Reduction

“ Reduc′tive, having the power to reduce.—Reduce to the ranks, to degrade, for misconduct, to the condition of a private soldier; Reductio ad absurdum, the proof of a proposition by proving the falsity of its contradictory opposite; Reduction works, smelting works. ”

“ It may be said that the farming interest cannot subsist under a twenty per centum ad valorem duty. My reply is, ‘sufficient for the day is the evil thereof.’ I will leave it to the day when the reduction takes effect, to settle the question. When the reduction takes place, and the farmer cannot live under it, what will he do? ”

“ Population regulates itself by the funds which are to employ it, and therefore always increases or diminishes with the increase or diminution of capital. Every reduction of capital is therefore necessarily followed by a less effective demand for corn, by a fall of price, and by diminished cultivation. ”

“ The necessity of the reduction of our revenues is so apparent as to be generally conceded, but the means by which this end shall be accomplished and the sum of direct benefit which shall result to our citizens present a controversy of the utmost importance. ”

“ A reduction in the hours of labor which is neither universal nor uniform will tend to reduce the net product available for division among the producing classes, but such reduction may be lessened or counteracted by greater efficiency in labor and in the use of capital. ”

“ An enhancement of it is a source of secure gratification and self-respect, and a reduction of it has a very substantial contrary effect. (25*) A reduction of the pecuniary showing is submitted to only reluctantly and tardily, after it has become unavoidable, and only to the least feasible extent. ”

“ Therefore the reduction must be, that the bodies or parts of bodies so intermingled as before be of a certain grossness or magnitude; for the unequalities which move the sight must have a further dimension and quantity than those which operate many other effects. ”

“ These are the men in whom the development is rather low, whose souls are coarsely compounded, so that the reduction is coarse, a sort of activity of coarse hate.
But the men of finer sensibility and finer development, sensuous or conscious, they must proceed more gradually and subtly and finely in the process of reduction. ”

“ Every experiment in the way of reduction which has been made by the Post Office has shown its fallacy; for every reduction whatever leads to a loss of revenue, in the first instance: if the reduction be small, the revenue recovers itself; but if the rates were to be reduced to a penny, revenue would not recover itself for forty or fifty years. ”

“ Now there seems to be an evident connection between the immense sums thus taken from the people and the privations of the lower classes, and it is upon a superficial view natural to suppose that a reduction in the enormous burdens thus uselessly imposed would make it easier for the poorest to get a living. ”

“ Everyone desires a reduction of taxes, and there is a great preponderance of sentiment in favor of taxation reform. ”

“ The Two Needful Readjustments It has been our fate, among all the innumerable generations of mankind, to face the most frightful calamity that has ever befallen the world. There is a basic fact which cannot be denied, and should not be overlooked. For a most important deduction must immediately follow from it. That deduction is that we, who have borne the pains, shall also learn the lesson which they were intended to convey. ”

“ In deduction the law is given, and the effects are required to be found; that is a comparatively easy task in which you will readily excel. But in induction, on the contrary, the effects are given and the law is required to be found ; that is a hard task, in which you often fail, but in which you must, and will, learn to excel. ”

“ This is why there is real utility in the process of deduction, which goes from the general to the general, or from the general to the particular, as well as in the process of induction, which goes from the particular to the particular, or from the particular to the general. It is an old debate among philosophers whether deduction ever gives new knowledge. ”

“ Yet the doctrine that this is so, as well as the law of the force, were established only by this and the like demonstrations. The doctrine which is the hypothesis of the deductive reasoning, is the inference of the inductive process. The special facts which are the basis of the inductive inference, are the conclusion of the train of deduction. And in this manner the deduction establishes the induction. The principle which we gather from the facts is true, because the facts can be derived from it by rigorous demonstration. Induction moves upwards, and deduction downwards, on the same stair. ”

“ The Interrelation of Induction and Deduction.—Induction and deduction must go hand in hand in building up our world of knowledge. Induction gives us the particular facts out of which our system of knowledge is built, furnishes us with the data out of which general truths are formed; deduction allows us to start with the generalization furnished us by induction, and from this vantage ground to organize and systematize our knowledge and, through the discovery of its relations, to unify it and make it usable. ”

“ Deduction is abstraction which posits induction, and induction is abstraction when deduction is posited. Deduction and induction cannot be carried on apart, for deduction is dependent upon induction, and induction is dependent upon deduction, and the attempt to dissever them leads the mind into a fog of speculation where men are lost on the shoreless sea of metaphysics or the endless trail of unrelated facts. ”

“ I assert that in the recent psychology of reasoning, the nature of the deductive process and its principal purpose have been equally misunderstood. Deduction in its more developed forms simply does not consist in an analysis of the premises. Nor is it intended to make you believe the conclusion. The true interest of deduction lies in the fact (1) that it is a process possessing an inexhaustible fecundity, and (2) that this fruitfulness results in giving you a knowledge that certain premises imply certain conclusions. ”

“ That the deductions should be from the whole and not from a part only of the laws of nature that are concerned, would be desirable even if those omitted were so insignificant in comparison with the others, that they might, for most purposes and on most occasions, be left out of the account. ”

“ But Induction cannot march up with quite so sure a stride, nor Deduction descend with so large degrees of certainty, in relation to persons endowed with free-will, as in relation to physical substances held firm in the grip of unvaried law. Still, the doubt always attaches far more to the actions of an individual than to the actions of the masses of men. ”

