From owner-bhaskar Fri Jan 10 22:31:10 1997 Date: Fri, 10 Jan 1997 20:24:47 -0700 Message-Id: <> From: Hans Ehrbar <> Subject: BHA: rts2-22 Actualism and the Concept of a Closure 69 2. REGULARITY DETERMINISM AND THE QUEST FOR A CLOSURE So far I have been content merely to identify a closed system as one in which a constant conjunction of events obtains. But we must now establish exactly what this entails. It might be thought that the idea of a closed system could be elucidated quite simply as a fragment or sector of the world effectively cut off for a period of time from non-constant external influences. Although this gives one clear sense of `a closed system' such a system would not necessarily satisfy the criterion of invariance implicit in the empiricist analysis of law. For one thing conditions would have to be placed on the individuals composing the system and the way in which the states of the system were to be specified. But even if this were done there would still be no guarantee that the criterion of invariance would be satisfied. The assumption that it would be depends upon the metaphysical thesis of regularity determinism. This may be defined as follows: For every event y there is an event x or set of events x_1 . . . x_n such that x or x_1 . . . x_n and y are regularly conjoined under some set of descriptions.11 That is, the world is so constituted that there are descriptions such that for every event the simple formula, `Whenever this, then that' applies. 11 The concept `event' functions here syncategorematically. Its purpose is, in context, to generate the appropriate redescriptions of the events concerned. 70 A Realist Theory of Science Such a thesis stands to the practice of science as a regulative principle. Such principles are, as is well known, neither empirically nor theoretically refutable (or confirmable). But I will contend that they are metaphysically so. My procedure will be to see what this thesis entails about the nature of the world and about the nature of science; and to assess its adequacy in these respects in relation to other possible regulative standpoints. To do so I will work out critical or test conditions for the thesis of regularity determinism; that is, conditions such that if they were known to be satisfied and the constant conjunction formula was not vindicated the regularity determinist would be bound to admit his thesis refuted. In this way I hope to show just how restricted in its ontological presuppositions and restrictive in its methodological responses regularity determinism is. In developing these limit conditions for a closure I will thus be developing the conditions under which, on the supposition that regularity determinism is true, a constant conjunction of events must obtain. However, I will define a `closed system' simply as one in which a constant conjunction of events obtains; i.e. in which an event of type a is invariably accompanied by an event of type b. Clearly the possibility of such a system does not depend upon the truth of regularity determinism. Nor need such a system be `closed' in any more picturesque sense of the word. Regularity determinism must be straightaway distinguished from two other forms of determinism: which may be called `ubiquity' and `intelligibility' determinism. Ubiquity determinism asserts that every event has a real cause; intelligibility determinism that every event has an intelligible cause; regularity determinism that the same (type of) event has the same (type of) cause. The concepts of `cause' involved in the three determinisms are of course distinct. For the ubiquity determinist the cause is that thing, material or agent which is productive of an effect; for the intelligibility determinist it is simply that which renders an event intelligible to men;12 for the regularity determinist it is the total set of conditions that regularly proceeds or accompanies an event.13 Of the three determinism, regularity 12 See e.g. W. Kneale, Probability and Induction, p. 60. 13 See e.g. J. S. Mill, A System of Logic, Vol. I, Bk. III, Chap. 3, Sect. 3, or A. J. Ayer, Foundations of Empirical Knowledge, Chap. 4, Sect. 17. As has been frequently pointed out, by Mill and Ayer among others, this concept does not accord well with our normal usage; so in practice the Humean tends to modify it in the direction of the intelligibility concept by making the cause an individually critical factor in a jointly sufficient set. On the other hand, to the extent that the intelligibility theorist is committed to the doctrine of empirical realism he must rely on a background of empirical generalizations to justify his citation of the cause. Actualism and the Concept of a Closure 71 determinism is clearly the most restrictive; and ubiquity determinism is more general than intelligibility determinism, because it licenses no presumption that the real cause of an event will always be intelligible to men. The realist, intelligibility and regularity concepts of cause are of course naturally associated with the transcendental realist, transcendental idealist and classical empiricist philosophies of science. All three determinisms must be distinguished from the idea of `computational' determinism. This is the supposition that for each characteristic or trait of any material body at any moment of time there exists at least one set of statements from which, together with the relevant antecedent state-descriptions, that trait is deducible. It is important to realize that because no restriction is placed on the statements used in the deduction of traits, computational determinism is a truism. It says merely that given any system it is possible to work out an algorithm for the successful computation of its traits; or, in other words, that there is a consistent way of describing the development of any system over any finite period of time. Moreover in general there will be an infinite number of ways of doing so. It is therefore an uninteresting truism - save perhaps to remind us that the notion of disorder or chaos is always relative to a particular type of order or class of functions;14 and that the criterion of deducibility is too easily satisfied to be capable of functioning alone as a decision rule for the selection of `law-like' or `theoretical' statements and requires at the very least supplementation by criteria that place some restriction on the number, type or interpretation of the statements concerned. It is especially important to distinguish regularity >from computational determinism. For it is at least part of the intention of the former to assert (a) that the same cause and effect sometimes as a matter of fact recurs and (b) that the same cause and effect could always logically recur. For unless (a) 14 Cf. e.g. E. Nagel, The Structure of Science, p. 334. 