151. Explain precisely how it is that O admits of ordinary conversion if the principle of the quantification of the predicate is adopted, although not otherwise. [K.]
152. Draw out a table, corresponding to the ordinary Aristotelian table of opposition, for the six propositions, A, Y, E, I, η, O (some being interpreted in the sense of some at least). [K.]
CHAPTER VIII.
THE EXISTENTIAL IMPORT OF CATEGORICAL PROPOSITIONS.[212]
[212] It will be advisable for students, on a first reading, to omit this chapter.
153. Existence and the Universe of Discourse.—It has been shew in section [49] that every judgment involves an objective reference, or—as it may otherwise be expressed—a reference to some system of reality distinct from the act of judgment itself. The reference may be to the total system of reality without limitation, or it may be to some particular aspect or portion of that system. Whatever it may be, we may speak of it as the universe of discourse.[213] The universe of discourse may be limited in various ways; for example, to physical objects, or to psychical events, or again with reference to time or space. But in all cases it is a universe of reality in the sense in which that term has been used in section [49]. The nature of the reference in propositions relating to fictitious objects, for example, to the characters and occurrences in a play or a novel, may be specially considered. We may say that in a case of this kind the universe of discourse consists of a series of statements about persons and events made by a certain author; and it is clear that such statements have objective reality, although the persons and events themselves are fictitious. It follows that, as regards 211 the reference to reality, such a proposition as “Hamlet killed Polonius” must be considered elliptical. For the reference is not to real persons or to the actual course of events in the past history of the world, as it is when we say “Mary Stuart was beheaded,” but to a series of descriptions given by Shakespeare in a particular play. These descriptions have, however, a reality of their own, and (the different nature of the reference being clearly understood) I am no more free to say that Hamlet did not kill Polonius (that is, that Shakespeare did not describe Hamlet as killing Polonius) than I am to say that Mary Stuart was not beheaded.
[213] “The universe of discourse is sometimes limited to a small portion of the actual universe of things, and is sometimes co-extensive with that universe” (Boole, Laws of Thought, p. 166). On the conception of a limited universe of discourse, compare also De Morgan, Syllabus of a Proposed System of Logic, §§ 122, 3, and Formal Logic, p. 55; Venn, Symbolic Logic, pp. 127, 8; and Jevons, Principles of Science, chapter 3, § 4.
The substance of the above has been expressed by saying that reality is the ultimate subject of every proposition. Every proposition makes an affirmation about a certain universe of discourse, and the universe of discourse (whatever it may be) has some real content. In this sense then every proposition has an existent subject.[214] A further question may, however, be raised, namely, whether—using the word “subject” in its ordinary logical signification—all or any propositions should be interpreted as implying the existence (or occurrence) of their subjects within the universe of discourse (or particular portion of reality) to which reference is made. It is mainly with this problem, and the ways in which ordinary logical doctrines are affected by its solution, that we shall be concerned in the present chapter.
[214] Compare Bradley, Principles of Logic, p. 41.