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in our author's own account of their origin"-(Examination, p. 392); but presently, as if this were too generous, he adds: “But his theory is a complete condemnation of his practice. He affirms that Nominalism and Conceptualism are the same, and on this justification expounds all the operations of the intellect in the language of Conceptualism, and on the assumptions of Conceptualism. Hamilton has never affirmed that Nominalism and Conceptualism are "the same," though, if he had, a good deal might be said to show that it is in the main, or substantially, true. But, taking them as two theories, Hamilton shows that there is truth in each, and showing what this truth is, brings them into complete harmony by his own doctrine. And on the basis of the reconstructed theory, he uses language which only such a critic as Mill would distort as exclusively conceptual.

Mill asks, “Is it correct to say that we think by means of concepts? Would it not convey both a clearer and a truer meaning to say that we think by means of ideas of concrete phænomena, such as are presented in experience or represented in imagination, and by means of names which, being in a peculiar manner associated with certain elements of the concrete images, arrest our attention on those elements?" Sir W. Hamilton has told us that a concept cannot, as such, be "realised in thought," or "elicited into consciousness. Can it be that we think

and reason by means of that which cannot be thought, and of which we cannot become conscious? To the latter question any tyro would answer that the same argument would prove that because we cannot think the half of a whole by itself, or as such, we must think the whole by means of that of which we cannot become conscious. The same

tyro might answer to the first question, that if we have only the idea of a concrete phænomenon, and the name of parts of the concrete image, we cannot think at all, seeing we should never be able to say whether any other idea or any other phænomenon agreed with or differed from the first-never, in a word, be able to perform the first function of thought-discrimination-name the part or the whole as we please. Thinking by means of names-the symbolical thinking of Leibnitz-is putting names "in lieu of notions. This is a kind of thinking fully recognised by Hamilton; but it is recognised by him and others as possible only because there is another sort of thinking in the first place, and at the root of the whole-viz., Intuitive thinking, or thinking through a definite representation of the attributes conceived as common to the class. We may think symbolically, but we must be able to think intuitively, or by means of the image plus the conceived relation, ere even symbolical thinking can be regarded as symbolical of anything. And did we only think symbolically, we should have no test either of clearness, distinctness, or even truth in our thinking. We could never bring it to the test of experience, or lend it the enlightenment of intuition. It would be literally "blind thinking "-the blind leading the blind.

(On Mill's chapters on General Conceptions, Judgment, and Reasoning, the reader may refer to an admirable criticism in Hamilton versus Mill, a publication of which, unfortunately, only two parts appeared (Edinburgh, 1866). The exposure of the sophistries of the criticism in those chapters is most thorough.)

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CHAPTER XI.

THE CONCEPT-ITS CHARACTERISTICS SPECIALLY CONSIDERED-COMPREHENSION AND EXTENSION RELATION TO LANGUAGE

INTUITIVE AND SYMBOLICAL THINKING.

§ 120. It follows from what has been said on these points that every concept has a double or twofold side. As embodying the idea of an attribute or attributes, it has a meaning, content, or comprehension (Inhalt). As through the attribute or attributes applicable to several objects, it has a compass, breadth, or extension (Umfang). It takes in objects or classes: in the former aspect it indicates attributes, in the latter it denotes objects; but it cannot denote unless it first of all indicate or connote. So that connotation is the ground of denotation-comprehension is the ground of extension. In the notion Man, the attributes life, sensation, reason, free-will make up the content or comprehension; in the same notion, white man, black man, coppercoloured man make up the extension.

The attributes in the comprehension of a concept are fixed; these do not vary. But the species, classes, or individuals contained within the extension, vary according to our principle of division. The specification now given is according to colour, but we may divide man equally well according to nationality. Here we should speak of Englishman, Scotsman, Frenchman, Prussian, Russian, and Turk. Or we may divide man according to his religion, as Mohammedan, Christian, Buddhist. Or under Christian we may take Papist, Presbyterian, Lutheran. The comprehension is thus invariable; the extension is variable, according to the principle of division, For the proper use of this word see below, p. 173.

which of necessity introduces a new attribute external to the comprehension of the notion divided.

As has been well pointed out,-in reply to the question, What is an object ?—we speak in comprehension. What is art? It is skill in production. Which are the arts? The answer is in extension. Painting, Sculpture, Architecture, &c., are arts.

§ 121. The inadequacy of a concept as a representation, already noticed, is increased in proportion as the width of the extension of the concept is increased. Thus, take the individual-say Sir Isaac Newton. First, I represent him as astronomer. This implies or connotes certain attributes, as that he is man and intelligent; but it does not give me the individual Newton. It leaves out Englishman, Master of the Mint, Professor of Mathematics. Newton may be astronomer, though he is none of these. Astronomer applies to him only in one relation, and in this relation it might apply to, i.e., represent, a hundred men besides.

Then, if I represent him simply as a man, the less do I think of his proper individuality. I have given up even what is distinctive in astronomer; for he might be the former, and not the latter. If I think of him simply as existing or being, my notion of him falls still short of the individual. In a word, the more extensive my view of the individual or his qualities, the less adequate and the more faint is my picture of the individual. In technical language, the more extensive my knowledge, the less comprehensive is it,the less does it hold the features of the individual.