72 A Realist Theory of Science were true instances would not fall under it and unless (b) were true they could not fall under it; so that it would be at best vacuous and at worst false. On the other hand computational determinism is consistent with `law-like' formulations which are so specific and detailed as to reduce the practical likelihood of the event's recurrence towards zero or which mention the spatio-temporal location within which it occurred or which individuate it with a definite description or a proper name (e.g. The Battle of Edge Hill). We need not dwell on these possibilities here. For they have been thoroughly explored by philosophers concerned to defend the autonomy of historiography from (Positivist) science.15 For the regularity determinist the necessity for such formulations merely indicates the ignorance of the describer. The anti-regularity-determinist, on the other hand, may take it as a sign of emergence or novelty in nature or even of the self-determination of some agent or structure. Unlike computational determinism, regularity determinism is not trivially satisfied. It does however share with it the feature that if there is one set of law-like statements which satisfies it there will be an infinite number of such sets. Hence it too requires supplementation by additional criteria, such as simplicity, intelligibility or realism, if it is to be capable of yielding a unique decision procedure for the selection of laws'. The total cause (in Mill's sense) of an event will normally be a complex set of conditions x_1 . . . x_n rather than a single event x. One could distinguish here between the individual or component events or states and the total or conjunct event or state; and refer to the case where more than one factor is at work, following Mill, as that of `multiple causation'. In the same way the consequent event will also normally be complex, i.e. y_1 . . . y_n rather than simply y; and so we could talk of a corresponding `multiplicity of effects'. There is a genuine `plurality of causes' when the same effect arises >from different (i.e. alternative) sets of conditions.16 Is a plurality of causes consistent with regularity determinism? Note it is consistent with 15 See e.g. P. Gardiner, The Nature of Historical Explanation; W. Dray, Laws and explanation in History; C. B. Joynt and N. Rescher, `The problem of Uniqueness in History', History and Theory, Vol. 4; and M. Scriven, op. cit. 16 Cf. M. Bunge, Causality, p. 122. Actualism and the Concept of a Closure 73 predictability. For given a knowledge of the conditions which actually prevail, the effect is uniquely predictable. But it is not consistent with retrodictability. For given the effect, we cannot uniquely infer the cause. And this requirement is explicit both in the Laplacean ideal, which places the past on a par with the future, and the Humean definition of cause (`in other words, where if the first object had not been, the second never had existed'), which makes the cause both necessary and sufficient for the effect.17 To satisfy this requirement the idea that every event has one and only one cause (or set of causes) must be incorporated into our definition of regularity determinism. This must now read: the same cause always has the same effect and the same effect always has the same cause; so eliminating both the possibility of a disjunctive plurality of causes and of a disjunctive plurality of effects. Now suppose we had a system such that events of type a were invariably followed by events of type b. We could then say that a closure had been obtained. A closure is of course always relative to a particular set of events and a particular region of space and period of time. Now supposing that at some time t' an event of type a was not followed by an event of type b we would have to say that the system was `open', our criteria of open-ness just being the fact that events of type a had not been invariably followed by events of type b under their given descriptions; i.e. the instability, in space or over time, of actually recorded empirical relationships. Should we say that the system had been closed but was now open or that it was open all along ? There is nothing at stake here - it depends entirely on the time period for which `the system' is defined: if and only if it includes t' it is open. `System' here carries no independent semantic force. Either way the natural response of the regularity 17 Cf. Newton's 2nd Rule of Reasoning in Philosophy: to the same natural effects we must, as far as possible, assign the same natural causes', ibid. And Hume: `the same cause always produces the same effect, and the same effect never arises but from the same cause', A Treatise on Human Nature, p. 173. The rationale for this requirement lies in the counter- intuitive nature of the implication that the future be better known than the past. Moreover given the logical reversibility of the connective and the classical concept of time a disjunctive plurality of causes could be transformed into a disjunctive plurality of effects so as to produce a radical indeterminism in nature, i.e given x then y_1 or y_2 . . . or y_n! 74 A Realist Theory of Science determinist to this situation would be to suppose that we had left out of our state-description an individual or variable that made a difference: that the conjunct events referred to under the same description `a' before and after