From owner-bhaskar Fri Jan 10 22:31:10 1997
Date: Fri, 10 Jan 1997 20:24:47 -0700
Message-Id: <199701110324.UAA09156@marx.econ.utah.edu.utah.edu>
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.
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