12 - THE DEFINITIONS AND AXIOMS OF INFERENCE AND PROBABILITY

Summary

1. It is not necessary for the validity of what follows to decide in what manner the set of propositions is determined, which is fundamental to our universe of reference, or to make definite assumptions as to what propositions are included in the group which is specified by the data. When we are investigating an empirical problem, it will be natural to include the whole of our logical apparatus, the whole body, that is to say, of formal truths which are known to us, together with that part of our empirical knowledge which is relevant. But in the following formal developments, which are designed to display the logical rules of probability, we need only assume that our data always include those logical rules, of which the steps of our proofs are instances together with the axioms relating to probability which we shall enunciate.

The object of this and the chapters immediately following is to show that all the usually assumed conclusions in the fundamental logic of inference and probability follow rigorously from a few axioms, in accordance with the fundamental conceptions expounded in Part I. This body of axioms and theorems corresponds, I think, to what logicians have termed the laws of thought, when they have meant by this something narrower than the whole system of formal truth. But it goes beyond what has been usual, in dealing at the same time with the laws of probable, as well as of necessary, inference.