I have read with interest Allins paper of the above name, which does
seem relevant to the debate on econometrics which has been going
on on the list.
I would like to make a few observations about it though.
First I must admit to ignorance of Bhaskar's work, so that I may
be misunderstanding part of what Allin is saying.
Allin says that Bhaskar defines a closed system, one capable of
generating a constant conjuction of events as requiring 3 conditions:
1. Outside influences must either be negligable or must be constant
over time.
2. The individuals of the system must be atomic (lacking in internal
structure) or their internal conditions must be unchanging over the
period in question.
3. The overall states of the system must be capable of representation
by an additive function of the individual components of the system.
I want in particular to question the last condition since this seems to
be seriously at variance with any reasonable calculus of states.
Suppose that I have a system with two sub components A and B.
Let us suppose that A has two possible states and B has 3 possible
states. Then the system (A,B) has, in the absence of some extra
constraints 6 possible states, not 5, since each possible state of
A can be combined with each possible state of B. Thus one would
normally say that the state of a combined system is the cartesian
product of the states of its components. The relevant principle is
multiplicative rather than additive.
In order to obtain an additive principle for states, one has to take
the logarithms of the number of possible states of the sub-systems.
Now the logarithm of the number of possible states of a system is
proportional to its entropy or information content, and it seems reasonable
to argue that the information content of the system is the sum of
the information content of the parts, but this is not the additive principle
Allin gives.
My question is does Bhaskar really mean the states of the system must
be additive, or does he mean that the entropies must be additive?
If he means that the states must be additive he is imposing remarkably
strict constrains on state composition.
Secondly relating to Lawsons argument that the reality of free human
choice implies that we can expect to see few if any regularities in the
social realm.
It strikes me that were this objection to be true, then it would not apply
to the social realm alone. At a microscopic level, quantum indeterminacy
implies that particles can chose which path to follow in an non-deteministic
fashion. This would apparently rule out the detection of regularities in
the physical realm. Of course this turns out not to be the case: although
individual events are unpredictable, the mean rate of such events can
exhibit remarkable regularities.
One of the facts which appears to have excited the greatest
alarm, out of all pointed to in my work, is naturally that relating
to the constancy with which crime is committed. From the
examination of numbers, I believed myself justified in inferring,
as a natural consequence, that, in given circumstances, and
under the influence of the same causes, we may reckon upon
witnessing the repetition of the same effects, the reproduction
of the same crimes, and the same convictions.
Now, what do these facts teach us? I repeat, that in a given state
of society, resting under the influence of certain causes, regular
effects are produced, which oscillate, as it were, around a fixed
mean point, without undergoing any sensible alterations.
Observe, that I have said under the influence of the same
causes; if the causes were changed, the effects also would
necessarily be modified. As laws and the principles of religion
and morality are influencing causes, I have then not only the
hope, but, what you have not, the positive conviction, that
society may be ameliorated and reformed. Expect not, however,
that efforts for the moral regeneration of man can be
immediately crowned with success; operations upon masses are
ever slow in progress, and their effects necessarily distant.
(Quetelet)
--
Paul Cockshott
paul@cockshott.com
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