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Hypothesis defined, 115. Theory, 115. No explanation of uniform-

ities, 116. The "laws of nature," 116. Incident in the life of Darwin, 117.

Rules for legitimacy of hypotheses, 118. Vera causa, 118. Mill's defini-
tion, 119. Discovery of planet Neptune, 120. Darwin's theory of coral
islands, 121. Helmholtz on forming hypotheses, 124. Whewell on the

Greek physical philosophy, 125. Davis on function of hypothesis, 126.

Value of false hypotheses, 127.

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Helmont, 161. Post hoc, ergo propter hoc, 162.

INDUCTIVE LOGIC.

CHAPTER I.

INTRODUCTORY.

INDUCTIVE Logic is the Science of the Discovery of Facts not directly observable. A few facts are known to us without discovery. Such are our personal identity, moral freedom, and obligation. Certain truths also are recognized by the mind as certain as soon as they are suggested. Evidence is not required to establish them, nor can it in any way confirm them. Of these are the axioms of Mathematics and the canons of Deductive Logic. This furniture is the same for all minds and the possession of it is what makes thinking possible. Only all minds do not with equal clearness analyze their own operations, and the most lack the patience, concentration, and strength to follow admitted principles to their ultimate consequences.

Whole sciences have been built up by simply developing the necessary implications of the few simple but universal truths intuitively perceived by every mind. Deductive Logic and Mathematics are examples. One peculiarity of them is that they are the same for all minds, and that when the terms used are precisely understood there is no difference of opinion possible among sane men. These are pure sciences; they do not depend upon the actual existence of any person or thing, but we know that whatever does exist, necessarily conforms to them. If numbers or quantities of objects exist anywhere, they are in mathematical relations; if correct thinking upon any subject is done by rational beings anywhere, it is done according to the rules of deductive logic.

But the great bulk of our knowledge does not come to us by intuition. Beyond the few facts and truths with which the mind starts, lies the whole universe of reality, which we can know only through observation. Over against the pure sciences stand the applied sciences. The main value of the pure sciences is in the fact that they furnish the principles for constructing the applied sciences. The latter have no new formal principles of their own.

This last point is of supreme importance for the purpose now in hand. It has been extensively supposed that the field of thinking was divided into two kingdoms, ruled by two sovereigns, Deductive and Inductive Logic, under dissimilar constitutions, and that what was bad law in one kingdom might be good law in the other. It has been assumed that sometimes two thoughts which could show no right to union in the domain of Deduction could cross the border and, by a sort of Gretna Green marriage, make a synthesis in the kingdom of Induction. A little reflection should have shown all this to be a huge mistake. The canons of deductive logic are the universal laws of thought. They are invariably true, if ever true. The only

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