t' were not really the same in all relevant respects; in short that the system had been incompletely described (or enumerated). For example if the system was a classical mechanical one, where the presupposition was that mass, position and velocity were the only relevant variables, it would be natural to suppose that a relevant individual had been omitted from the specification of the overall state of the system, i.e. the total conjunct event. To fix the point, imagine a universe composed of a finite number of different kinds of knives, forks and spoons. Suppose that we attempted to work out a general rule which would enable us to predict that when the knives and forks were in a certain position (including naturally the datum of whether they were on the dining-room table or in the kitchen drawer) they were invariably followed by another constellation of positions at the next meal. We might find this impossible, unless we took into account the positions of the spoons; so that we could say that our system had been incompletely described in the former case, owing to the omission of a causally relevant (in the Humean sense) variable. Of course in time we might find that we could only satisfy the demands of regularity determinism by taking into account further variables, e.g. the shapes and number of glasses at the meal; or even variables of an entirely different kind, e.g. the room temperature - to distinguish say between winter breakfasts when porridge was the rule and summer ones when grapefruit was. Subject to an important qualification to be discussed below it can thus be seen that regularity determinism implies a particular kind of response to the phenomenon of open systems, i.e. to the instability of empirical relationships, viz. to assume that some causally relevant individual or variable has been left out of the description. On the other hand, even if this were the case, stable empirical relationships might still be possible as long as the values of the omitted variables remained constant. A closure thus depends upon either the actual isolation of a system from external influences or the constancy of those influences. Actualism and the Concept of a Closure 75 Assuming that a system was effectively isolated from non-constant external influences and regularity determinism was true would this then ensure the satisfaction of the `whenever this, then that' formula? Let us suppose that we are interested in explaining (in the sense of Hempel and Hume) the behaviour of some individual N, say an elephant. Would a knowledge of the total antecedent state-description enable us to predict its behaviour ? No - for if N is characterized by internal structure and complexity it may behave differently in the same external circumstances in virtue of its different internal states. Thus what happens when I prod an elephant depends at least in part upon what state it is in, e.g. whether it is asleep or not; and thus to that extent the total state of the universe, of which the elephant occupies a part, will be a variable. So either the absence or the constancy of internal structure must also be a condition for a closure. And the regularity determinist now has another possible response to the condition of open-ness, namely to assume that the individuals of the system have not been given a simple or atomistic enough description. It is easy to see that an actual isolation and atomistic individuals will be preferred, on epistemic grounds, by the regularity determinist to constant external and internal conditions. For the regularity determinist has no warrant for assuming that these conditions will remain constant.18 Whether they do or not will depend upon a whole host of factors concerning which ex hypothesi he has no knowledge and about which he is not therefore in a position to make any kind of claim. Only with an actual isolation of atomistic individuals will the regularity determinist be able to categorically predict the future; without it, it always remains on the cards that an unpredicted change in the external circumstances of the system or the internal states of its individuals will occur so as to upset an established regularity and so render inapplicable any hypothetical predictions, formulated subject to two ceteris paribus clauses. I have been tacitly assuming up till now that the overall states of the system can be represented as an additive function of the states of the individual components of the system. This 18 Regularity determinism does not make a claim about the constancy of conditions. Its claim concerns the constancy of the conjunction between conditions, whether conditions should happen to be changing or not. 76 A Realist Theory of Science represents a third kind of requirement for a closure. Here again a closure is possible if the principle of organization is non-additive, provided it remains constant; though here again the regularity determinist will prefer the alternative of additivity on epistemic grounds. Behind the assumption of additivity lies of course the idea that the behaviour of aggregates and wholes can always be described in terms of the behaviour of their component parts. The assumptions of atomicity and additivity are closely connected. For to say of some system that it is irreducible (in this sense) to its component parts is presumably to say that it must be viewed as a thing in its own right, at its own level (I am not concerned with the grounds for this now.) Conversely to suppose that it is always possible to give an atomistic description of prima facie complex things is to suppose that they can always be viewed as systems or parts of systems which can be analysed in terms of their component parts, conceived as atomistic individuals. The critical conditions for a closure are set out in Table 2.1. The satisfaction of one each of the system, individual and organizational conditions is sufficient, on the supposition that regularity determinism is true, for a closure; but not necessary for it. If a recorded regularity breaks down the regularity determinist must assume that it is because one of these conditions