ABSTRACT
The kind of deductive reasoning considered in the preceding sections may be described as qualitative deduction. It consists in the application of general propositions to certain cases or classes of cases which are of a certain kind, namely, of the kind referred to in the general propositions applied. Quantitative deduction is the commonest type of deduction in the exact sciences, but it is common enough even elsewhere. Syllogism is usually described at once as mediate inference and as deductive inference, and also as confined to propositions which express the relation of attribute to substance. If this conception were strictly adhered to, the term syllogism would coincide with only those mediate inferences which have a general middle term, or with relations which are reducible to those of identity or of difference. The general rules of the syllogism and the corollaries state what kind of premises, as regards quality and quantity, can or cannot justify a conclusion.
