Deductive or Syllogistic Inference, from universal to particular, e.g.
In this syllogistic analysis two points must always be considered: one, that we usually use premises in thought which we do not express; and the other, that we sometimes use them unconsciously, and therefore infer and reason unconsciously, in the manner excellently described by Zeller in his Vortrage, iii.
But even the normal proposition in the syllogistic form tertii adjacentis, with subject, predicate and copula, is seldom a complete expression of the judgment.
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.
The aim of his logic is represented as having been the devising of rules for the discovery of syllogistic middle terms; this system for aiding slow-witted persons became known as the pons asinorum.
Sophistry appeared to him to be like it, except that it is a fallacious deduction either from merely apparent probabilities in its matter or itself merely apparently syllogistic in its form (cf.
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.
He had been bred by his father in a great veneration for the syllogistic logic as an antidote against confused thinking.
But it is often thought without being expressed, and to judge the syllogism by its mere explicit expression is to commit an ignoratio elenchi; for it has been known all along that we express less than we think, and the very purpose of syllogistic logic is to analyse the whole thought necessary to the conclusion.
Luckily, or, to speak with a reverence proper to the occasion, providentially, mankind are not disposed to embark the blessings they enjoy on a voyage of syllogistic adventure to obtain something more beautiful in exchange.