Popular usage has been and still is in the advance of them. The arithmetics still present many units of measure of which no use is made, unless it be by those who remain of a former generation or perhaps in some isolated localities.

There is one of these units which is rapidly falling into disuse to which I wish to call especial attention. I desire to ask who of our generation has ever seen a rod measure or has seen a distance measured by anything a rod long? Doubtless our ancestors used the rod as a real unit of measure and kept in their lofts a pole of that length to measure by. The very name of the synonym of rod-a-pole tells that this was the case; but none of us have ever used such a pole or even seen one. It is true that in country districts we occasionally hear of distances estimated in rods, but this usage alone is not enough to justify the use of rods as one of the main units of measure in our tables, and have all our children drilled how to perform all those difficult operations which its fractional scale necessitates. We often hear values measured by shillings and quarters, but would any teacher on this account desire to have the table of our money taught to little children in this fashion?

In all our cities and villages no use is made of rods in any measurement. Inches, feet and yards are the only units of small measures. In the country, land is measured by chains and not by rods, and there is much greater need that the country children have a vivid idea of the length of a chain than of a rod. In fact, were it not for the tedious drill to which all country teachers subject their children, I doubt if one in a hundred of them would know what a rod is. And if the rod is of little use to their children, how much more absurd is it for city and village teachers to waste the children's time and dissipate their energies teaching them a unit of measure which they will never use or even hear of again?

The chain is now the real unit of measure between a yard and a mile and should be inserted into the linear table instead of the rod. By this change the fractional scale of our present table would be avoided and our land measure would be brought, as it

should be, into vital relation to the other measures of distance. So long as the chain is not made a unit of linear measure, the children do not associate it with the other units of measure which they see and use, such as inches, feet and yards. That a chain as a measure is a real chain with links like other chains which they have seen, they never realize until they are grown, and perhaps not even then. As a result, land measure remains a shadowy something which they do not half understand, and in this distant realm it will always remain so long as teachers continue to waste their time drilling them to use antiquated rods instead of modern chains.

If this thought be carried out the tables of linear and square measure would be given in the following manner:

If these changes were made the last of the fractional scales would be discarded from our system. Denominate numbers could be treated in a much more simple manner than is now possible so long as rods are used. The whole subject could be developed independently of fractions. It would be less complicated and would require less maturity of thought than fractions, and hence could be placed in the arithmetics before the systematic development of fractions. Our number work would then harmonize to a much greater degree with the laws of the mental growth of the child and thus avoid those many weary hours-disagreeable both to teacher and pupil — which are now needed to overcome those unnatural impediments to progress which we have inherited from

our ancestors.

It would not require much effort on the part of teachers to effect this change. If a few of our best schools once discarded the fractional units of measure by using chains instead of rods they would be supported by earnest teachers everywhere. We might then

hope that our publishers would break away from the traditions of the past and present us with new arithmetics in which the different topics would be developed in that order which corresponds most closely to the needs of the growing powers of the child. Only when our methods of teaching have been thoroughly reconstructed and our textbooks are brought into harmony with them, can we expect those results from the study of arithmetic for which all lovers of mathematics have been so long working with the hope that this study might be made a much more efficient means for developing the logical faculties now so deficient both in man and child.

CIES

GERMAN PHILOSOPHY SINCE HEGEL.

BY B. C. BURT,

Docent in History of Philosophy, Clark University.

II.

NIESZKOWSKI attempts a more logical construction of history than the Hegelian, which he criticises as departing from the trichotomous method in the philosophy of history. The three periods of history are the thetic period of antiquity, the antithetic period of the Christian Germanic world, and the synthetic period now beginning. History not only suggests categories to analogical investigation, but actually embodies them in itself. The philosophy of history has a further and higher problem than the merely logico-speculative treatment of history: it must give the first place to will instead of speculative reason; must be the theory of action and life instead of a merely contemplative ideal

ism.

