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On Purely Probabilistic Theories of Scientific Inference

Published online by Cambridge University Press:  14 March 2022

David G. Blair
David G. Blair*
Affiliation:
New South Wales Institute of Technology
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Abstract

This paper derives a mathematical expression giving the development of the probability of a scientific hypothesis with the number of confirming tests, as determined by Bayes's theorem, in a special case in which all the tests are “independent” of one another. The simple expression obtained shows clearly how the various factors influence the growth of the probability. The result is used to set a numerical lower bound on the probabilities representing the a priori beliefs of humans in generalizations that become accepted. By making a comparison with the predictions of a “logical atomic” model in the case of physical laws, it is argued that humans have significant a priori “knowledge” in a weak sense.

Type
Research Article
Information
Philosophy of Science , Volume 42 , Issue 3 , September 1975 , pp. 242 - 249
Copyright
Copyright © 1975 by the Philosophy of Science Association

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Footnotes

†

The work reported here was carried out while I was at the Royal Military College of Canada. I am grateful to Professor Wesley C. Salmon and Professor J. J. Russell for their encouragement and helpful comments.

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