for that duration. This concept of actuality, with this consequence, fitted well with the world view of the ancient Greeks, but does not today seem so likely to be true. It agreed with the Greek explanation of gravity, according to which all place admits of the distinction of up and down, and each of the bodies is naturally carried to its appropriate place and rests there'' 6.5 . That is, for each body there is a place where it can rest immutably for some finite duration. For heavy bodies, their place would be anywhere on the surface of the earth.
This account is no longer plausible, as we no longer believe that there are `resting places' for natural bodies. It seems unlikely that there would be any bodies satisfying this suggested definition of actuality. We cannot of course rule on the impossibility of the Greek concepts of place and actuality, only that they should not be the only choices we have before us.
Actualities are not now identical with the act of their becoming, but can be reasonably be identified with the facts, the concrete facts, of their becoming. Since, also, the actualities produced by past-events need never perish, the set of actualities in the world never decreases - it can only remain the same, or increase with the addition of new individuals. When a new event occurs, a new actuality is generated which is a `concrete fact'. This means that new concrete facts may be generated, while historical concrete facts remain everlastingly true. They neither become false, nor disappear. We can say not only that `past-events were actual after they happened', but also that `past-events are (now) actual', and remain fully determinate beings, where, again, `past-events' are the actualities produced by past events.
The space-time manifold of events is therefore not laid down all at once, but only from the distant past up to the present. Events are added as they occur: a new fully-determinate past-event then comes to exist, to mark the fact and the permanency of each event's occurrence. The coming to be of these actual past-events is an addition to the significance the events have for changes to present and future substances. The view of time involved here will be further discussed in chapter 8.
We now have past-events which are actual and `rest' at a single place, rather than stages of continuing objects. Continuing objects can now be conceived as acting and producing actualities without themselves ever `resting' at a place for any length of time. This option is more in agreement with the Galilean and Newtonian theories of motion, which have that uniform rectilinear motion is not an event and hence need not be associated with the production of actual past-events. How exactly objects and their interactions should be conceived will be discussed in chapters 10 and 11.
Next: 7. Potentiality Up: 6. Actuality Previous: 6.2 Finite or Infinite? Prof Ian Thompson