and others, must always be imperfect, or, if they approximate completeness, must always indicate at least as many blanks as there are departments already occupied. Whether we try to distribute the various branches of knowledge, as Bacon did, according to the different faculties of the mind which they respectively call into play; or, with Locke, according to the several ends in view; or, with Descartes, as followed by Comte, according to the order of their development, as determined by their degrees of simplicity; some Sciences will appear redundant, others as defective, and many as having an equally good title to be ranked under two or three different heads.

As one of the best specimens of these attempts at classification, we may take Dr. Thomson's account of the arrangement proposed by Comte, on the basis of Descartes's aphorism, that knowledge should advance from the simpler to the more complex phenomena.

"Mathematics, or the science of quantities, is at once the most simple in its elements and the most general in its application, entering, more or less, into all the sciences of Nature, and constituting almost the whole of that which comes next it in the order of dependence. Astronomy, or the science of the heavenly bodies, is the application of mathematical truths to the laws of matter and motion; matter and the motions of material bodies being the new conceptions which belong to this science. Physics, being the science, or rather group of sciences, which is conversant with the general laws of the world, so far as they relate to beings without life or organization, would come next; and it imports, in addition to the conceptions of Astronomy, those of light, of heat, of sound, of electricity, of magnetism, and many others. Chemistry would rank next, which is the science of the decomposition and combinations of the various substances that compose and surround the earth. Next in order of complexity would rank Physiology, founded

on the additional conception of vegetable and animal life. To this would succeed Anthropology, or the science of man's nature; and to this, Social Science, which ascertains the laws that govern men when combined in cities and nations. Each of these departments may be divided into many branches; as Physics into Acoustics, Optics, Electricity, and the like; or Social Science into Morals, Politics, Political Economy, Law, and the like.

"On comparing scientific works, differences in the mode of teaching the same subject become apparent. In one, the pure theory of Astronomy is presented; in another, the striking features of its historical progress as a science, with speculations on the historical sequence of the phenomena themselves; in a third, the practical applications of which the Science admits in respect to the comfort and progress of mankind. This threefold mode of treatment runs through all the Sciences, and in a table of them might well be expressed. The classification would thus embody all that is valuable of another system of classes, that according to the purpose towards which the Science was directed.

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"A classification which advances on Descartes's principle, from the more simple to the more complex subjects, which commences from the notions of extension and quantity, and proceeds through material things up to living, intelligent, and moral agents, ought to coincide with the order in which the sciences themselves have reached maturity. And this it certainly does. Mathematics had made good its ground when Astronomy was yet in its infancy; Physics began to obtain a sure footing later than either; whilst the Sciences which relate to Life are still very immature; and some of the main problems of Social Science are yet matter of controversy even in our own days."

It is an obvious imperfection of this scheme, that it takes no notice of the numerous branches of that Science, Natural History, which, as it depends solely upon observation,

and thus gives us our first knowledge of all the objects of study, would seem to constitute the basis of all the other Sciences. In explanation of this defect, Comte remarks, "we must distinguish between the two classes of Natural Science; the abstract or general, which have for their object the discovery of the Laws which regulate phenomena in all conceivable cases; and the concrete, particular, or descriptive, which are sometimes called Natural Sciences in a restricted sense, whose function it is to apply these Laws to the actual history of existing beings. The first are fundamental; and our business is with them alone, as the second are derived, and, however important, not rising into the rank of our subjects of contemplation. We shall treat of Physiology, but not of Botany and Zöölogy, which are derived from it. We shall treat of Chemistry, but not of Mineralogy, which is secondary to it." But this remark is inconsistent with the previous assertion, that this order of classification "coincides with the order in which the Sciences themselves have reached maturity." In the order of time, certainly, Zoology and Botany had been cultivated to a considerable extent before men had obtained more than the crudest notions of the physiological processes of animal and vegetable life; just as Civil History, the basis of another department, had been very fally treated before it first suggested the idea of Social Science. In what may be called the logical order, or the order of ideas, however, it is true that the Sciences which embody principles and general results take precedence of those which afford only the material of knowledge.

CHAPTER XI.

DEMONSTRATIVE REASONING AND DEDUCTIVE EVIDENCE.

WE

E have already said, that the principal object of the researches of Science is, to determine whether this or that object, or class of objects, has the special characteristics which entitle it to be placed in a certain class, and called by a certain name.

Most of such questions, if they relate only to one thing, or to a very few things, are answered directly, and without difficulty, by observation or intuition. We answer one of them, in fact, whenever we perceive any object and call it by its appropriate Common Name. For instance; - this thing which I now hold in my hand I call a pen, a rose, or an apple, because I perceive that it has the attributes which are the Marks connoted by that name. In like manner, I pronounce the animals now before me to be dogs, horses, or cows, according as I recognize their distinctive qualities.

Writers like Dr. Brown, Mr. J. S. Mill, and Mr. Bailey, who have laboriously attempted to restrict the range and depreciate the utility of the Syllogistic process, have seemingly failed to notice the fact, that we must reason syllogistically whenever we use language with any perception of its meaning, that is, when we call anything by its appropriate name. If I had not already spread out before my mind the Marks which constitute the Intension of the Concept apple, or rose, I could not designate the object now presented to me by that appellation. This process of reasoning, which we are performing almost every moment

of our lives, and therefore so quickly and easily that its several steps are taken almost unconsciously, is thus spread out into the formal process.

The Concept or Class-notion apple has, as Marks, a nearly spherical shape, a red color, a moderate hardness, and a certain smell;

This object has all these Marks;

Therefore, this object is an apple.

This is what Hamilton calls Reasoning in Intension, for, in each of the Premises, the Predicate is contained in the Subject. Moreover, the Reasoning is not only logical, — i. e. valid in Form, but it is also Demonstrative, -i, e. absolutely certain in respect to its Matter. It is Demonstrative, because the Major Term, which is here the Subject of the Major Premise, is a Concept or Class-notion, which, being a mere creation of the mind, cannot have any other Marks or qualities than those which we voluntarily attribute to it. As we know by Intuition, that the object has all the Marks which we included in the Concept, it is certain that it should be designated by the name of that Concept, — that is, that it should be included under its Extension.

On the other hand, if the Reasoning is made to concern, not a mere Concept in the mind, but a class of real things, which, as we have seen, always have an unknown and unknowable number of qualities and relations, then I cannot be sure that the object in question possesses all these qualities, but can only doubtfully infer that it has all, because I know that it possesses some, of the more important of them. An element of uncertainty is introduced; the Reasoning ceases to be Demonstrative, and becomes merely Probable or contingent. For instance; -if, in the Major Premise of the preceding Syllogism, we say, not "the Concept or Class-notion apple," but "All apples" - i. e. All the actual, objects which we have been accustomed to call apples" have a nearly spherical shape, a red color, a mod