THE REASONING PROCESSES.

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aspect of the phenomena to be studied-I have indicated a third, which, although not radically distinct from these, deserves separate notice; I mean analytic force, or the tendency to separate the effects that an object has on the senses or the mind, and to concentrate the regard on one particular at a time. Thus we have seen that a falling body produces a very complex impression-a gross and multifarious effectand this total mass of sensation and feeling is the popular notion of the phenomenon. No accurate knowledge can grow out of such aggregates; they are the soil of poetry, not of science. I shall illustrate afterwards the nature of this force, or impulse, that resists the totalizing influence of a complex object, and isolates for study and comparison its individual effects; I note it here as the volitional, or what may be loosely styled the moral, element of the scientific intellect; it stood forth in singular grandeur in the mind of Newton.

REASONING AND SCIENCE IN GENERAL. ·

34. Not to mention the examples that we have just parted from, many of the instances of Similarity already adduced in the course of our exposition are strictly of the nature of science. I think it right, notwithstanding, to devote a separate head to the operation of the law in the various scientific processes, with a view to elucidating farther both it and them. I shall therefore make the illustration fall under the four divisions of Abstraction, Induction, Deduction, and Analogy.

ABSTRACTION, Classification, Generalization of Notions or Concepts, General Names, Definitions.-These designations all point substantially to the same operation-the identifying a number of different objects on some one common feature, and the seizing and marking that feature as a distinct subject of thought; the identification being a pure effort of Similarity. Thus we identify the different running streams that have come under our observation, in consequence of the sameness that appears prominent in the midst of much diversity; any

new one will recall the previous ones; and they are assembled together in the mind not as a miscellaneous aggregate, but as a class strung on a common thread. In this connexion, they add to our information of each; some we know chiefly at the sources, others at the mouth, some in the mountains, others in the plains; accordingly, we supply gaps in our knowledge of any one by means of the rest. We may go the length of deriving out of the fragmentary views an unbroken whole, an ideal river, that shall include all the features of a complete river; or we may simply choose one that we know better than the rest, as our representative instance, and from it supply blanks in our view of such as we have less perfectly examined. This mutual supply of defects in our knowledge of individuals, is one of the advantages of assembling objects in a class; a second advantage is the substitution of one for another in any practical end; we know, for example, by some single experience, that a river bank is a convenient site for a town or village, and so we can choose any one of all the rivers in our knowledge for the same object. Here, then, we have first a classification, assembled by the attraction of similarity; secondly, a generalization, or general notion, concept, or abstract idea, being some typical river that fairly represents the group, and in which we include 'only what they all have in common; this typical river may be one of the number, or it may be a composition out of several. Thirdly, we have the application of a general name to the class, the name 'river,' which shall express both the whole, and what each has in common with every other. A fourth operation is all that is necessary to complete the work, namely, to furnish a definition, or an expression in language, of the agreeing features or common properties of the class. This exhausts the series of operations connected with the generalization of objects taken as a total or a unity; of these, the first grows out of pure Similarity, the others suppose a somewhat more complicated process, to be afterwards described.

A river may be defined 'a natural current of water flowing in an open channel towards the sea,' or to that effect.

Take next the genus of Round bodies. As before, these are first mustered by the attraction of sameness; their identification has the effects, already specified, of mutual enlightenment and mutual exchangeability. Following up this operation, we seize upon some one instance as a representative or typical instance, and our idea of this we call the abstract, or general idea. We can here adopt a very refined method; we draw an outline circle, omitting the solid substance, and presenting only naked form to the eye; this is an abstraction of a higher order than we could gain by choosing a specimen circular object, as a wheel, for it leaves out a greater number of the features wherein circular bodies differ. The mathematical Diagram is thus more of an actual abstraction, than the idea of a river or of a mountain derived from a fair average specimen, or than a composite river or mountain. We may advance, however, from the diagram to a Definition by descriptive words, and we may adopt this as our general conception, and use it in all our operations instead of, or along with, the other. (A circle is defined to be a line everywhere at an equal distance from a point which is the centre.) The definition is, in fact, the highest form of the abstract idea, the form that we constantly fall back upon as the test or standard for trying any new claim of admission into the class, or for revising the list begun with.

