1. The theory of probability deals with the relation between two sets of propositions, such that, if the first set is known to be true, the second can be known with the appropriate degree of probability by argument from the first. The relation, however, also exists when the first set is not known to be true and is hypothetical.

In a symbolical treatment of the subject it is important that we should be free to consider hypothetical premisses, and to take account of relations of probability as existing between any pair of sets of propositions, whether or not the premiss is actually part of knowledge. But in acting thus we must be careful to avoid two possible sources of error.

2. The first is that which is liable to arise wherever variables are concerned. This was mentioned in passing in § 18 of chapter 4. We must remember that whenever we substitute for a variable some particular value of it, this may so affect the relevant evidence as to modify the probability. This danger is always present except where, as in the first half of chapter 13, the conclusions respecting the variable are certain.

3. The second difficulty is of a different character. Our premisses may be hypothetical and not actually the subject of knowledge. But must they not be possible subjects of knowledge?