hand, the matter of Thought and the Sciences--such as Metaphysics and Natural Sciences--which inquire into the matter, and, on the other, the Form of thought, and the Science which inquires into the Form, namely, Logic.

The question is now this: are these the rational and real boundaries of Logic; and how can Logic, or any other Science whatever, be constituted if all matter of knowledge is excluded therefrom? And even granted that Logic is the Science of Form, is the Form such as it has been conceived by old Logic the truly rational Form? In order to place these points in a proper light, let us draw the outline of Logic such as it has been realized to the present day.

As there can be no thought without some defined forms, there must be some general elements of thought. These elements have been called by some logicians Terms, by others Categories or Concepts, by others Genus and Species.

Now if, from terms or categories, or whatever name they be called, according to what we have stated, we subtract their objective and material value-be these derived from experience or from Reason--there will be only left their magnitude or quantity, and Logic will be the Science of the Quantity of Thought. Hence the relation-or, to speak more properly, the confusion--of Logic and Mathematics. For Terms, when stripped of their contents, are like numbers and geometrical figures, and their combination may be compared to a numerical proportion or to concentric circles.†

According to this criterion, the essential character of terms. will be what logicians call Comprehension and Extension, which are a certain number-a sum-of characters belonging

* If, for instance, from the term man we take away the real existence and the qualities of man, the only character or entity which can possibly remain in man will be his quantity, i.e. man considered as a whole, or as a part, or as an individual.

+ Euler, for instance, compares syllogisms to three concentric circles, the middle circle playing the part of middle term-(Letters to a German Princess). Ploucquet identifies Logic and Reckoning, and, after having converted syllogism into calculation, he concludes by the following words: "Posse etiam rudes mechanice totam logicam doceri, uti pueri arithmeticam docentur, ita quidem, ut nulla formidine in ratiociniis suis errandi, torqueri vel fallaciis circumveniri possint, si calculo non errant." It must be said that Leibnitz had already set the example to this superficial and illogical manner of treating Logic by submitting syllogism to combinatory calculation, by calculating the number of combinations into which the proposition may be adjusted in syllogism. (See Leib. Op. T. II. p. 1.)

to each term. Let us take, for instance, the term Tree. Tree is a genus and a species. It is a genus if we consider the inferior narrower terms-oak, fir, apple, &c.—it contains; it is a species if we consider the superior or wider terms-organic matter, being, &c.-in which it is contained. The aggregate of the former character constitutes its extension, the aggregate of the latter its comprehension. Hence follows, 1°. that the Comprehension and the Extension are in inverse ratio, and consequently that whilst the one increases the other diminishes, the Comprehension increasing in a series of terms from upwards downwards, and the Extension from downwards upwards; 2°. that if we picture to ourselves the whole series of terms, we shall see that at the one end of the series -the upper end-there is a term having the widest Extension but no Comprehension, and at the opposite end--the lowest end-there is a term possessing the widest Comprehension but no Extension.

Now terms, considered singly and apart from all connection between them, are but indeterminate elements which do not constitute any positive thought. This property they acquire by their mutual association, and by reflecting, as it were, a part of themselves upon each other. Indeed, their own constitution points to this association. For as each term possesses both Comprehension and Extension, each term points to the term of which it forms either the Comprehension or the Extension.

Now the most elementary and fundamental connection of terms is the Proposition. The proposition is nothing but the development and (as it were) the actual position of the relation of terms--of the relation virtually implied in each term separately considered; in other words, the proposition is the actual affirmation of the twofold elements contained in each term. In the terms "man" and "mortal," for instance, there is a certain number of characters, some of which constitute their Comprehension and some their Extension. With regard to the term "mortal," man is a part of its Extension; and with regard to the term "man," mortal is a part of its Comprehension: so that these two terms, as parts of a whole -of the whole series of terms and thought--stand in a reciprocal and inverse relation, which relation is affirmed by the insertion of the copula is. In the proposition, "Man is

mortal," man, being the species, constitutes a part of the Extension of mortal; and mortal, being the genus, constitutes a part of the Comprehension of man.

Now, as the Proposition evolves itself out of Terms, so likewise the Syllogism evolves out of the Proposition. And as a series of Terms virtually contains a series of Propositions, so a series of Propositions virtually contains a series of Syllogisms. Nay, Syllogism is already contained in Terms, and, like the Proposition, it is but the actual development of the elements involved in Terms. For each term possessing Comprehension and Extension, i.e. being so constituted as to form, on the one side the Comprehension, and on the other the Extension, of other terms, not only points to a Proposition, but to a Syllogism. The terms "man," "mortal," "plant,” "white," "good," &c., possessing each of them these twofold sides, may be combined in a syllogism; and they may moreover, each in its turn, be a middle term, a major and a minor term, in different syllogisms.