I do not here enter into the great controversy of Nominalism and Realism, having done so in another place (MENTAL and MORAL SCIENCE, Appendix A). There is considerable subtlety in stating the precise nature of that mental element called an abstract idea, notion, or concept. The view now prevailing approaches more or less closely to Nominalism; denying alike the separate existence of abstractions (Realism), and the power of mentally conceiving them as such (Conceptualism). An abstract idea, as stated in the text, is one of three things:—(1) the assembled group of concrete instances, which may be momentarily represented by a single individual; (2) a skeleton outline or diagram, ́which is still a concrete instance; a circle in Euclid has a definite colour and size, and therefore is not any and every circle; (3) a verbal definition. Sometimes we may have all the three.

The foundation of abstract reasoning must always be an adequate host of particulars. To reason about Justice, we must be able to recall a sufficient variety of just actions to bring to view all the characters connoted by justice, and to exclude those that are not connoted. So with regard to Roundness; we must keep in view several circles differing in material, colour, and size, so as to affirm nothing but what belongs to all circles.

The verbal definition provides a mode of seemingly evading this requirement of a plurality of concrete instances. It cannot dispense with the concrete altogether; but it may make one instance suffice. To understand the definition of matternamely, something inert, or resisting-it would be enough to have one example before us, as a cannon ball, provided we understand that all the properties of the ball are to be excluded from our consideration except its inertness. We may, and do in some subjects, contract the habit of looking at an individual concrete in this exclusive way, which is the greatest stretch of abstraction within the competence of the mind. But this is the act of the mature intelligence.

35. INDUCTION, Inductive Generalization, Conjoined Properties, Affirmations, Propositions, Judgments, Belief, Laws of Nature. The contrast between Abstraction and Induction, as here understood, may be expressed thus in the one a single isolated property, or a collection of properties treated as a unity, is identified and generalized; in the other a conjunction, union, or concurrence of two distinct properties is identified. We exemplify the first process, when we bring all rivers into one class, and define the property common to all; the second process, Induction, is exemplified when we note the fact that rivers wear away their beds, or the fact that they deposit deltas at their mouths. In this case two different things are conjoined; the flow of water over a country to the sea in an open channel, which makes the idea. of a river, is associated with the circumstance of depositing or forming land in a particular situation. This conjunction makes an Affirmation, or a Proposition; the idea of a river by itself, or anything expressed by a noun, is not an affirmation. When we affirm the uniform co-existence of two dis

tinct facts, we have a Law of Nature, an intellectual possession respecting the world, an extension of our knowledge, a shortening of labour. Of the two conjoined things, the presence of one is at any time sufficient to assure us of the presence of the other, without farther examination. As surely as we meet with a river, so surely shall we find the carrying down of mud to be deposited at the mouth, if the two facts be really connected as we suppose. An abstraction or definition gives us a general idea; it assembles a class of things marked by the presence of this common feature,-the class river, the class eircle, the class red, the class planet, the class just, but does not convey a proposition, a law of nature, a truth.

In forming these inductive generalizations, we need the identifying impetus very much as in abstractive generalizations. The case is distinguished only by being more complex; it is properly a stage beyond the other in the order of discovery, although the two are often accomplished by one and the same effort of the sense and the understanding. Still, in order to arrive at the knowledge that rivers form bars and deltas, we require to have observed the peculiarities of rivers, and to have been arrested by their identity on this point; standing at the mouth of one, and observing the island which parts its stream, we are reminded, by a stroke of reinstating similarity, of the mouth of some other where a similar formation occurs, with perhaps many points of diversity of circumstances. These two coming together will bring up others, until we have assembled in the mind's eye the whole array that our memory contains. Such is the first stage of an inductive discovery; it is the suggestion of a law of nature, which we are next to verify. The conflux of all the separate examples in one view indicates to the mind the common conjunction, and out of this we make a general affirmation, as in the other process we make a general notion or idea. Now, a general affirmation by language makes a proposition, not a definition; it needs a verb for its expression, and is a law or a truth, something to be believed and acted on.