[1] Read Mill, ch. iv. (Bk. I.), on Propositions; Venn, Empirical Logic, ch. ix., x. Cf. Knowledge and Reality pp. 57-8; and Venn, p. 264. Ordinary statement, Jevons, p. 60, ff.; cf. p. 163.
Why we need an arrangement
(a) If we attended purely to the propositions in common use, we should get an unmanageable variety of forms, though the reality of thought would be fairly represented. We cannot quite do this; we must try to select the forms which for some reason are the most fundamental and constant.
On the other hand, it is possible to think simply of what is convenient in logical combination; and then for working with syllogistic Logic we get the well-known scheme of four propositions, each with Subject and Predicate; and for working with symbolic Logic we get the existential scheme in which Subject and Predicate disappear, and “All S. are P.” turns into “There exists no S. which is not P.”; or we get Jevons’ Equational Logic, in which “All A is B” stands as A = AB. Now every Judgment has a great many aspects, {113} being really a very complex systematic act of mind, and a logical method can be founded on any of these aspects which is sufficiently constant to stand for the Judgment. You can take “All men are mortal” to mean “There are no not-mortal men,” or “Men = some mortals,” or two or three more meanings. The two former are artificial or formal corollaries from the natural Judgment, representing it for some purposes but omitting a great part of its natural meaning. They tell you nothing about a relation of causality between the content of man and the property mortal, and they destroy all implication of existence in the Subject man.
What we want is neither to follow mere everyday language, nor be guided by mere convenience of logical combination. We want to look at the Judgment on its merits with reference to its power of expressing the principal kinds of our experience, which in fact are constructed in the medium of Judgment. The great kingdoms of intellectual experience are Perception, History, and Science, and of these three, Science, including Philosophy, is the form towards which all knowledge presses on, and its judgment must therefore be considered as the most complete type.
The common scheme
(b) With this purpose in mind, let us look at the traditional scheme, omitting the negative Judgments of which we have not yet spoken. We may dismiss the Indefinite Judgment “Men are mortal” as imperfect by not being “quantified,” and we have left, as Categorical Judgments, the Particular Affirmative “Some men are mortal,” the Universal Affirmative “All men are mortal,” and the Singular Affirmative “Socrates is mortal.” The Singular Affirmative, however, is not treated of any further under the old scheme, {114} because in it the Subject is taken in its full extent, and therefore the Singular Affirmative Judgment is ranked with the Universal Affirmative. So as Categorical Judgments we have left the Particular Affirmative and the Universal Affirmative.
Outside the account of the Categorical Judgment we find the Hypothetical and Disjunctive Judgments touched on as a sort of Appendix, standing as “Conditional.” The historical reason of this is, that they were not recognised by Aristotle, and have never been incorporated in the diagram of judgments employed in traditional Logic. Then on the ordinary scheme we have—
Categorical. Conditional.
Particular Universal Hypothetical Disjunctive
Judgments. Judgments, Judgments.
including
Singular
Judgments.