cealing them under abstract words, dividing and transforming them, so that we are frequently puzzled to recognize them: whenever we pierce to the basis of our words and ideas, we find them and nothing but them. Mill says:

"Take the following example: A generous person is worthy of honour. Who would expect to recognize here a case of coexistence between phenomena? But so it is. The attribute which causes a person to be termed generous is ascribed to him on the ground of states of his mind, and particulars of his conduct; both are phenomena; the former are facts of internal consciousness, the latter, so far as distinct from the former, are physical facts, or perceptions of the senses. Worthy of honour, admits of a similar analysis. Honour, as here used, means a state of approving and admiring emotion, followed on occasion by corresponding outward acts. Worthy of honour' connotes all this, together with an approval of the act of showing honour. All these are phenomena; states of internal consciousness, accompanied or followed by physical facts. When we say, A generous person is worthy of honour, we affirm coexistence between the two complicated phenomena connoted by the two terms respectively. We affirm, that wherever and whenever the inward feelings and outward facts implied in the word generosity have place, then and there the existence and manifestation of an inward feeling, honour, would be followed in our minds by another inward feeling, approval."

In vain we turn about as we please, we remain still in the same circle. Whether the object be an attribute or a substance, complex or abstract, compound or simple, its material is to us always the same; it is made up only of our modes of being. Our mind is to nature what a thermometer is to a boiler we define the properties of nature by the impressions of our mind, as we indicate the conditions of the boiling water by the changes of the thermometer. Of both we know but condition and changes; both are made up of isolated and transient facts; a thing is for us but an aggregate of phenomena. These are the sole elements of our knowledge: consequently the whole effort of science will be to link facts to facts.

Section III.-The Two Corner-Stones of Logic

This brief phrase is the abstract of the whole system. Let us master it, for it explains all Mill's theories. He has defined and restated everything, from this starting-point. In Mill's " Logic," 110.

all forms and all degrees of knowledge, he has recognized only the knowledge of facts, and of their relations.

Now we know that logic has two corner-stones: the Theories of Definition and of Proof. From the days of Aristotle logicians have spent their time in polishing them. They have only dared to touch them respectfully, as if they were sacred. At most, from time to time, some innovator ventured to turn them over cautiously, to put them in a better light. Mill shapes, cuts, turns them over, and replaces them both in a similar manner and by the same means.

Section IV.-Theory of Definitions

I am quite aware that nowadays men laugh at those who reason on definitions; the laughers deserve to be laughed at. There is no theory more fertile in universal and important results; it is the root by which the whole tree of human science grows and lives. For to define things is to mark out their nature. To introduce a new idea of definition is to introduce a new idea of the nature of things; it is to tell us what beings are, of what they are composed, into what elements they are capable of being resolved. In this lies the merit of these dry speculations; the philosopher seems occupied with arranging mere formulas; the fact is, that in them he encloses the universe.

Take, say logicians, an animal, a plant, a feeling, a geometrical figure, an object or group of objects of any kind. Doubtless the object as its properties, but it has also its essence. It is manifested to the outer world by an indefinite number of effects and qualities; but all these modes of being are the results or products of its inner nature. There is within it a certain hidden substratum which alone is primitive and important, without which it can neither exist nor be conceived, and which constitutes its being and our notion of it.1 They call the propositions which denote this essence definitions, and assert that the best part of our knowledge consists of such propositions.

1" According to idealist logicians, this being is arrived at by examining our notion of it; and the idea, on analysis, reveals the essence. According to the classifying school, we arrive at the being by placing the object in its VOL. III.-24

group, and the notion is defined by stating the genus and the difference. Both agree in believing that we are capable of grasping the essence. Mill's "Logic," i. 127.

On the other hand, Mill says that these kinds of propositions teach us nothing; they show the mere sense of a word, and are purely verbal. What do I learn by being told that man is a rational animal, or that a triangle is a space contained by three lines? The first part of such a phrase expresses, by an abbreviative word, what the second part expresses in a developed phrase. You tell me the same thing twice over; you put the same fact into two different expressions; you do not add one fact to another, but you go from one fact to its equivalent. Your proposition is not instructive. You might collect a million such, my mind would remain entirely void; I should have read a dictionary, but not have acquired a single piece of knowledge. Instead of saying that essential propositions are important, and those relating to qualities merely accessory, you ought to say that the first are accessory, and the second important. I learn nothing by being told that a circle is a figure formed by the revolution of a straight line about one of its points as centre; I do learn something when told that the chords which subtend equal arcs in the circle are themselves equal, or that three given points determine the circumference. What we call the nature of a being is the connected system of facts which constitutes that being. The nature of a carnivorous mammal consists in the fact that the property of giving milk, and all its implied peculiarities of structure, are combined with the possession of sharp teeth, instincts of prey, and the corresponding faculties. Such are the elements which compose its nature. They are facts linked together as mesh to mesh in a net. We perceive a few of them; and we know that beyond our present knowledge and our future experience, the network extends to infinity its interwoven and manifold threads. The essence or nature of a being is the indefinite sum of its properties. Mill says:

