The author began by defining probability as being that state of mind in which we are inclined to believe a proposition, without being absolutely convinced that it is true. Objectively, every proposition is either true or false; subjectively, it may be certainly true, probable, or impossible.

The measure of probability he shewed to be the same as the measure of the cause producing it; that is, the ratio of the reasons inclining us to believe a proposition, to the whole number of reasons bearing upon it, whether for or against; all of which reasons are founded, either upon necessary inference from experience, or from testimony.