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belief, any simple idea, any sentiment, any principle of right or of beauty? To what is appeal To be made in disproving or bringing into doubt one of these original ideas, or in asserting even the fact that the existence of such ideas has been brought into controversy?
All languages exhibit words signifying knowledge, certainty. Whence comes this idea of knowledge? To deny the possibility of knowledge implies an idea of the thing denied. If we have the idea of knowledge, what is it? Can it be anything less clear than that which is seen in its own light, without aid from anything more clear? Is it not absurd to suppose a thing to be proved by anything less clear than that which it proves?
Knowledge, we have just said,cannot be denied without implying an idea of what it is to know. What then would be knowledge, if it were possible? Anything different from what we already have? Could it be anything more than conscious seeing, immediate, direct, distinct intuition? If such a thing'may be, and if what we now call knowledge has all the marks which any supposable knowledge can be conceived to have, what more have we reason to demand?
The higher, the fundamental philosophy, it is clear, does not attempt to contradict or to supersede the Baconian or the Aristotelean logic; it, consists entirely with the methods of reasoning employed in the sciences; indeed, its grand aim is, instead of destroying, to justify these methods, and to place their results in the mental and the material worlds, beyond the reach of scepticism or cavil, by showing that nothing is assumed in our induction or deduction which has not the sanction of our mental constitution, and therefore of Him who so mysteriously and wonderfully organized our physical and spiritual being.
What then, according to this philosophy, may I be said to know? Why, undoubtedly, in the first place, all that is proved, demonstrated; and secondly, all that I see clearly without proof, directly, intuitively. There is no third way of knowing, possible or conceivable. That which is proved depends upon something else which is not proved; no argument can commence without an assumption; it may be a definition as in Mathematics, or a fact as in Chemistry, or a proposition dependent on a foregoing demonstration. Ultimately, all reasoned truths will be found to rest upon truths which are not reasoned, not obtained by any induction, truths seen in their own light, not capable of proof for the very reason that they need no proof; so plain that nothing plainer can be found to illustrate them. What is proved then, at last, is traced to what is seen directly, without the aid of proof. If it were not so, inasmuch as every argument is substantially an inference of something not known from something known, the. series of arguments must be infinite. And besides, in all demonstration, every step involves an intuition; each successive step is indeed an intuition. In the first Theorem of Euclid, the idea of a point, a line, a circle, an angle, a triangle, is intuitive; and the perceptions of equality and coincidence, which constitute the several stages of the argument and the conclusion itself, are each and all direct judgments of the intellect. And therefore the whole demonstration is but a series of intuitions or direct judgments; and every mathematical demonstration is resolved at last into propositions not proved and not admitting of proof — self-evident, intuitive propositions.
The same is true of moral reasoning—of all reasoning. The premises, whether matters of fact or primary judgments of the reason, and the successive conceptions on to the final proposition, are all immediate, direct cognitions, original acts of knowledge. Thus, in Paley's Argument for the Divine Benevolence, the first proposition is a primary judgment of the reason; "when God created the human species, either He wished their happiness, or He wished their misery, or He was indifferent about both." In this proposition (to say nothing of the ideas attached to each word, as " God," "created," etc.) in the general proposition, we have expressed an original immediate judgment; the truth of the alternative presented is seen directly, not by any induction, not by means of any intermediate idea; he who does not assent to it cannot be induced to do so by argument; it is as much an intuitive perception as that of coincidence or equality in the demonstration of the first Theorem in Euclid. Of the same nature is the second proposition in Mr. Paley's Argument: u If He had wished our misery, He might have made sure of His purpose by forming our senses to be so many sores and pains to us," etc. Again: "If He had been indifferent about our happiness or misery, we must impute to our good fortune both the capacity of our senses to receive pleasure and the supply of external objects fitted to produce it." But either of these, and especially both of them, being too much to be attributed to accident, nothing remains but the first supposition, that God wished our happiness. The propositions implied in this part of the argument, viz.: that such adaptations cannot be the work of accident, and that therefore God wished our happiness, are expressions of immediate, intuitive judgments. And so of every proposition in the following form of the argument: " Contrivance proves design; the predominant tendency of the contrivance indicates the disposition of the designer. The world abounds with contrivances, and all the contrivances which we are acquainted with, are directed to beneficial purposes. We conclude therefore that God wills and wishes the happiness of His creatures." The first two of these propositions are primitive judgments of the reason; the two following, judgments of the reason upon the intuitions of sense or the testimony of others; the conclusion, the final sequence, a simple judgment of the reason. Arguments are, then, all resolvable into primary intuitions, either of sense or of reason.
In searching for the elements or original ideas of the human mind, we may thenceforth assume them to be contained in the intuitions of which we are made capable by our intellectual constitution; in being capable of which our intellectual constitution consists; to fit us for which was to create us rational beings; for evidently if we could know nothing directly, we could know nothing at all, all knowledge acquired by demonstration depending ultimately, as we have just seen, upon immediate, intuitive judgments.
What then are these original, intuitive ideas? Why, 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 aesthetic 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, Ot 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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