ABSTRACT
The syllogism in all its figures belongs to Symbolic Logic, and would be the whole subject if all deduction were syllogistic, as the scholastic tradition supposed. It is from the recognition of asyllogistic inferences that modern Symbolic Logic, from Leibniz onward, has derived the motive to progress. Symbolic Logic is essentially concerned with inference in general, and is distinguished from various special branches of mathematics mainly by its generality. What symbolic logic does investigate is the general rules by which inferences are made, and it requires a classification of relations or propositions only in so far as these general rules introduce particular notions. The subject of Symbolic Logic consists of three parts, the calculus of propositions, the calculus of classes, and the calculus of relations. The propositional calculus is characterized by the fact that all its propositions have as hypothesis and as consequent the assertion of a material implication.
