Frequencies and the Mathematics of Probability

Abstract

Of the many sorts of questions that can be asked of a specific piece of reasoning in natural science the following three may be distinguished: 1.Does it follow? That is, are the conclusions so related to the evidence (or premises) that they may be said necessarily to follow from them? This first question is independent of any question of truth or falsity. It is designed strictly in terms of what might be called consistency.2.Is it true? This usually comes to the question Are the premises true?, or, Are the data correct?, though it must be remembered that true conclusions can follow from false premises. For that reason we must distinguish questions about the truth of an argument from questions about the consistency of the same argument. Ptolemaic astronomy is consistent but false, and there are arguments in modern physics which, though they turn up answers that are true, are nevertheless formally inconsistent.We have had occasion to discuss all this before. But not much has been said about the following question:3.How is the truth of the premises established?