is not satisfied. Until now in developing the conditions for a closure I have been using the categories `internal' and `external'. But the categories `intrinsic', and `extrinsic' are better in that they are not explicitly tied to a spatial characteristic and Table 2.1 Limit Conditions for a Closure, i.e. for the Stability of Empirical Relationships ------------------------------------------------------------------------ Conditions (1) Epistemically (2) Epistemically for a Closure Dominant Case Recessive Case ------------------------------------------------------------------------ (A) System Isolation Constancy of Extrinsic Conditions (B) Individuals Atomicity Constancy of Intrinsic Conditions (C) Principle of Additive Constancy of Non- Organisation Additive Principle ------------------------------------------------------------------------ Actualism and the Concept of a Closure 77 hence to things of a certain type. Thus the category `intrinsic' includes some properties of things which lie outside their spatial envelope, e.g. a magnet's field, and others which cannot be identified spatially at all, e.g. a person's charm. And it excludes others which do lie within their spatial envelope, e.g. properties belonging to things of another type. `Isolation' must also be interpreted metaphorically; but there is a sense in which `atomicity' must be taken literally. Now it is easy to see that once an actual isolation and an atomistic description are set up as norms two regresses are initiated, viz. to systems so vast that they exclude nothing and to individuals so minute that they include nothing. These regresses are typically manifest in research programmes, characteristic of positivistic science, which could be dubbed `interactionism' and `reductionism' respectively. It is clear that they can only be halted by constituting a level of autonomous being, somewhere between the universe and atomistic individuals. But for the empiricist committed to regularity determinism to do so involves an enormous risk. For it means he must be prepared to snap the Humean link that ties the justified performance of cognitive acts such as the ascription of causes to a knowledge of empirical invariances; and to say `yes I know a is not invariably followed by b, yet a caused b here'. These regresses generate notorious paradoxes in their wake. For since in the first case there are at the limit no conditions extrinsic to the system a full causal statement would seem to entail a complete state-description (or a complete history) of the world. Similarly as in the second case there can be no conditions intrinsic to the thing a causal statement entails a complete reduction of things into their presumed atomistic components (or their original conditions). In the first case we cannot make (or can at best only make in a pragmatic way) the distinction between causes and conditions; in the second case that between individuals and variables or between a thing and its circumstances. In neither case do we have the key concept of a causal agent; i.e. the thing that produced or the mechanism that generated, in the circumstances that actually prevailed, the effect in question. Open systems situate the possibility of two kinds of possibility statements: epistemic and natural. The regularity determinist 78 A Realist Theory of Science can accommodate the former but not the latter. For he may allow that an event may be uncertain due to the describer's ignorance of the complete atomistic state-description necessary to deduce it. But he cannot allow that there is a sense to a statement about what an individual can do independently of whether or not it will do it. For natural possibility statements to be possible condition B1 must be unfulfilled; i.e. there must be complex things, possessing intrinsic structure, to which the natural possibility is ascribed. Without this, the distinction between a power and its exercise would be indeed, as Hume supposed, entirely `frivolous'. So in part the issue between the regularity determinist and realist turns on the question of whether there are objects not susceptible of an atomistic analysis and in what way this is significant for science. A special and very important case of the individual conditions for a closure is thus given by: B1' the absence of powers, which is dependent upon the absence of intrinsic structure (implied by atomicity); and B2' the constancy of powers, which is dependent upon the constancy of intrinsic structure. If there are complex things then it becomes important to distinguish between the subjects and the conditions of action. For conditions is an epistemic, not an ontological category. The conditions change, but they do not have the power to change. Only things and materials and people have `powers'. I have argued in effect in Chapter 1 that for experimental science to be possible the world must be open but susceptible to regional closures. Now corresponding to the view of the world as open and the view of the world as closed we have two entirely different conceptions of science. The transcendental realist sees the various sciences as attempting to understand things and structures in themselves, at their own level of being, without making reference to the diverse conditions under which they exist and act, and as making causal claims which are specific to the events and individuals concerned. And he sees this not as a tactic or manoeuvre or mechanism of knowledge; but as according with the ways things really are, the way things must be if our knowledge of them is to be possible. The regularity determinist, on the other hand, will seek in his quest for a closure, if the very special conditions specified in Table 2.1 are not satisfied, to incorporate more and more elements Actualism and the Concept of a Closure 79 into his descriptions and/or to break down his units of study into finer and finer constituents in an effort to stabilize his field. And he must see this merely as an attempt to vindicate to himself the rule, which may be fairly styled a dogma, that like follows like or whenever x then y. --- from list --- .