UNIVERSITY OF DURHAM RIDDELL MEMORIAL LECTURES Eighteenth Series
SCIENCE, FAITH AND SOCIETY BY MICHAEL POLANYI GEOFFREY CUMBERLEGE
OXFORD UNIVERSITY PRESS LONDON 1946 CONTENTS L Science and Reality
.... 7 II. Authority and Conscience ... 28 III. Dedication or
Servitude ... 49 APPENDIX 1. Premisses of Science . . . . 71 2.
Significance of New Observations ... 75 3. Correspondence with
Observation . . 78 SCIENCE, FAITH AND SOCIETY I SHALL re-examine
here the suppositions underlying our belief in science and propose
to show that they are more extensive than is usually thought. They
will appear to co extend with the entire spiritual foundations of
man and to go to the very root of his social existence. Hence, I
will urge, our belief in science should be regarded as a token of
much wider convictions. I SCIENCE AND REALITY What is the nature of
science Given any amount of experience, can scientific propositions
be derived from it by the application of some explicit rules of
procedure Let us limit ourselves for the sake of simplicity to the
exact sciences and conveniently assume that all relevant experience
is given us in the form of numerical measurements so that we are
presented with a list of figures representing positions, masses,
times, velocities, wavelengths, etc., from which we have to derive
some mathematical law of nature. Could we do that by the
application of definite operations Certainly not. Granted for the
sake of argument that we could discover somehow which of the
figures can be connected so that one group determines the other
there would be an infinite number of mathematical functions
available for the representation of the former in terms of the
latter. There are many formsof mathematical series such as power
series, harmonic series, etc. each of which can be used in an
infinite variety of fashions to approxi mate the existing
relationship between any given set of numeri cal data to any
desired degree. Never yet has a definite rule been laid down by
which any particular mathematical function can be recognized, among
the infinite number of those offering themselves for choice, as the
one which expresses a natural law. It is true that each of the
infinite number of available functions will, in general, lead to a
different prediction when 8 SCIENCE, FAITH AND SOCIETY applied to
new observations, but this does not provide the requisite test for
making a selection among them. If we pick out those which predict
rightly, we still have an infinite number on our hands. The
situation is in fact only changed by the addition of a few more
data namely, the predicted data to those from which we had
originally started. We are not brought appreciably nearer towards
definitely selecting any particular function from the infinite
number of those available. Now, I am not suggesting that it is
impossible to find natural laws but only that this is not done, and
cannot be done, by applying some explicitly known operation to the
given evidence of measurements. And to bring my argument a little
closer to the actual experience of science, I shall now restate it
as follows. We ask Could a mathematical function connecting
observable instrument readings ever constitute what we are
accustomed to regard as a natural law in science For example, if we
were to state our knowledge concerning the path of a planet in
these terms That setting certain telescopes at certain angles at
certaintimes a luminous disc of a certain size will be observed
does that properly express a natural law of planetary motion No it
is obvious that such a prediction is not equiva lent to a
proposition concerning planetary motion...
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