I don’t have much to say on Peirce and QM. Although I have the following quote
in my notes that might be of interest. I’m not sure it’s fair to say that
Peirce is anticipating QM in this although there clearly are some interesting
parallels.
. . . Let us next consider how a state of fortuitous distribution is
brought about. How, for example, is it that the throws of a dice occur in the
utterly irregular way in which they do? It is because when we turn over the
dice box, there are slight differences in the motion, and also when we put the
dice into the box there are small differences in the motion; and no regularity
connects the differences of one kind with those of the other. Still, these
circumstances would not in themselves give the character of fortuitous
distribution to the throws were there not a fortuitous distribution either in
the differences of our motion in putting the dice into the box or else
fortuitous distribution in the variations of motion in throwing them out. We
see, then, that in this case the fortuitous distribution arises from another
fortuitous distribution in one or more of the conditions of the production of
the phenomenon. All this has been carefully studied by various writers on the
theory of errors. Suppose we put into a jar some hot nitrogen and then some
cold oxygen. At first, the molecules of nitrogen will be moving with various
vires vivae distributed according to a modification of the probability curve
and therefore fortuitously, while the molecules of oxygen will likewise have
vires vivae distributed according to the same general law, but on the average
their motion will be much slower. In the first state of things, therefore, the
distribution of vires vivae among all the molecules considered as one
collection will not be fortuitous. But there will be continual encounters of
molecules, which, in these encounters, will be governed by conservative forces,
generally attractions. In consequence of the different modes of these
encounters being distributed fortuitously, which is itself due to the
fortuitous distribution of the molecules in space, and the fortuitous
distribution of the directions and velocities of their motions, continual
interchanges of vis viva will take place, so that as time goes on there will be
a closer and closer approximation to one fortuitous distribution of vis viva
among all the molecules. There we see a fortuitous distribution in process of
being brought about. That which happens, happens entirely under the governance
of conservative forces; but the character of fortuitous distribution toward
which there is a tendency is entirely due to the various fortuitous
distributions existing in the different initial conditions of the motion, with
which conservative forces never have anything to do. This is the more
remarkable because the peculiar distribution which characterized the initial
distribution of vires vivae gradually dies out. True, traces of it always
remain; but they become fainter and fainter and approach without limit toward
complete disappearance. The fortuitous distributions, however, which equally
have nothing but initial conditions to sustain them, not only hold their
ground, but, wherever the conservative forces act, at once mark their character
in the effects. Hence, it is that we find ourselves forced to speak of the
"action of chance.". . . (CP 6.81)
The following is also of interest a few pages later.
Let us now consider non-conservative actions. These are all distinguished by
asymptotic approach to a definite state of relative rest. Conservative force
can never bring about any state of rest except for an instant. It can only
produce, I believe, three permanent changes. Namely, it can permanently change
the direction [of] motion of a body, and this it does because the body moves
away out of the range of the force, or it can cause one body to rotate round
another in an inward spiral, more and more rapidly. And third, a planet like
Jupiter may turn the motion of a small body and then move away and leave the
small body performing permanently, or quasi-permanently, an orbit round the
sun. In course of time, however, Jupiter will come round again in such a way as
to throw it out. This is a very curious case. Chance is an important factor of
it. But all the non-conservative quasiforces produce states of relative rest.
Such, for example, is the effect of viscosity. These states of relative rest
are states of uniform distribution which upon minuter inspection turn out to be
really states of fortuitous distribution. They betray their real nature by the
probability curve, or some modification of it, playing a part in the
phenomenon. Such, for example, is the case in the conduction of heat.
When we ask why chance produces permanent effects, the natural answer which
escapes from our lips is that it is because of the independence of different
instants of time. A change having been made, there is no particular reason why
it should ever be unmade. If a man has won a napoleon at a gaming table he is
no more likely to lose it than he was to lose a napoleon at the outset. But we
have no sooner let slip the remark about the independence of the instants of
time than we are shocked by it. What can be less independent than the parts of
the continuum par excellence, through the spectacles of which we envisage every
other continuum? And although it may be said that continuity consists in a
binding together of things that are different and remain different, so that
they are in a measure dependent on one another and yet in a measure
independent, yet this is only true of finite parts of the continuum, not of the
ultimate elements nor even of the infinitesimal parts. Yet it undoubtedly is
true that the permanence of chance effects is due to the independence of the
instants of time. How are we to resolve this puzzle? The solution of it lies in
this, that time has a point of discontinuity at the present. This discontinuity
appears in one form in conservative actions where the actual instant differs
from all other instants absolutely, while those others only differ in degree;
and the same discontinuity appears in another form in all non-conservative
action, where the past is broken off from the future as it is in our
consciousness. Thus, although the other instants of time are not independent of
one another, independence does appear at the actual instant. It is not an
utter, complete independence, but it is absolute independence in certain
respects. Perhaps all fortuitous distribution originates from a fortuitous
distribution of events in time; and this alone has no other explanation than
the Law of Sufficient Reason, that is, is an absolute First. It is a truth well
worthy of rumination that all the intellectual development of man rests upon
the circumstance that all our action is subject to error. Errare est humanum is
of all commonplaces the most familiar. Inanimate things do not err at all; and
the lower animals very little. Instinct is all but unerring; but reason in all
vitally important matters is a treacherous guide. This tendency to error, when
you put it under the microscope of reflection, is seen to consist of fortuitous
variations of our actions in time. But it is apt to escape our attention that
on such fortuitous variation our intellect is nourished and grows. For without
such fortuitous variation, habit-taking would be impossible; and intellect
consists in a plasticity of habit.
What is time? Shall we say that it is the form under which the law of
logical dependence presents itself to intuition? But what is logical dependence
objectively considered? It is nothing but a necessitation which, instead of
being brute, is governed by law. Our hypothesis therefore amounts to this, that
time is the form under which logic presents itself to objective intuition; and
the signification of the discontinuity at the actual instant is that here new
premisses, not logically derived by Firsts, are introduced. (CP 6.85-7)
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