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On these considerations, the fundamental principle of the Syllogistic theory, the principium de continenti et de contento a term that contains and is contained-rests. For each term by its Extension-as genus-contains, and by its Comprehension--as species--is contained; so that each term is, in its turn, a middle term, a major and a minor extreme. In the syllogism,

"All created beings are mortal:

Man is a created being;

Therefore," &c.,

man is the minor extreme. In the syllogism,

"All men are mortal:

The Europeans are men;

Therefore," &c.,

man is become middle term. In another syllogism it would become major extreme, and so it should be with the other terms. Thus the whole series of terms is a series of proposi

*The principle of "De continenti et de contento" is more specially applied by logicians to the middle term, which contains the minor extreme, and is contained in the major extreme. But if we take a larger view of the matter, and consider a series of syllogisms, we shall see that not only the middle term of a single syllogism, but all terms, contain and are contained. Let us take A, B, C, and suppose B to the middle term; B would contain and be contained. But B may be also a major or a minor extreme, and A or C a middle term, in another syllogism.

tions and syllogisms, and these latter are only a development of the elementary theory of terms realized as genus and spécies, or as quantities either containing or being contained in other quantities.

Now the complex of these forms and operations constitutes Method, which, as we have stated, is a mere subjective orga non of knowledge, an ensemble of rules guiding the mind in the discovery of Truth, but being neither Truth itself, nor having any objective relation with it; so that when we reason, define, divide, &c., we perform operations which lead the mind to the knowledge of things, but which possess no existence whatever without the mind, nor bear in any manner upon the nature of the things themselves. Now the condition of all thought and knowledge is that these should not deny or (as it were) destroy themselves. Consequently, to the above rules and principles must be added the principle of Contradiction, called also (by Kant) the "principle of Identity," which may be enunciated as follows: "A thing must be identical to itself," or "A thing cannot be other than itself at the same time and in the same respect"-a principle which is held out as the highest criterion of knowledge and truth.

These are the main features and principles of old Logic, of the Logic which claims Aristotle for its founder-with what reason we shall see hereafter-which has been for ages and is still officially taught, and forms the frame-work of all logical writings published until Hegel's Logic, whatever may be the difference in their external arrangement and some secondary points.

§ 3. Is Aristotle the founder of Formal Logic?

Though this question has only an historical and extrinsic value, yet, owing to the greatness of the name, to the influence which his writings exercise, and will exercise in future. ages, and to the fact that his logical disquisitions are and will be the starting-point of all logical studies, it is important for the guidance of the student, as well as for historical truth and for science's sake, to bring this point to its proper light, and to see what is Aristotle's true notion of Logic. That Aristotle did not clearly perceive either the object of Logic, or the link which connects this with other sciences

with Metaphysics, for instance; that there is a tendency in his theories to reduce all logical principles and operations to the empty formulas and figures of formal Logic, I will readily admit. But it does not follow therefrom that the Greek philosopher considered Logic as a mere science of subjective forms, absolutely separating it from what has been subsequently called Ontology and Metaphysics. For the most cursory glance at his writings will convince the reader, that, pursuing, like Plato, the unity of knowledge, he applied himself to connecting Logic with Metaphysics, by placing them on a common ground, and by attributing to them the same order of researches. Thus, after having, in his Logic, laid down the Categories as principles of Thought, in his Metaphysics he considers them as attributes of Being. It is the the same relation he has in view when in both the same writings he examines the principle of Contradiction, or when he introduces in his Analytics as well as in his Book of the Soul his theory of the Intellect, which is intimately connected with his theory of Being or Essence-Entelechia. Indeed, within the limits of Logic we find Aristotle occupied in defining and enlarging the object of this science, and inquiring into the material and objective meaning of its laws. For after having analyzed the Proposition in its general and indeterminate form, he analyzes it in its more determinate and more objective meaning (in his theory of Modal); and after having considered the middle term as Species, and in its quantitative relation with the extremes (First Analytics), he considers it from the point of view of Cause and Essence (Second Analytics), connecting here also Logic with his ontological theories, and pointing out the essence of things as the absolute middle term or principle of demonstration, in which the demonstration and the thing demonstrated, the form and the matter of thought, are intimately blended and raised to the identity of their nature.

This is Aristotle's real conception of Logic, as it is proved by his writings; and those who appeal to him to justify the separation of Logic and Metaphysics, do it either from obstinacy, or from ignorance and want of an accurate and comprehensive survey of his writings.