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7 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 ) 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.
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 similar to that of Whitehead's `extensive continuum', which is the `coordination of all possible standpoints'. Whether this is an `absolute' or `relative' view of spacetime depends on how particular possibilities are individuated and identified. This is discussed in subsection 8.2, and further in chapter 11.
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.
It is not logically necessary for actual events to be points in ordinary space and time, but this is a `contingent identification' between our theory and its application. This contingency follows the same pattern we found previously for dispositions in section 2.6, for mathematics in chapter 6, and for general philosophies of nature in chapter 5. In chapter 11, we will consider an alternative identification of what is actual, and thus an alternative identification of the `space-time of places' wherein actualities are at single points.
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. Following the arguments of chapter 7, they are certainly not `possible events', or any kind of events which in some way `subsist' without actually existing. As Quine 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?'' 8.1
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.
Finally, the `possibilities for events' are not reducible to talk of `possible worlds', especially since I am interested in what possibilities there are in and for this world. According to the usual theory of `possible worlds', the actual world is just one possible world, to be selected by a knowledge of what actually happens at all times. Knowledge of which actual world we are in, therefore, is equivalent to knowledge of all past and future events. Any indeterminism in nature must be only a certain `looseness' in the laws that link events at different times, and cannot be linked to any different ontological status between the past and the future. I want to have a natural ontology in which actualities only exist for past events, with none for any future events. It is difficult to accommodate this ontology within the framework of a `possible worlds' theory of modality. It could only be done by making each temporal state of each possible world to be the set of all past events up to that time. Even if I do not use this formulation, I can still talk of futures `accessible' at a given time, given the past history up to that time. I argue, however, that these futures are part of our one present world, and, moreover, are present only as possibilities, not in full actuality.
The important thing is to take possibilities seriously, and not to confuse them with actuality. We saw in chapter 6 how, from the mathematical point of view, 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. We have seen previously how Whitehead warns against the mistake of confusing mere potentiality with actuality.
Next: 8.2 Extensiveness, Space and Up: 8. A Theory of Previous: 8. A Theory of Prof Ian Thompson