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Where the classical logic spoke of major and minor premises without establishing any really important difference between the two, Peirce draws a distinction between the premises and the guiding principle of our argument. All reasoning is from some concrete situation to another. The propositions which represent the first are the premises in the strict sense of the word. But the feeling that certain conclusions follow from these premises is conditioned by an implicit or explicit belief in some guiding principle which connects the premises and the conclusions. When such a leading principle results in true conclusions in all cases of true premises, we have logical deduction of the orthodox type. If, however, such a principle brings about a true conclusion only in a certain proportion of cases, then we have probability.

This reduction of probability to the relative frequency of true propositions in a class of propositions, was suggested to Peirce by Venn’s Logic of Chance. Peirce uses it to establish some truths of greatest importance to logic and philosophy.