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evidently, directly or indirectly, all that we are made capable of knowing; all knowledge at last appears in this form. To enumerate these primary intuitions would of course be to detail the infinitely varied immediate acts of knowledge of the objects of human thought.

The most general and most marked division of them is into intuitions of sense and intuitions of reason; the former supposing always the use of some one of the external senses as the organ of the cognitive faculty, the latter including such intuitions as have their origin immediately in the thinking principle itself. This last class are again subdivided into intellectual, moral, and æsthetic intuitions, the first giving us our ideas of the true, the second our ideas of the good, the last our ideas of the beautiful.

Our remaining remarks will be confined chiefly to the first of these divisions, viz.: purely intellectual judgments; of themselves quite too numerous and too various to be intelligently treated under a single head, and therefore to some extent, for convenience, subdivided into distinct varieties. The most important of these varieties are the ideas of cause, of space, of time, of substance, of quality, of law, of number, of identity, of design, of infinity, etc.; the mathematical axioms, and the fidelity of the senses, of the cognitive power and of memory.

In support of the fact of the existence of such ideas, as the original furniture of the human mind, or more properly as necessary elements of its very first thoughts, provided for in its constitution, and indispensable, because constituent parts of all its subsequent knowledge, we appeal to human experience, the experience of mind. They are of course, if found anywhere, to be found in the consciousness. Whether they be indeed there, we learn as we learn the existence of thought or feeling in general, by introspection of ourselves. By a beautiful provision of nature, the existence of such truths is questioned only by cultivated, curious, reasoning mind; and such mind is fitted by its habits to settle the question which it raises. It is a philosophic question, disturbing philosphers only, and to be answered by philosophers, upon philosophic grounds.

Some of these ideas, or intellectual states, are of such a character as not to admit of denial or of doubt. To deny one's own existence is an absurdity; to doubt it is an absurdity. A denial or a doubt supposes a denier or a doubter. To see, supposes something seen; to question the truth of a past sensation or thought implies the continued existence of the thinker, his personal identity. Action, reflection, hope, all pre-suppose a feeling of our own existence and identity, and a dependence on the truthfulness of our powers, and the connection of cause and effect. On no other grounds could we hope or fear, or remember or act. Thus, while reasoning sometimes fails to convince, we are daily and hourly impelled by this voice of our Maker speaking through our very constitution, to every action, precaution and enterprise, every hope and fear of life, even while at the same time we may be questioning the voice that directs us.

The notion of an argument to prove or disprove such truths is absurd; for argument is made up of them. The mind that denies them cannot be reasoned with; it wants the common features, the characteristic, essential elements of reason.

The only account to be given of original, intuitive ideas, is to describe them, so to mark them as to direct the consciousness of others to them, among the phenomena of their own minds. If they be able to recognize them there, they need no other evidence of their existence; if not, there is no way of proving them.

The foregoing remarks suggest the true distinction between mathematical and moral science. Mathematics has important incidental peculiarities in the definite nature of its subjects, viz.: extension and quantity, and the corresponding fewness and measure of its terms. The logical process is, of course, more simple and therefore somewhat easier and in these respects more infallible than the complicated processes involved in extensive argument upon matters of fact, in which numerous circumstances are to be considered, and the meaning of words watchfully guarded.

A more essential peculiarity of mathematical reasoning is, that the data are mere assumptions, definitions, concep

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tions of our own, while the moral sciences start with facts. This circumstance accounts in part for the singular definiteness of its terms; if these terms conform to our ideas, that is all we require. In the sciences of fact, we demand that our ideas should conform to nature, as well as our words to our ideas. It would, however, be extravagant to assert that on account of these differences, truth is confined to Mathematics. It were hardly more extravagant to say that truth is not found in Mathematics. Fact, reality, is certainly not found there. Not setting out with facts, its reasonings can never lead to facts. It is hypothesis all. If we can be said to know nothing certainly out of Mathematics, we can be said to know nothing really anywhere.

But is it so ? Is nothing certain beyond the sphere of Mathematics?

Mathematical truth rests ultimately on definitions, conceptions of the reason, ideas of lines, angles, circles, etc. Moral reasoning rests for the most part upon ideas of sense or of consciousness.

