Table Of ContentPROBABILITY
AND SCIENTIFIC
INFERENCE
1
PROBABILITY
AND SCIENTIFIC
INFERENCE
G. SPENCER BROWN
Research Lecturer of Christ Church, Oxford
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First published 1957
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PREFACE
Philosophers arc sometimes thought to engage themselves
in hair-splitting activities with no other purpose than to
exercise the disciplines needed to perform them. It is not
always suspected that the most prized advancements in
scientific and other knowledge come through the application
of these disciplines. Briefly, to philosophize is to criticize
what is said in its relation to what is seen, and we should,
therefore, set about such criticism whenever we begin to
suspect that what we see is being distorted or occulted by
what we say.
A well-known example of word-made obscurity lies in the
concept of simultaneity fundamental to Newtonian mechanics.
Einstein’s mechanics begin, in the best tradition, with a destruc
tive analysis of this concept.
All concepts arc destructible and it is not always obvious
which to destroy. I have been concerned with the destruction
of one such concept which has, I believe, obscured and
occulted to a distressing extent certain facts of observation
which would otherwise have been clearly seen.
Some philosophers, struck with the recent discovery that
no one set of metaphysical assumptions is necessary to
communication, have fallen into the fallacy of thinking that
we can communicate without any metaphysics at all. I.ockc
fell into the same kind of error when he supposed that
because what he called primary qualities were dependent for
their perception upon no one sense, they were therefore
qualities which matter possessed independently of sense. It is
one of the greatest, if not the greatest, of discoveries in 2000
VI PK PFACli
years to have seen that no one system of metaphysics is neces
sary; but it is a simple mistake to suppose that none is.
What must be clone in the field of Probability is to replace
an old metaphysical system with a new one. This means
undertaking two tasks: first, to show where old assumptions
were inadequate; and then, to work out better ones. Each of
these tasks is a major one, and I do not think any purpose
would be served in attempting them both at once. An
advance in scientific theory depends ultimately upon carrying
forward informed opinion, and it is an ordinary biological
fact that opinion, however informed, cannot be carried through
too many stages at once.
The primary task of this book, therefore, has been one of
analysis; and though I have indicated how the synthesis must
follow, I have not completed it. That, if the opportunity be
given, will be my next task. But if anyone is impatient he has
only to follow me to the end of the book and lie will be ready
to make the synthesis himself.
I have been criticized for not publishing before now my
v evidence from random number counts. This delay occurred
first because of illness, after which I gave priority to the task
of discovering why certain things had happened rather than to
the task of trying to convince people at this stage that they
had happened. I hope my colleagues will forgive this slight
departure from current practice. But I should, in defence,
point out that my claim, first published in 1953, was a scientific
prediction and therefore public property. It has since then
been open to verification or falsification by anyone willing to
spend a few weeks counting. Perhaps one of the fruits of the
initial withholding of the details was the subsequent striking
confirmation of the prediction by a relatively hostile observer.
PREFACE Vil
When I answered Mr Oratn’s paper I still envisaged
publishing the results of my counts on the Tippett,.tables. I
don’t think I shall do this now, for, though they arc in some
ways more striking than the rest, I do not feel, now that we
know why such results occur, that it is necessary to establish
by repetition of similar instances that they occur. In any case,
observations by independent observers should carry more
weight than my own.
Anyone who has worked with chance machines knows
very well how difficult it is not to observe certain oddities
in their behaviour; it is only that classical probability, not
having a place for them, has always prevented our talking
about these oddities in terms of chance. The fact that the
machine does something noticeably improbable has not been
connected with the fact that it logically cannot do anything else.
I am grateful to many friends for their help in making this
book. Some of these'I have already thanked in the text, but
there are others, perhaps not mentioned there, to whom I am
equally grateful; to Sir Ronald Fisher for his early encourage
ment, and to Professor A. C. Hardy for enabling me to begin
work on this thesis in his Department; to Mrs Eileen J.
Garrett of the Parapsychology Foundation Incorporated, and
Mrs K. M. Goldncy of the Society for Psychical Research, for
their generous practical help despite the gradual divergence
of my opinions from the tradition of their field; to Mr Robin
Farquharson and to my supervisor, Mr W. C. Kncalc, with
whom many of the ideas here presented were first discussed
and clarified; to Dr Handel Davies and Mr Garry Arnott for
checking some of the algebra; to the Rev. Dr Eric Mascall
and Mr R. II. Dundas for kindly reading the proofs; and to
Mr John Howard Barton for making the index.
Vlll PREFACE
I should like, finally, to thank the Governing Body of
Christ Church whose patronage has enabled me to put
together and publish the work I have done.
G. S. B.
Oxford, Dcccmber"i956
Acknowledgements '
The thesis in Chapter X was originally given in a paper to
the Mathematical and Psychological Sections of the British
Association in September 1954. I am grateful to the organizers
for encouraging me to present it in a publishable form. The
gist of Chapter XIV is taken from a paper read to the Third
London Symposium on Information Theory and published
by Messrs. Butterworth & Co. (Publishers) Ltd. whose
permission to re-present the argument here I acknowledge
with thanks. I also acknowledge with thanks the permission
of the Editor of the Journal of the Society for Psychical Research
and Mr A. T. Oram to reproduce the paper ‘An Experiment
with Random Numbers’ and subsequent correspondence.
CONTENTS
CMAPT1 1R PAGE
I 'The Real World I
II Worlds and Alodels
5
III The Classical Problem 15
IV Dissolution of the Classical Problem 20
V Truth 26
VI Measuring Probability
32
VII Probability as an Indicator 35
VIII. The Random Series
43
IX The Paradoxes o f Probability
57
X Critical Series 67
XI Bias and Stretch 82
XII Bernoulli’s Theorem 88
XIII Some Practical Considerations 92
XIV The Chance Machine 100
XV The Diminishing Field 106
Appendix I On Miracles 109
Appendix II On Practice T 13
Commentary 136
Index 151
IX