=

Thus, let X astronomer, and A, B, C, D, E, the other qualities of the individual Newton not implied in X. These taken together make up a perfect image of him. When I think of him as one of the X's, I do not think of him-i.e., necessarily think of him, as A, B, C, D, E. My knowledge of him, accordingly, as given in the concept X, is less than an adequate representation of the individual by A, B, C, D, E.

§ 122. The neglect of attention to this distinction in our concepts leads to the blank of thought itself, to mere verbalism, to using terms which are literally nonsensical. And it is the source of nine-tenths of our controversies; for unless we first of all ask ourselves and our opponents what precisely each means by the term to be applied to an object-what is its comprehension - it is obvious that, as

opposing parties, we may be fighting absolutely in the dark. We may literally attach no meaning to the word we use, or each of us may attach a totally different meaning to it, and so be in agreement, while we suppose we are in mortal conflict. Definition, the unfolding or explication of the comprehension of terms,-is the first requisite to clear and distinct thinking in our own minds, and it is essential to the understanding of the position of other people.

(a) In the view of the concept now given, I have regarded it as identical with what other writers call the General Conception, allegemeine Vorstellung, schema, notio, conceptio, representatio communis, or generalis, or universalis. But concept or notion has been taken by some logicians in a narrower sense.

We are told by Ueberweg, for example, that the notion (Begriff, Notio, Conceptus) is that conception in which the sum total of the essential attributes, or the essence (Wesen, essentia) of the object under consideration is conceived. By the phrase-attributes (Merkmale, Nota), of the object we include not only the outward signs by which it is known, but all its parts, properties, activities, and relations,—in short, whatever belongs in any way to the object. The essential (essentialia) are those attributes which (a) contain the common and persistent basis for a multitude of others; and on which (b) the subsistence of the object, its worth and its meaning, depend. . . . Attributes are also called essential which are necessarily united to marks essential in the stricter sense, and whose presence, therefore, indicates with certainty the presence of those others. The other characteristics

of an object are called non-essential (accidentia, modi). The possibility of modi, or the capability to take this or that modification, must have its foundation in the essence of the object. In perfect knowledge, notions are valid only as they correspond to the types of the real groups of their (natural or mental) objects.

We recognise and distinguish the essential (a) in ourselves immediately by feeling and mediately by ideas. . . . The knowledge of our own essence depends both on the consciousness of the ethical ideas, and on the amount of our actual existence in them.

(b) By means of the knowledge of the essence in ourselves, we recognise the essence of persons beyond us more or less adequately in proportion to their relationship with ourselves...

(c) The essence or the inner purpose of nature is the analogue of the ethical duty of man, and is to be known in the proportion of this analogy.

(d) With the inorganic objects of nature, existence, as an end in itself, and self-determination, come after existence as a mean for another, and the mechanically becoming determined by another.(Ueberweg, Logic, p. 153.)

The construction of a notion "purely according to objective laws, on the basis of what is most essential for the object in itself," is the problem of science, in its various departments. It is not the problem

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of any one science; and its laws are simply those treated of in Inductive Logic. To define notion as identical with the knowledge of essence, is to be guilty of narrowness in definition, or to abuse the term. It is, besides, to miss the essential character of the notion itself, and to pass beyond the whole laws of thinking ultimate in the construction of a notion quâ notion. When we ask-" According to what marks are objects to be grouped together and their notions formed? -what are the marks of the essential as distinguished from the nonessential or accidental attributes?-there are really two questions involved. (1.) What kind of attribute is essential? (2.) What attribute in a given case is essential? An answer might be given by logic proper to the former question,-in saying that an attribute is essential when it is of such a kind that the object in which it inheres would not be, or not be what it is, in its absence. Such an attribute is extension in body. This would further fulfil the test of being the permanent ground of other derivative attributes, such as figure, position, directly; and colour indirectly. It will be found, however, that the application of such a test is limited really to necessary concepts. When we descend to the properties of individual objects, and to the classes of things, we may go back a certain way and find grounding attributes, but we can never be certain that these are the ultimate and thus the absolutely essential. What attribute in a given case is the essential one? Shall we say that it is that without which the object could not be? But then this supposes that we have already defined the object in its essential character. Shall we say that it is an attribute which affords a permanent ground for other attributes? But can we call this properly essential, or constitutive of the being of the object, quâ object? Suppose we know, as we only can know, by observation and induction, what, then, is to be our test of the essential in an object as compared with the accidental? Suppose this test is, that at a given point in the history of physical science we find certain attributes prior to others in the order of nature, on which those others depend, are we at once to say that these are the essential attributes of the object? If so, what happens when we find, through further analysis, that those so-called essential attributes are themselves dependent on others?-are themselves derivative? And where is this process of analysis to stop? Can we at any time say that we have found the essential attributes of any object, taken objectively? Or rather is it not the case, that in every stage of inductive inquiry we can only say that we have found attributes prior to others, but the ultimate and permanently essential still necessarily escape us? Could we get at the prius of all the objects of our sensible experience, or of even one object of that experience, then, and then only, could we determine the essential attribute or attributes of the object. In fact, the term essential, as objectively implied, has properly only reference to hypothetical constructions, in which we deal with a limit subjectively imposed, or to mathematical constructions in which the grounding concept of extension, necessarily conceived, is modified by us according to certain implied requirements, by means of definition. Line, surface, triangle, square, can each be given in its essence, but this only ideally, for there are metaphysical questions regarding the prius of