See R. Harré on Pierre Simon de Laplace (1749-1827)
(from Paul Edwards (ed), Encyclopedia of Philosophy, Macmillan,
1967)
Summary
It seemed to Laplace that there
was no phenomenon that the improved and polished Newtonian physics was
incapable of handling. He came to regard the enormous explanatory
power of the system as practically a demonstration of its truth.
New observations would only confirm it further, he thought, and their consequences
were as certain as if they had already been observed. What had produced
this remarkable confidence was a series of complete successes. Newton
had never been convinced of the stability of the solar system, which he
suggested might need divine correction from time to time.
go back to summary
Laplace showed, in effect, that every known
secular variation, such as the changing speeds of Saturn and Jupiter, was
cyclic and that the system was indeed entirely stable and required no divine
maintenance. (It was this triumph that occasioned his celebrated
reply to Napoleon's query about the absence of God from the theory; Laplace
said that he had no need of that hypothesis.) He also completed the
theory of the tides and solved another of Newton's famous problems, the
deduction from first principles of the velocity of sound in air.
Laplace added a very accurately estimated correction for the heating effect
produced by rapidity of the oscillation, which was too short to allow the
heat of compression to be dissipated.
go back to summary
Determinism and probability
Not only was Laplace confident of the Newtonian theory,
but he was also greatly struck by its determinist nature. Where one
could gather accurate information about initial conditions, later states
of a mechanical system could be deduced with both precision and certainty.
The only obstacle to his complete knowledge of the world was ignorance
of initial conditions. Laplace's confidence in Newtonian theory is
exemplified in the introduction this Philosophical Essay on Probabilities,
in which he envisaged a superhuman intelligence capable of grasping both
the position at any time of every particle in the universe and all the
forces acting upon it. For such an intelligence "nothing would be
uncertain and the future, as the past, would be present to its eyes.
The human mind offers, in the perfection which it has been able to give
to astronomy, a feeble idea of this intelligence" (Philosophical Essay,
p. 4). But this ideal is difficult to attain, since we are frequently
ignorant of initial conditions. The way to cope with the actual world,
Laplace thought, is to use the theory of probability. The superhuman
intelligence would have no need of a theory of probability. Laplace
would have regarded as ridiculous the idea that there could be systems
that would react to stimuli in only more or less probable ways. He
said, "The curve described by a simple molecule of air or vapor is regulated
in a manner just as certain as the planetary orbits; the only difference
between them is that which comes from our ignorance" (ibid., p. 6).
He then defined a measure of probability as follows:
The theory of chance consists in reducing all the events of the same
kind to a certain number of cases equally possible ... and in determining
the number of cases favorable to the event whose probability is sought.
The ratio of this number to that of all the cases possible is the measure
of this probability, which is thus simply a fraction whose numerator is
the number of favourable cases and whose denominator is the number of all
the cases possible. (Ibid., p. 6).
This is the definition of probability known today as the proportion of
alternatives. Then as now, it involves the very tricky notion of
equipossible cases. Laplace deals with this notion by glossing equipossible
cases as those that "we may be equally undecided about in regard to their
existence" (ibid., p. 6).
This account does have its difficulties. Equal
indecision is not at all easy to determine and may, in the end, hinge upon
states of mind quite irrelevant to a sound estimate of probabilities.
Throughout his study of probability Laplace refers to such subjective factors
as honesty, good judgment and absence of prejudice, which are required
in using probability theory. However, he does give a much sounder
criterion for its practice; it encourages one to reckon as equally possible
those kinds of events instances of which we have no special reason to believe
will occur. Equality of ignorance then becomes his criterion for
equality of possibility. Laplace is quite happy about this, since
he believed - perhaps rightly - that the proper occasion for the recourse
to probability is ignorance of the initial conditions, the relevant theory,
or both. Actual estimates of probability are made statistically.
In his practical examples he appears to depend on a further distinction,
which also seems correct. It is the distinction between the meaning
of the statement of probability for a certain kind of event (that is,ratio
of number of favorable to equipossible kinds of events) and the usual estimate
of this probability, which is the relative frequency of actual events of
the kind under consideration among all appropriate cases.
GO BACK TO THE MAIN PAGE
ON CHANCE