constitution of the mind itself, and are virtually prior to all experience, they cannot all of them be referred to Laws of Thought properly so called. For thought, as thought, cannot be limited to any special class of objects: its laws must operate in all cases alike, whatever be the matter on which it is engaged. That every triangle has its angles equal to two right angles, is indeed a necessary truth; but it is true of triangles only, and cannot be applied to any other object. But that the same subject cannot possess contradictory attributes, is a principle equally applicable to the objects of geometrical demonstration and to the most contingent facts of sensible experience. It is equally certain, that no man can at once be standing and not standing, as that the angles of a triangle cannot be both equal and unequal to two right angles. Hence the criterion of absolute - necessity, though valid as far as it goes, is not his adequate to determine the whole question. It serves to distinguish judgments à priori from judgments of experience: it does not distinguish between different classes of the former, nor explain their several relations to the mind, which is the common source of all. Of the various judgments which have been enumerated by philosophers as necessary truths, it will be sufficient for our present purpose to select three classes, which may be severally distinguished as Mathematical, Metaphysical, and Logical Necessity. All these, being

in different ways regarded as absolutely and universally necessary, must be considered as in different ways dependent on laws of our mental

constitution. From all, must be distinguished what

is commonly called Physical Necessity, or belief in the permanence of Laws of Nature. The several distinctions may be represented by the following questions.

I. Why do I judge, that a triangle can under no circumstances whatever have more or less than two right angles?

II. Why do I judge, that every sensible quality must belong to some subject, and that every change is and must be brought about by some cause?

III. Why do I judge, that two contradictory attributes can under no circumstances whatever coexist in the same subject?

IV. Why do I judge, that the alternations of day and night will not, under the existing circumstances of our globe, cease to take place?

The last of these obviously stands on a different ground from the other three. I am immediately cognisant of law only as I am conscious of its obligation upon myself. The law itself may be physical, intellectual, or moral; but to know it as a law, I must know it as a condition which I cannot or ought not to transgress. Law, in this sense, as a discerned obligation, can obviously exist only in relation to a conscious agent; and

kids ecerrily

even with regard to conscious agents, other than myself, I only infer the existence of the law from a supposed similarity between their constitutions and my own. But, as regards unconscious agents, Law means no more than a constantly observed fact in its highest generalization. When I speak of the alternations of day and night as consequent on a law of nature, I mean no more than that the alternation has invariably been observed to take place and, when I resolve such alternations into the law of the earth's rotation, I mean only that the earth does constantly revolve on her axis once in twenty-four hours. Or, if I could resolve all the phenomena of the material world into an universal law of gravitation, I should obtain no more than the universal fact, that all particles of matter in the universe do gravitate towards each other, and that certain subordinate combinations of those particles present certain phenomena in so doing. But I have not, by this resolution, got any nearer to necessity; for the gravitation of bodies in the inverse ratio of the square of the distance is, like the ebb and flow of the tides, or the elliptical orbits of the planets, an observed fact in the order of nature, and it is no more. My belief in the continuance of this observed order may perhaps be explained by some law of my mental constitution; but, as thus explained, it is a law of mind, and not of matter. Under what

* See Stewart, Elements, vol. ii. ch. 2. sect. 4.

circumstances certain facts of nature may be resolved into others, and what kinds of experiment and observation will contribute to this end, are questions which, with all their importance, are totally distinct from those which form the object of the present inquiry.

I shall only observe here, that to call such questions a portion of Logic, that is, to regard the New Organon as a supplement to the Old, and both as forming parts of the same Science, is to confound two essentially distinct branches of knowledge, distinct in their end, in their means, and in their evidence". "We do not enlarge the sciences," says Kant, "but disfigure them, when we suffer their boundaries to run into one another." The confusion produced in the present instance is perhaps the most injurious of all to sound thinking, a confusion between the mental self and its sensible objects, the ego and the non-ego, the positive and negative poles of speculative philosophy.

On this distinction some excellent remarks will be found in M. Jouffroy's Preface to his translation of Reid, p. 43.

CHAP. IV.

ON THE PSYCHOLOGICAL CHARACTER OF MATHEMATICAL NECESSITY.

IT has been already observed, that whatever truths we are compelled to admit, as every where and at all times necessary, must have their origin, not without, in the laws of the sensible world, but within, in the constitution of the mind itself. Sundry attempts have, indeed, been made to derive them from sensible experience and constant association of ideas; but this explanation is refuted by a criterion decisive of the fate of all hypotheses; it does not account for the phenomena. It does not account for the fact, that other associations, as frequent and as uniform, are incapable of producing a higher conviction than that of a relative

a

"La preuve originaire des vérités nécessaires vient du seul entendement, et les autres vérités viennent des expériences ou des observations des sens. Notre esprit est capable de connoitre les unes et les autres, mais il est la source des premières, et quelque nombre d'expériences particulières qu'on puisse avoir d'une vérité universelle, on ne sauroit s'en assurer pour toujours par l'induction, sans en connoitre la nécessité par la raison." Leibnitz, Nouv. Essais, 1. i. ch. 1.

b See, for example, Mill's Logic, vol. i. p. 305.