CHAPTER II.

THE THEORY OF PREDICATION AND THE IMPORT OF

PROPOSITIONS.

§ 1. WHAT is the import or meaning of a proposition or predication? What is the thought or fact expressed by it? What is the signification of its subject, of its predicate, and of its copula? In other words, in all propositions or predications of the type "A is B" (or "A is not B"), what is A, what is B, and what is the relation between them? A consistent answer to this question is a theory of Predication and of the import of Propositions. On this most important subject, there is great difference of opinion among logicians. It is proposed to give here an account of their views, as far as possible, in their own language and from their own point of view.

§ 2. I. The natural view seems to be that 'B' is an attribute, and that this attribute is referred or said to belong to the objects denoted by 'A,' as in the proposition 'Snow is white,' 'whiteness' is said to belong to the thing called 'snow.' This view is thus explained and defended by Dr James Martineau : "In saying 'Birds are warm-blooded,' we neither think of class within class, nor of attribute within attribute: the word 'warmblooded' represents to us no conception of a genus; it is not a name, but a mere attributive. The word 'birds' expresses to us no attribute, as such; it is not a mere attributive, but a name. The term in the predicate acts upon the mind by its connotation, or in its comprehension; the term in the subject, by its denotation or in its extension; and the foregoing sentence has its

import in this,—that we refer the attribute 'warm-blood' to the class of objects 'birds.' Hence it is that, while a purely connotative word (an adjective) is all that is required in the predicate, a denotative term is indispensable in the subject.......The mind predicates nothing except about substantive objects of thought; and of them (in the class of propositions now under consideration) it predicates nothing but attributes1." According to Dr Martineau, the Denotative or Class Theory of Predication and Mill's Connotative Theory are both psychologically false.

All propositions do not, according to Dr Martineau, express the relation of substance and attribute. There are classes of propositions which express other relations. "The notion of substance and attribute, with the relations of genera and species to which it introduces us, is but one......of several categories of thought." "It is the basis of all class-reasoning, and supplies the common logical canon of necessity, that 'what is true of the containing is true of the contained.”” But all Demonstrative Reasoning should not be forced into this single type. There are other types of Demonstrative Reasoning founded upon other relations expressed by propositions. Propositions may, for example, express the relations of time and space, of cause and effect, of resemblance and difference, and give rise to types of Demonstrative Reasoning quite distinct from that of classreasoning. "The attempt," says Martineau, "to coerce all reasoning into this single type-comprehensive as it is-appears to us arbitrary in itself, and precluded from success except on condition of much violent psychology. The ideas of space and time, of cause and effect, of resemblance and difference, seem to involve distinct laws of thought, to create for themselves special elements and functions of language, and to require separate canons of Logic."

According to Martineau, therefore, there are different classes of propositions expressing different categories of thought, and there are as many distinct types of Demonstrative Reasoning as

1 Essays, Vol. I. p. 351.

there are fundamental laws of thought arising from these categories.

§ 3. II. Hamilton's view :—

"To judge is to recognize the relation of congruence or of confliction, in which two concepts, two individual things, or a concept and an individual, compared together, stand to each other. This recognition considered as an internal consciousness, is called a Judgment, considered as expressed in language, it is called a Proposition or Predication." This definition is then explained. "When two or more thoughts are given in consciousness, there is in general an endeavour on our part to discover in them and to develop a relation of congruence or of confliction, that is, we endeavour to find out whether these thoughts will or will not coincide,—may or may not be blended into one; if they coincide, we judge, we enounce their congruence or compatibility: if they do not coincide, we judge, we enounce their confliction or incompatibility. Thus, if we compare the thoughts, water, iron, and rusting, we find them congruent, and connect them into a single thought, thus, water rusts iron; in that case we form a judgment1." Hamilton finally defines a judgment as follows: "We may, therefore, articulately define a judgment or proposition to be the product of that act in which we pronounce that of two notions thought as subject and as predicate, the one does or does not constitute a part of the other, either in the quantity of extension, or in the quantity of comprehension ?"