“ First, Induction more or less busy for two thousand years has given at last an exact and acceptable definition of the Science, and impliedly an exact description of the class of facts with which it is conversant, namely, the Science of Sales, or what is exactly equivalent, the Science of Value; and Deduction at all points along this slow road has helped to correct and to broaden successive imperfect inductions, which an inquisitive and tentative and cautious spirit—the mainspring of Constructive Science—has instituted from time to time. ”

“ He therefore linked induction and deduction closely together, and conceived them as necessarily complementary in scientific investigation. Either induction or deduction alone is absurd and impossible. By induction alone we should be obliged to examine all cases, an impossible undertaking. By deduction alone we should be in the same straits as the Scholastics, and never discover new laws. ”

“ Induction is the mental process by which we ascend to the discovery of general truths; deduction is the process by which the law governing particulars is derived from a knowledge of the law governing the class to which particulars belong. ”

“ The increased wants increase the outlay, which in most cases does not square with the income, and therefore the accounts of many close with a deficit The consequences of this deficit for the happiness, and even for the morals of the family, I leave untouched. ”

“ He prefers induction to deduction, especially the sanctioned unverified deductions of social order. For nature affords the only verification for the logical process of deduction. 'We fear nature too much, to say the least.' For most of us hold to other men's theories instead of making our own. ”

“ And as far as possible in processes of deduction the ideas are emphasised throughout; there is no mere putting in at one end and taking out at the other; the result is examined and described at every stage. ”

“ Yet every movement which we accomplish implies a change in our debit and credit of vital economy, a change in our balance of bodily and mental expenditure and replenishment; and this, if brought to our awareness, is not only interesting, but interesting in the sense either of pleasure or displeasure, since it implies the more or less furtherance or hindrance of our life-processes. ”

“ But deduction, starting from a premise about all the members of a class, compels a conclusion about every and each of necessity. One border-war may be similar to another, and the whole number may be similar, without being similarly evil; but if all alike are evil, each is evil of necessity. ”

“ Because I'm like all reformers, cursed with a certain amount of surplus energy which I don't know how to direct in a more reasonable way. It would be better to spend it on myself—except that there's nothing I want. ”

“ Over against these problems of the psychology of deduction which are possibly capable of a more or less direct experimental research, there are vast numbers of problems of deduction which can be attacked more indirectly, some of them by following the records of formation of new habits, some of them by means of more or less exact study of social processes. ”

“ What we have illustrated of physical induction holds good also of the results of deduction. Every explanation must rest on the inexplicable, and every demonstration must rest on the indemonstrable, while the last alleged inexplicable and indemonstrable belief is an instinct of human nature. ”

“ I have already asserted that induction is the inverse operation of deduction, but the difference is one of such great importance that I must dwell upon it. There are many cases in which we can easily and infallibly do a certain thing but may have much trouble in undoing it. A person may walk into the most complicated labyrinth or the most extensive catacombs, and turn hither and thither at his will ”

“ Whether we regard Induction and Deduction as correlative Processes belonging to one Method, each of which has been disproportionately in vogue at different epochs, or as distinctive Methods, having each their own Deductive and Inductive Processes, in either aspect, Induction is only a preparative labor, leading in the more important work of the application of the Law or Principle derived. ”

“ The necessity of such a survey is confirmed by the consideration, that the stronger inductions are the touch-stone to which we always endeavor to bring the weaker. If we find any means of deducing one of the less strong inductions from stronger ones, it acquires, at once, all the strength of those from which it is deduced; and even adds to that strength; since the independent experience on which the weaker induction previously rested, becomes additional evidence of the truth of the better established law in which it is now found to be included. ”

“ But it is an essential principle of life that a faculty to which circumstances do not allow full exercise diminishes; and that a faculty on which circumstances make excessive demands increases. And so long as this excess and this deficiency continue, there must continue decrease on the one hand, and growth on the other. ”

“ Deduction shows to be necessary, as induction makes familiar, the truths that the value of food for purposes of growth depends not on the quantity of the various organizable materials it contains, but on the quantity of the material most needed; that given a right proportion of materials, the pre-existing structure of the organism limits their availability ”

“ And if a considerable number of labourers are driven elsewhere, the amount of destitution produced by the change is far greater even than that indicated by a threefold increase in the amount of relief given. ”

“ But the fact that they have not been gathered in the interest of a theory but are set down merely as material for deduction, gives them a value, not always attached to figures, and will make them serve as the basis of many a practical reform. ”

“ For this reason, deduction and induction are only then to be relied upon when the first form of reasoning has for its middle proposition one that expresses causality, community of species, or totality, and the latter form of reasoning takes these for its point of departure. The analysis of Deduction is of worth as clarifying and confirming thought, and thus extending its field as often as the syntheses of Induction stand the proof of the process of clarification. ”

“ It lays its foundations upon firm ground. The premises from which it makes its deductions are truths that have the highest sanction; they are axioms that we all recognize; upon them we safely base the reasoning and actions of everyday life and they may be reduced to the metaphysical expression of the physical law that motion seeks the line of least resistance - namely, that men seek to gratify their desires with the least exertion. ”

“ In the other case, the answers were given in words conveying ideas which were supposed to be those most acceptable to the teacher.
It is often helpful to state the opposite of the common expression of a generalization and to suggest that you are willing to maintain this point of view. The best lesson that the writer ever conducted on induction and deduction was begun with the statement: “Induction always begins with a generalization and moves to the consideration of particulars. Deduction always begins with a particular and moves to a generalization.” ”