any

verbal analysis". But ideas, in this sense, have no connection with logical definition. Locke's ideas of sensation, simple or complex, are all excluded from the province of definition, as being individuals, i. e. as not being concepts at all. On the other hand, the concept whiteness, as a species of colour, is capable of definition by its optical differentia, as a colour produced by equal mixture of the simple rays. An example adduced by Descartes, as well as by Locke and Leibnitz, will illustrate the distinction still more clearly. The concept of a chiliogon is a regular polygon of 1000 sides. As addressed to the sense, this definition would not enable any man to distinguish an individual figure of the kind by sight from another which had 999 sides; but, as addressed to the understanding, it is sufficient for the demonstration of the mathematical properties of the figure. This is one example, among many that might be adduced, of the confusion that has arisen from the vague and vacillating employment in modern philosophy of the term Idea.

The same distinction will furnish a ground for criticising certain popular systems of logical notation. If Logic is exclusively concerned with Thought, and Thought is exclusively concerned with Concepts, it is impossible to approve of a practice, sanctioned by some eminent Logicians,

P Arist. Anal. Post. II. 7. οὐ γὰρ δὴ δείξει γε τῇ αἰσθήσει ἢ τῷ dakrúλ. Cf. Mill's Logic, vol. i. p. 183.

in a

of representing the relation of terms in a syllogism by that of figures in a diagram. To illustrate, for example, the position of the terms in Barbara, by a diagram of three circles, one within another, is to lose sight of the distinctive mark of a concept, that it cannot be presented to the sense, and tends to confuse the mental inclusion of one notion in the sphere of another, with the local inclusion of a smaller portion of space larger. The diagrams of Geometry in this respect furnish no precedent; for they do not illustrate the form of the thought, but the matter, not the general character of the demonstration as a reasoning process, but its special application as a reasoning about magnitudes in space. Still less is such a practice justified by the test of conceivability which has been mentioned above, the possibility, namely, of individualizing the attributes comprehended in a concept. For, whereas

q "Da der Mensch die Sprache hat," says Hegel, "als das der Vernunft eigenthümliche Bezeichnungsmittel, so ist es ein müssiger Einfall, sich nach einer unvollkommnern Darstellungsweise umsehen und damit quälen zu wollen. Der Begriff kann als solcher wesentlich nur mit dem Geiste aufgefasst werden. Es ist vergeblich, ihn durch Raumfiguren und algebraische Zeichen zum Behufe des ausserlichen Auges und einer begrifflosen, mechanischen Behandlungsweise, eines Calculs, festhalten zu wollen." While dissenting totally from the Hegelian view of Logic, I cannot resist quoting the above passage, as applicable to every view of the Science which recognises the essential distinction between thought and intuition.

that test is employed to determine the conceivability of the actual contents of each separate concept, the logical diagrams are designed to represent the universal relations in which all concepts, whatever be their several contents, formally stand towards each other. The contrast between these two, as legitimate and illegitimate appeals to intuition, will more fully appear in the sequel.

CHAP. II.

ON THE THREE OPERATIONS OF THOUGHT.

CONCERNING the threefold division of the mental operations usually acknowledged by Logicians, it has been questioned, whether they are properly to be regarded as distinct acts of Thought or not. The question may be considerably simplified, by discriminating between different principles of identity or distinctness, as applicable severally to mental and material objects. The only natural and necessary principle of distinction between objects is the numerical diversity of individuals. In this respect, not only the several acts of Simple Apprehension, Judgment, and Reasoning, but every single act of each class is distinct from every other. An act of reasoning which I perform today is numerically distinct from any act performed yesterday, though both may be governed by the same laws and applied to the same objects. Beyond this, any principle of specific identity or diversity is to a certain extent arbitrary and artificial. The only ground of distinction between a natural and an unnatural classification of individuals depends upon the frequency with which

E

we have occasion to view them in this or that relation; in other words, on the respective utility of different points of view for certain given purposes. On this ground, Apprehension, Judgment, and Reasoning are rightly and necessarily regarded as distinct classes of mental operations, relatively to Logic, inasmuch as their several products, the Concept, the Judgment, and the Syllogism, exhibit distinct logical forms, and require a distinct logical treatment.

Psychologically, the question must be examined on somewhat different grounds. It may be urged, for example, on the one side, that the several operations are the product of the single faculty of Comparison; that they are not in act ever separable from each other, Apprehension being always accompanied by Judgment, and Judgment by Apprehension, and Reasoning by both; that the mind, one and indivisible, is wholly employed in each. On the other side, it may be answered, that acts of Comparison may be regarded as specifically distinct, as engaged on distinct objects; that the comparison of attributes with each other, of concepts, immediately in themselves, or mediately with a common third concept, are pro tanto distinct acts, requiring distinct mental powers; that the same mind is not always equally` skilful in all three; and other arguments of the like kind. Both these opposite opinions may be accepted as true, if we attend to the different points of view