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.
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.
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