parts, were discussed under the first part. Definition and division, as dependent on a knowledge of genus, species, and differentia, are also here treated under the second part of Logic, though they are ordinarily discussed under the first.

Note 2.-On the vexed, and somewhat subtle, question of the Import of Propositions, or, as it is sometimes called, the Theory of Predication, the student may be referred to Hobbes' Computation or Logic, ch. iii., Mr. Mill's Logic, bk. i., ch. 5, Mr. Mansel's Prolegomena Logica, ch. ii., Sir W. Hamilton's Lectures on Logic, Lects. viii. and xiii., and Mr. Mill's Examination of Sir W. Hamilton's Philosophy, ch. xviii. The view we should adopt may be briefly summarized as follows: wherever the predicate is a singular or collective term, or, though a common or abstract term, a synonym of the subject, the theory of Hobbes, that the predicate is a name of the same things of which the subject is a name, furnishes a sufficient account; in all other cases, Hobbes' theory is true, though insufficient, for, where the predicate is an attributive or an abstract term (not being a synonym), the predicate also asserts or denies certain attributes of the subject, and where it is a common term (not being a synonym), not only are certain attributes asserted or denied of the subject, but the latter is referred to or excluded from the group of individuals denoted by the predicate. From this it will be seen that we do not agree with Mr. Mill in regarding all predication (except when the predicate is a singular or collective term) as a predication merely of attributes.

CHAPTER VI.

On Verbal and Real Propositions.

AFFIRMATIVE propositions in which the subject is a common or abstract term may be divided into Verbal and Real. A verbal proposition expresses merely the connotation or part of the connotation of the term, a real proposition expresses either solely, or in conjunction with part of the connotation of the term, properties, accidents, or both. Thus a verbal proposition simply states what might be gathered from a due consideration of the name, as 'All men are rational,' 'All triangles are three-sided; whereas a real proposition imparts knowledge which could not be gathered from the name alone, as 'All triangles have the sum of their angles equal to two right angles,' 'Some men are black.'

Note.-The distinction between verbal and real propositions is otherwise expressed by that between Analytical and Synthetical judgments (Kant), Explicative and Ampliative judgments (Sir W. Hamilton and Abp. Thomson), Essential and Accidental propositions (the schoolmen). Tautologous propositions (All A is A), and propositions in which the predicate is a synonym of the subject (as e.g. 'Charity is love'), should be referred to the head of verbal propositions.

CHAPTER VII.

On Definitions.

A DEFINITION is an exposition of the connotation of a term. It may always be represented in the form of a proposition, of which the term defined forms the subject and the exposition the predicate1.

As a definition expounds or enumerates the attributes which a term implies, it is plain that singular and collective terms, inasmuch as they do not in themselves connote any attributes, are incapable of definition. They may, however, be described by means of the various common terms which are predicable of them, as well as by designations which are peculiar to themselves. Thus I may say 'John is a tall man of fair complexion, is by profession a London solicitor, and occupies such and such a house in Bedford-row.' This may be called a Description of a Singular or Collective Term, in order to distinguish it from the Description of a common term, which is noticed below, and which we shall call simply Description. Besides singular and collective terms, a term expressing a single attribute, which is incapable of analysis into other attributes, is incapable of definition. Thus it has been maintained that it is useless to attempt to define such terms as pleasure, pain, colour, thing, attribute, &c.

1 It is indifferent whether we speak of the entire proposition as the definition, or merely the exposition which forms the predicate; similarly in the case of a description.

In defining a term, it would of course be impossible, in every case, to state the definition in terms expressive of attributes which were themselves incapable of analysis, even if we were agreed as to what are terms of this character. The terms employed in the definition may therefore express groups of attributes, provided that, when taken together, they exhaust the connotation of the term defined. Thus each of the words 'rational' and 'animal' expresses a large group of attributes, but if, when taken together, they exhaust the connotation of the word 'man,' the definition may be accepted as legitimate.

In seeking to define a term, I invariably contrast it with some other term; often, when I imagine it to be difficult to exhaust the connotation, with a variety of rther terms, from which I seek to distinguish it. Thus in seeking to define 'monarchy,' I contrast it with other forms of government; in seeking to define 'triangle,' I contrast it not only with other rectilineal figures but with spherical triangles; in seeking to define 'light,' I contrast it with heat, sound, electricity, and other impalpable powers of nature. Now that portion of the definition

which is common to the term defined and to the other terms with which it has been compared is called the genus, the term defined standing to it in the relation of a species, as has already been explained; that portion which distinguishes the term defined from the terms with which it has been compared is called the differentia, or sometimes, when there is more than one distinguishing

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attribute, the differentiæ. Thus, if we were distinguishing rectilineal triangle from spherical triangle, 'threesided figure' would be the genus; if from other rectilineal figures, the genus would be rectilineal figure;' if from both spherical triangles and other rectilineal figures, the genus would be simply 'figure.' It will be observed that the genus is always expressed in the form of a common term, or of an abstract term which is used as a common term, and that it may be qualified by an attributive. This is the case even in defining abstract terms, as e. g. in the definitions, 'Justice is a virtue which respects our relations to other men in society,' Temperance is a virtue which respects the control of our own desires,' the genus is a virtue,' an abstract term which has come to be used as a common term.

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A Definition being an exposition of the meaning of a term, it is obvious that all definitions must be limited by the state of our knowledge at the time when we frame them. But some terms have been expressly framed or have been appropriated to express a small number of attributes. Such terms are monarchy, anarchy,

2 Some logicians simply use the word differentia' for the purpose of expressing the distinguishing attributes, whether one or many; others, as Aristotle, would in the latter case speak of the differentiæ.'

3 Whenever abstract terms are defined or divided, or occur as portions of definitions or divisions, they seem invariably to be treated as if they were common terms, and hence in the definitions of abstract terms, as in other definitions, the term defined may be regarded as a species; for the same reason, when an abstract term is divided, its relation to the dividing members may be described as that of genus to species.