1. Determinism is the doctrine that the universe is to some extent, in some way, determinate. I want to consider some of the ways in which this might be the case.
2. First, an extreme case. If we accept the notion of a proposition, and accept that the truth value of a proposition is timeless, then in some very weak sense the universe might be said to be completely determinate. Usually we would get a bit more window dressing. If something is going to happen then it is true now and allways has been true that it will happen. If it is true that something is going to happen, then it is going to happen, whatever else happens, and so it is inescapable. (p implies (q implies p)) Everything that will happen, will happen, and so the universe is determinate.
3. Perhaps my account is defective, but this does not greatly matter. This deterministic thesis has the following characteristics:
|a)||It is absolute; those things which are determinate are unconditionally determinate.|
|b)||It is complete; everything is determinate.|
|c)||It offers no way of establishing what is, was, or will be the case, except, possibly, by direct observation. Though events are determinate, they are not necessarily determinable. This sort of determinism is compatible with a universe in which scientific activity is completely ineffective.|
|d)||The doctrine is established 'a priori'. Its proponents would probably claim that it is analytic.|
4. Now consider this hypothesis: All truths are analytic. This shares with the previous example characteristics a,b and d. The extent to which it differs in respect of characteristic c depends on the nature of analytic truths. It would differ most if analytic truths were held to be decidable, but even then, only if the decision procedure were given. If such a decision procedure were known then the universe would be, under this hypothesis, completely determinable, and determinable a priori. If such a decision procedure is known to exist, a (priori), and yet we do not know what it is, then we are caught in a strange hinterland, our theory certainly claims that the universe is determinate (in some sense) but are we, on the basis of this thesis to claim that the universe is determinable?
5. And so I must bring out into the open (as far as possible) the way in which I am using these words. Determinate I use loosely, so as to encompass even the most vacuous theories, and so I shall not attempt to define it. Determinable, however, was introduced to sort out the empty from the substantial. The universe is determinable if we can establish what the facts are. That the universe is determinate (to some extent) is a necessary but not a sufficient condition of its being determinable (to that same extent). This 'can establish' covers a wealth of problems; to understand 'establish' we need a theory of knowledge, but I am leading to a theory of knowledge, for if it is simply a question of logical possibility then the determinable stands in danger of encompassing the whole of the determinate, and if it is not logical possibility that is required then what sort of possibility is it?
6. So 'determinable' is not much easier to pin down than 'determinate'. I shall leave it vaguely pointing, for the moment, to the possibility (of some sort) of discovering or establishing (in some way) the facts in a determinate universe. What concerns me about theories of determinism is whether in any sense they claim the facts to be determinable, and if so, in what way the theory suggests that they are to be established.
7. Returning to the hypothesis of para.4, what ways of establishing facts are here offered? Let us consider more closely the conditions necessary for this to give us a complete a priori determinability. I want here to use an important notion from mathematics, the notions of an 'effective procedure'. Informally I shall define an 'effective procedure' in this way; there is an 'effective procedure' for accomplishing some task if and only if it is possible to program a digital computer in such a way that, given an unlimited amount of storage space (but not an infinite amount), the computer will allways accomplish the task in some finite amount of time (though not necessarily less than any given finite amount of time). Alternatively, an 'effective procedure' is one which can be broken up into elementary steps in wuch a way that the procedure will allways be completed in a finite number of such steps. An elementary step in this latter definition must be something unequivocally finite and plausibly mechanisable, not more complex than the execution of a single machine instruction of a simple digital computer.
8. Although my informal explications of the 'effective procedure' have referred to physical objects and mechanisability I must make clear there that when more properly defined the concept is not dependent upon the contingent capabilities of any mechanical device.