According to Hamilton, therefore, 'A' and 'B' in the typical judgment 'A is B' are two concepts, the one forming a part of the other. From what he says elsewhere, we know he maintains that in the quantity of comprehension, 'B' is a part of 'A,' and that in the quantity of extension, 'A' is a part of 'B.' That is, the proposition has a two-fold meaning according as you take the two concepts 'A' and 'B' in their comprehension or in their extension. When 'A' and 'B' are taken in their comprehension, the meaning of the proposition is that the elementary notions constituting the concept 'B' are a part of those constituting the 1 Hamilton's Lectures, Vol. III. pp. 226—7. 2 Ibid. p. 229.

concept 'A'; and when they are taken in extension, the meaning is that the individual things or objects included in the extension of 'A' are a part of those included in the extension of 'B.'

§ 4. III. Mansel's view :

"When I assert that A is B, I do not mean that the attributes constituting the concept A are identical with those constituting the concept B; for this is only true in identical judgments; but that the object in which the one set of attributes is found is the same as that in which the other set is found." For example, "when I assert that the rose is fragrant, I imply that the thing which affects in a certain manner my power of sight, is in some manner identical with that which affects in a certain way my power of smell." Mansel thus defines a concept and a judgment: "A concept is a collection of attributes united by a sign, and representing a possible object of intuition.” “A judgment is a combination of two concepts, related to one or more common objects of possible intuition." "The subjects of all logical judgments which are to be distinguished from the psychological, such as the spontaneous judgments of perceptive and imaginative faculties, are concepts 1."

According to Mansel, therefore, 'A' and 'B' are both concepts, and the meaning of the proposition (when not identical) is that the attributes signified by both 'A' and 'B' exist in the same object or objects.

§ 5. IV. Ueberweg's view:—

"The judgment is the consciousness of the objective validity of a subjective union of conceptions, whose forms are different, but belong to each other. It is the consciousness, whether or not the analogous combination exists between the corresponding objective elements. As the individual conception corresponds to the individual existence, so the judgment in its various forms corresponds to, and is the subjective copy of, the various objective relations. A judgment expressed in words is an assertion or proposition 2."

1 Prolegomena Logica, 2nd edition, 1860, pp. 67-69.

2 Ueberweg's Logic, p. 187.

According to Ueberweg, therefore, 'A' and 'B' are two conceptions or concepts, and the meaning of the judgment 'A is B' is that, corresponding to the union of the two concepts, there is an objective union. In other words, a mere combination of conceptions is not a judgment; but there must be the conviction that the combination has objective validity.

§ 6. V. Mill thus states the problem to be solved :—

"We have, then, to inquire, on the present occasion, not into judgment, but judgments; not into the act of believing, but into the thing believed. What is the immediate object of belief in a proposition? What is the matter of fact signified by it? What is it to which, when I assert the proposition, I give my assent, and I call upon others to give theirs? What is that which is expressed by the form of discourse called a proposition, and the conformity of which to fact constitutes the truth of the proposition1?"

§ 7. Mill declares at the outset that a proposition is not about our ideas or concepts of things, but about things themselves, and dismisses all the theories of predication which have our ideas or concepts for the subject and the predicate of the proposition, with the remark that "the notion that what is of primary importance to the logician in a proposition is the relation between the two ideas corresponding to the subject and predicate (instead of the relation between the two phenomena which they respectively express) seems to me one of the most fatal errors ever introduced into the philosophy of Logic, and the principal cause why the theory of the science has made such inconsiderable progress during the last two centuries 2." He then points out that Hobbes's theory that a predicate is a name of that of which the subject is a name, is a sufficient account when 'A' and 'B' are both proper names, but that it is inadequate for all propositions whose subject and predicate are not proper names, because it entirely overlooks the meaning of names in connotation.

1 Mill's Logic, Vol. 1. p. 99.

2 Ibid. p. 98.