Deductive or Syllogistic Inference, from universal to particular, e.g.
Thus, 1 - x would represent the operation of selecting all things in the world except horned things, that is, all not horned things, and (1 - x) (1 - y) would give us all things neither horned nor sheep. By the use of such symbols propositions could be reduced to the form of equations, and the syllogistic conclusion from two premises was obtained by eliminating the middle term according to ordinary algebraic rules.
He had been bred by his father in a great veneration for the syllogistic logic as an antidote against confused thinking.
In his Westminster review of Whately's Logic in 1828 (invaluable to all students of the genesis of Mill's logic) he appears, curiously enough, as an ardent and brilliant champion of the syllogistic logic against highfliers such as the Scottish philosophers who talk of "superseding" it by "a supposed system of inductive logic."
Judgment is completed in the syllogism; the syllogistic form as the perfection of subjective thought passes into objectivity, where it first appears embodied in a mechanical system; and the teleological object, in which the members are as means and end, leads up to the idea of life, where the end is means and means end indissolubly till death.