Wirth, at first a follower of Hegel, received impulses from Schleiermacher and Schelling carrying him away from his nominal Hegelian standpoint to a position enabling him to conceive the philosophy of religion as the essence of true philosophy. God, according to Wirth, is to be thought of, not precisely as personality, but as essence, life, central soul, and central spirit: is not apart from the universe, but contains in Himself an unconscious principle which is transfigured into knowledge and will. Man is God's image, but possesses freedom in, and because of, his likeness to God. God does not compel but communicates impulses

to us. The highest manifestation of the absolute spirit is morality, which includes in itself philosophy, religion, and art as successive stages. The sequence of these stages is understood if the life of spirit be conceived as a constantly new creation. The world is to be conceived as an eternal-temporal world, and the true theory of it must be ideal-realism. Hegel must be reconciled with empiricism.

To be classed with the ideal-realists, though his aim is speculation in the highest sense, is Leopold George, a pupil of Hegel and of Schleiermacher. According to George, the starting-point of pure philosophy is the notion Nothing, the method, the speculative (from which Hegel's is distinguished as the dialectical, and Schleiermacher's as the architectonic), the end, the thinking-after the thought of God and so uniting transcendence and immanence. George criticises the doctrines of both Hegel and Schleiermacher as without system in spite of their method. He attempts to supply their chief deficiency. His method, instead of being triadic, like that of Hegel, or tetradic, like that of Schleiermacher, is enneadic. The notions Nothing and Being, uniting in Becoming; Appearance and Disappearance, uniting in Existence; Nothing and Appearance uniting in Beginning; Being and Disappearance uniting in Subsistence; Becoming, Existence, Beginning, Subsistence, uniting in Eternity, -yield a single complex of categories (nine in number), forming what is termed the first Ennead, Being. The Ennead Difference, Identity, and Mediation enables us, according to George, to avoid the extremes pantheism and deism, and conceive God as self-determination. The principle of ideal-realism receives exemplification in George's psychology and logic in his careful regard for both the sensuous and the intellectual, the particular and the universal elements in experience - there is, in his view, no soul without a corresponding nervous system, no thought without sensation, no faith without cognition, no analysis without synthesis, no induction without deduction, no theory without practice, and vice versa — the terms of each of these pairs uniting organically to produce a third which is higher than either. Finally, philosophy, according to George, is not antagonistic to, but rests upon, all other sciences; its pillars as well as theirs are experience and experiment. The system of George presents a formidable appearance, and is not easily characterized intelligibly.

As with George the truth in philosophy lies midway between the standpoints of Hegel and Schleiermacher, so with Chalybæus it is to be found in a combination of the Hegelian and Herbartian principles. To Chalybæus, Hegel represents the ancient objectivity of view, and Herbart the modern subjectivity; in Hegel's doctrine, Being is lost in Becoming, while in Herbart's Becoming is swallowed up in Being; Hegel must be criticized for not uniting principle and method and so forming a system, and for depriving philosophy of teleological coloring, and Herbart for separating unwarrantedly theoretical and practical philosophy, etc. The real end of all human wisdom is ethical personality; and in the fundamental science, which is the theory of knowledge, ethical categories should have a place along with logical and physical, and indeed the highest place. Human thought, as an after-thinking of the divine thought, must bring us to a being (God) who wills, i. e., loves, the truth, and is therefore self-conscious subject. In the concrete external world the fundamental reality, alone making possible all substantiality, causality, reciprocity, corporeality, life, soul is a spatially and temporally infinite materia prima or pura of an ætherial nature, which may be termed soul-æther. The basis of knowledge is consciousness with its (purely modal) categories. Esthetics, ethics, and the philosophy of religion must have a teleological foundation. Religion in man corresponds to revelation in God: these two are united in worship, which is the path leading us to the highest end, the absolute ideal. This last is made possible by the fact that the primal absolute is united with the world, through the realization and union in the world of the Ideas of the Beautiful, the Right and the Good.

The ideal-realism of Hermann Ulrici is of a very pronounced character. "Whenever," says Ulrici, "speculation and empiricism come into conflict, the former is, most probably, wrong." Even the Pythagorean theorem would have fared ill if it had not been verified by measurement. Philosophy without presupposition is a delusion. Every system of philosophy presupposes the fact of human thought, the explanation of which is the chief business of philosophy. Now thought is (1) activity, (2) distinguishing activity (though not simply the act of making distinctions), (3) consciousness and self-consciousness (since it distinguishes itself in itself), (4) can think only in distinctions, i. e., can have a thought only while and in so far as, it distinguishes it from another (hence "pure