DEDUCTION is a particular kind of reasoning or inference. In ordinary language, to deduce means to trace one thing to another as its cause, to show that one proposition follows from some other proposition or propositions. In logic, its signification is more definite. It is usual to oppose deduction to induction (q.v.), and to say that the latter consists in reasoning from particulars to generals, the former in reasoning from generals to particulars. In fact, however, every step in a deduction is also an induction. The several steps of a train of deductive reasoning consist of syllogisms (q.v.), and the major proposition of a syllogism is an induction, or a general proposition expressing the result of a previous induction. The whole object of this kind of reasoning is to show that some particular case or phenomenon really has the marks which bring it under the class to which the general proposition was meant to apply. Thus, the equality of the angles at the base of an isosceles triangle is deduced from the general proposition, "That magnitudes which can be applied to one another so as to coincide are equal," by show ing that the angles in question can be so applied.
Deduction is more properly opposed to experiment. Suppose the question to he as to the relation between the spaces and times in falling bodies, the point may be deter mined in two ways. We may institute experiments, and observe how far bodies do fall in different times, and conclude a general proposition from the particular instances we observed; or we may bring the case under two general principles already established, those, namely, expressed in the first law of motion, and in the nature of gravity as a moving force, and calculate from these how far bodies /eat or must fall in given times. The conclusion or law arrived at in both cases is the same; but in the one ease it is experimental, in the other deductive. It is the tendency of all sciences to become more and more deductive. Knowledge put on a deductive basis is sometimes spoken of as science, par excellence, and the immediate results of observation as empiricism. Mathe matics is essentially a deductive science, and most of the truths in natural philosophy have been gradually put on similar grounds. Chemistry remains almost wholly experi
mental; it can predict or deduce little or nothing regarding an untried case, except, perhaps, the proportion in which two bodies will combine. See REASONING.
DEE, the name of two rivers in Scotland. The larger and more important rises in five wells 4,000 ft. above the sea, near the top of Bracriach mountain, in the neighbor hood of Cairntoul and Ben 31aedhui, 25 m. n.w. of Castleton of Braemar. After flow ing 12 m. s.s.c., it joins the Geauley, at the height of 1294 ft. above the sea. It then tumbles through a narrow chasm in the gneiss rock, called the Linn of Dee, across which a person can leap. After this it runs o.n.o. through Aberdeenshire and a small part of Kincardineshire, and ends in the German ocean at the harbor of Aberdeen. In this course, 96 m. in all, it receives a number of tributaries—the Lui, Mule, Feugh, etc. The basin of the Dee, which is about 1000 sq.m. in area, consists of granite and gneiss in nearly equal areas. In the gneiss occur many beds of primitive limestone, and some masses of trap-rock and serpentine. On the Dee are Balmoral castle and several vil lages much resorted to in summer—Castleton of Braemar, Ballater...kboyne, Kincardine O'Neil, Banchory-Ternan, and Cults. The soil on the Dee is light and sandy and requires much rain. A railway extends up Deeside for 43 m., from Aberdeen to Balloter. See BALMORAL and BRAEMAR.—The smaller Dee rises in Kirkcudbrightshire, near the northern boundary of that county. Its general direction for the first 40 m. is south easterly, after which it flows w. to the Solway Firth, into which it falls at Kirkcud bright bay. The D. divides Kirkcudbright into two nearly equal portions, and near the' center of the county it expands to about the average breadth of a quarter of a mile, pre serving this appearance for about 10 in. of its course, and forming successively Loch Ken, Loch Dee. and Long Loch. It is about 50 m. in length, and is navigable for the last 7 miles. The waters of the D. are noted for their salmon, which are of a darker hue, and are fatter than those of most rivers in the s. of Scotland.