"Logical knowledge" can be understood in two ways: as knowledge of the laws of logic and as knowledge derived by means of deductive reasoning. Most of the following is concerned with the first of these interpretations; the second will be treated briefly at the end. Furthermore, only deductive logic will be treated: As yet, there is no set of laws of inductive logic enjoying the kind of consensus acceptance accorded to deductive logic.

To begin with, we must specify what is a law of logic—not an entirely straightforward task. There are three, not all mutually exclusive, conceptions of logic laws. First, one could take them to be valid schemata (of statements), such as the familiar law of excluded middle, "p or not p". A second conception is that they are valid rules of inference, such as the familiar modus ponens—that is, from "p→q...