That we truly have such ideas in both cases, we know by precisely the same means, the testimony of our own minds; they do see these ideas in themselves. That in the case of sight there is a thing seen and a seer, we know by the same testimony; we directly see both. Can evidence be higher or

clearer ?

We may make wrong inferences; but the senses do not deceive us. It was a wrong inference from the testimony of the senses, that the sun revolves about the earth; there is another alternative equally consistent with the testimony of the senses, viz., that the earth moves round on its own axis. The fact of a relative motion is all that is attested by the eye; this may be either motion in the earth or the sun; the visual effect will be the same in both cases, as we see illustrated in sailing along the shore, or passing a stationary train of cars upon a railroad; it is impossible to say, so far as the eye is concerned, which is moving, the boat or the shore, the standing or the passing train. If motion itself were denied, it would contradict the senses. The fact of motion they are competent to know; for our inferences they are not

responsible. So far are the senses from being uncertain inlets of knowledge that they, in fact, furnish us with our most expressive language of certainty; to be as clear as sight is to be past all doubt.

In the purely logical process, which is, as we have seen, intuitive at every step, in all reasoning, there can, of course, be no essential difference between mathematical and moral reasoning. The axioms that constitute the successive links of the chain in the one, are no more certain than those equally intuitive judgments which complete the other. That the whole is greater than a part is not clearer than that design implies a designer. Is my notion of sequence among the relations of lines and angles any more certain than my notion of antecedent and consequent among the feelings of my own mind? Is my idea of body or of space less certain than are my ideas of the admeasurements of body or space, their mathematical affections? Yet the ideas of body and of space, and even of extension itself, which the mathematician considers, are metaphysical. The notion of time, whose various portions the mathematician computes, is not itself giv en by Mathematics. The infinity to which his parallel lines are supposed to be extended, is a metaphysical idea. Indeed, the very subjects whose extension and quantity he deals with, and without a notion of which he could have no extension or quantity, are furnished by the metaphysician, and cannot be less certain than the notions built upon them.

Is any proposition in Euclid more certain than my own existence, or yours, or that of the earth, or of Paris, or of Bonaparte,-of matter and mind and God? If not, what becomes of the conceit that there is no certainty beyond the limits of the Mathematics? Scepticism without those limits is scepticism within them; truth in all science reposes on the same basis, the original laws of our mental constitution.

To a reasoner against the certainty of all but mathematical demonstration, may it not be replied: "Is your reasoning mathematical? If not, permit us to doubt; for mathematical reasoning alone is indubitable." And what has the reasoner to say? It is. not to be denied that the Mathematics, owing to the nature of the sub

jects as conceptions of our own minds, definitions, and in some degree also to the comparatively small number and unvarying use of its approprate words, has remarkable advantages over all the other sciences. It is no more to be doubted that its principles have, like the ideas of right and beauty, this dignity, that they seem to belong to the Eternal Mind as well as our finite intellect; all material nature is founded on them; though nowhere unmodified, they are everywhere involved as the ground principles of the physical universe. But that we are confined to the sphere of this science for all absolute certainty is incapable of proof, upon the very principle of the argument by which the proposition is maintained. Indeed, if we know nothing out of Mathematics, we for the same reason know nothing in Mathematics; for if our immediate intuitions are knowledge, they carry us into the whole field of nature and of mind; if they are not knowledge, what do we know of equality and sequence in the relations of our ideal lines and angles? Are these anything more than immediate intuitions?

The philosophy of human knowledge proposing, as we have said, to settle the laws of belief, the ground principles of all science, serves, we think, to throw some light upon another question of more moment still, if possible, the question, first raised, and naturally enough, in the bosom of the Roman Catholic church, but entertained to some extent among Protestants, between Faith and Reason. To deter awakening minds from inquiry and investigation, and to secure the credit of Tradition, an appeal has been made to the authority of revelation; the judgments of cultivated reason have been repressed as presumptuous and profane. By another class of theologians, the same appeal has been made from wholly different and infinitely better motives. Men of no worldly policy, and no design to prop a tottering fabric of superstition, have occasionally, at different periods, been so offended by the aberrations of opinion, and have become so impatient of the weary progress of truth in the world, that they have come to distrust our human capacities altogether, and to give up all hope of light but from a supernatural revelation. They are right, clearly, in despairing of the human mind

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