The definition, they say, unfolds the nature of the thing: but no definition can unfold its whole nature; and every proposition in which any quality whatever is predicated of the thing, unfolds some part of

"An essential proposition, then, is one which is purely verbal; which asserts of a thing under a particular name, only what is asserted of it in the fact of calling it by that name; and which, therefore, either gives no infor mation, or gives it respecting the name, not the thing. Non-essential or acci

dental propositions, on the contrary, may be called Real Propositions, in opposition to Verbal. They predicate of a thing, some fact not involved in the signification of the name by which the proposition speaks of it; some attribute not connoted by that name."Mill's "Logic," i. 127.

its nature.

The true state of the case we take to be this: All definitions are of names, and of names only; but in some definitions it is clearly apparent, that nothing is intended except to explain the meaning of the word; while in others, besides explaining the meaning of the word, it is intended to be implied that there exists a thing, corresponding to the word." 3

Abandon, then, the vain hope of eliminating from properties some primitive and mysterious being, the source and abstract of the whole; leave entities to Duns Scotus; do not fancy that, by probing your ideas in the German fashion, by classifying objects according to genera and species like the schoolmen, by reviving the nominalism of the Middle Ages or the riddles of Hegelian metaphysics, you will ever supply the want of experience. There are no definitions of things; if there are definitions, they only define names. No phrase can tell me what a horse is; but there are phrases which will inform me what is meant by these five letters. No phrase can exhaust the inexhaustible sum of qualities which make up a being; but several phrases may point out the facts corresponding to a word. In this case definition is possible, because we can always make an analysis, which will enable us to pass from the abstract and summary term to the attributes which it represents, and from these attributes to the inner or concrete feelings which constitute their foundation. From the term "dog" it enables us to rise to the attributes "mammiferous," " carnivorous," and others which it represents; and from these attributes to the sensations of sight, of touch, of the dissecting knife, on which they are founded. It reduces the compound to the simple, the derived to the primitive. It brings back our knowledge to its origin. It transforms words into facts. If some definitions, such as those of geometry, seem capable of giving rise to long sequences of new truths, it is because, in addition to the explanation of a word, they contain the affirmation of a thing. In the definition of a triangle there are

Mill's "Logic," i. 162.

"The definition above given of a triangle obviously comprises not one, but two propositions, perfectly distin guishable. The one is, There may exist a figure bounded by three straight lines'; the other, And this figure may be termed a triangle.' The former of these propositions is not a definition at all; the latter is a mere nominal defini

tion, or explanation of the use and application of a term. The first is susceptible of truth or falsehoods, and may therefore be made the foundation of a train of reasoning. The latter can neither be true nor false; the only character it is susceptible of is that of conformity to the ordinary usage of language."-Mill's "Logic," i. 162.

two distinct propositions-the one stating that "there may exist a figure bounded by three straight lines"; the other, that "such a figure may be termed a triangle." The first is a postulate, the second a definition. The first is hidden, the second evident; the first may be true or false, the second can be neither. The first is the source of all possible theorems as to triangles, the second only resumes in a word the facts contained in the other. The first is a truth, the second is a convention; the first is a part of science, the second an expedient of language. The first expresses a possible relation between three straight lines, the second gives a name to this relation. The first alone is fruitful, because it alone conforms to the nature of every fruitful proposition, and connects two facts. Let us, then, understand exactly the nature of our knowledge: it relates either to words or to things, or to both at once. If it is a matter of words, as in the definition of names, it attempts to refer words to our primitive feelings: that is to say, to the facts which form their elements. If it relates to beings, as in propositions about things, its whole effort is to link fact to fact, in order to connect the finite number of known properties with the infinite number to be known. If both are involved, as in the definitions of names which conceal a proposition relating to things, it attempts to do both. Everywhere its operation is the same. The whole matter, in any case, is to understand each other—that is, to revert to facts, or to learn-that is, to add facts to facts.

Section V.-Theory of Proof

The first rampart is destroyed; our adversaries take refuge behind the second-the Theory of Proof. This theory has passed for two thousand years for a substantiated, definite, unassailable truth. Many have deemed it useless, but no one has dared to call it false. On all sides it has been considered as an established theorem. Let us examine it closely and attentively. What is a proof? According to logicians, it is a syllogism. And what is a syllogism? A group of three propositions of this kind: "All men are mortal; Prince Albert is a man; therefore Prince Albert is mortal." Here we have the type of a proof, and every complete proof is conformable