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.
The form of exposition is that of dialogue; the method of reasoning is the syllogistic. The leading thoughts are the following.
Each inference contains three terms. In syllogistic inference the subject of the conclusion is the minor term, and its predicate the major term, while between these two extremes the term common to the two premises is the middle term, and the premise containing the middle and major terms is the major premise, the premise containing the middle and minor terms the minor premise.
Deductive or Syllogistic. Every M is P S is M.
Moreover, he tended to confine the term X6yos to syllogistic inference.
But even the normal proposition in the syllogistic form tertii adjacentis, with subject, predicate and copula, is seldom a complete expression of the judgment.
Quasi-syllogisms. - Besides reconstructions of the syllogistic fabric, we find in recent logic attempts to extend the figures of the syllogism beyond the syllogistic rules.
Here there is no syllogistic fallacy in the premises; but the question is what syllogistic conclusion can be drawn, and there is only one which follows without an illicit process of the minor, namely, " Some metals are fusible."
We do not mean that in Wundt's supposed " inferences of relation by comparison and connexion" the premises are of no further use; but those of the first kind are of no syllogistic use in the second figure, and those of the second kind of no syllogistic use beyond particular conclusions in the third figure.
It is the same with all the recent attempts to extend the syllogism beyond its rules, which are not liable to exceptions, because they follow from the nature of syllogistic inference from universal to particular.
When A, B and C are objects of sense, their relative positions are matters, not of inference, but of observation; when they are not, there is an inference, but a syllogistic inference with a major premise, induced from previous observations, " whenever of three things the first is to the right of the second, and the second to the right of the third, the first is to the right of the third."
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.
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.
It is comprised 3 in an early essay on the mistaken subtlety of the syllogistic figures, and a late compilation by a pupil from the introductory matter and ' Nouveaux essais, iv.
His name is perhaps best known in the history of logic in connexion with the fourth syllogistic figure, the first distinct statement of which was ascribed to him by Averroes.
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.
A fortiori arguments, for example, wherein relations of quantity are brought together, though syllogistic in type, are generally excluded.
Owing largely to the simplicity and symmetry of the syllogism it has been a commonplace of logic to make the syllogistic form the type of all thought.
Die falsche Spitzfindigkeii der vier syllogistischen Figuren, " The False Subtlety of the Four Syllogistic Figures" (trans.
The tract on the False Subtlety of the Four Syllogistic Figures, in which the view of thought or reason as analytic is clearly expressed, closes with the significant division of judgments into those which rest upon the logical axioms of identity and contradiction and those for which no logical ground can be shown.
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.
The rules which govern syllogistic arguments thus described are: i.
- Finally it is necessary to mention a complex syllogistic argument known as the Sorites (Gr.
Discussions of the syllogism will be found in all textbooks on Logic, and the more elaborate syllogistic forms are discussed in the article Logic.