Philosophy

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The overwhelming majority of our decisions are
based not on demonstrable certainties but on an estimate of probabilities.
Judges, for instance, often remind juries that they should find the prisoner
guilty if his guilt has been established “beyond all
*reasonable* doubt” and they distinguish between
“beyond all *reasonable* doubt” and
“beyond *all possible* doubt.” If, for instance, Ned
Kelly is stopped by a policeman within a hundred yards of a house,
subsequently proved to have been burgled, and if Kelly’s bag
contains jewellery subsequently identified as the jewellery missing from
the burgled house, the prosecution would not be expected to demonstrate
the physical and logical impossibility of Kelly’s defence that the
bag had been dropped by the real burglar, who had taken fright and run,
and that Kelly had picked it up with a view to taking it to the nearest
police station. Kelly would be convicted in spite of the fact that no
*coercive* disproof of his story was possible. He would be
convicted because on the balance of probabilities the case for the
prosecution was incomparably more plausible than the case for the
defence.

*Arnold Lunn*

It is a commonplace to say that the substantial
inferences of science, as opposed to those of logic and mathematics, are
only *probable*—that is to say, when the premises are true
and the inference correct, the conclusion is only *likely* to be true.
It is therefore necessary to examine what is meant by
“probability.” It will be found that there are two different
concepts that may be meant. On the one hand, there is mathematical
probability: if a class has *n* members, and *m* of them have
a certain characteristic, the mathematical probability that an unspecified
member of this class will have the characteristic in question is
*m/n*. On the other hand, there is a wider and vaguer concept,
which I call “degree of credibility,” which is the amount
of credence that it is rational to assign to a more or less uncertain
proposition. Both kinds of probability are involved in stating the
principles of scientific inference.

Bertrand Russell

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