During the last two centuries deduction has gone steadily out, and psychology come in.
An instantaneous deduction from the relation w= 2 n0 is that forms of uneven orders possess only invariants of even degree in the coefficients.
It is proportional, and is collected by deduction from salaries and pensions paid to servants of the state, where it is assessed on three-eighths of the income, and from interest on consolidated stock, where it is assessed on the whole amount; and by register in the cases of private individuals, who pay on three-fourths of their income, professional men, capitalists or manufacturers, who pay on one-half or nine-twentieths of their income.
The transcendental deduction, or proof from the possibility of experience in general, which forms the vital centre of the Kantian scheme, is wanting in Reid; or, at all events, if the spirit of the proof is occasionally present, it is nowhere adequately developed.
When he wrote his Logic he had learned from Comte that the a posteriori method - in the form which he chose to call "inverse deduction" - was the only mode of arriving at truth in general sociology; and his admission of this at once renders the essay obsolete.
On the gross products of mines of vein formation, and from Io% to 20% on those of mines of deposit formation; the percentages are calculated on the value of the mineral after deduction of freight, &c. to Europe and of treatment.
This theological deduction from his doctrine drew upon Roscellinus the polemic of his most celebrated opponent, Anselm of Canterbury (1033-1109).
As the amount of ash varies very considerably in different coals, and stands in no relation to the proportion of the other constituents, it is necessary in forming a chemical classification to compute the results of analysis after deduction of the ash and hygroscopic water.
The parts of the Critique of Pure Reason, more particularly the " Deduction of the Categories " in which this theory is worked out, may be said to have laid the foundation of modern idealism - " articulum stantis aut cadentis dectrinae."
Another deduction from the same proposition is that any corporation or private body which appears to exercise sovereign powers together with the state does so only by delegation.
That Smith does, however, largely employ the deductive method is certain; and that method is legitimate when the premises from which the deduction sets out are known universal facts of human nature and properties of external objects.
After every deduction it remains true that no contemporary showed equal genius as a colonial statesman, or in this 'department rendered equal service to his country.
This deduction harmonized the observations of Andrews and of Hess previously alluded to, and also accounted satisfactorily for the Law of Thermoneutrality.
In the East, mysticism is not so much a specific phenomenon as a natural deduction from the dominant philosophic systems, and the normal expression of religious feeling in the lands in which it appears.
" The distinction seems to be that if the destruction be permanent, though partial, the failure of the subject let will give relief by entitling the tenant to renounce the lease, unless a deduction shall be allowed, but that if it be merely temporary or occasional, it will not entitle the tenant to relief " (Bell's Prin.
This generalization was of great value inasmuch as it permitted the deduction of the atomic weight of a non-gasifiable element from a study of the densities of its gasifiable compounds.
The susceptibility is therefore constant and independent of the field, while its negative sign indicates that the substance is diamagnetic. There being no resistance, the induced current will continue to circulate 1 This deduction from Ewing's theory appears to have been first suggested by J.
Thus a universal science of matter and motion was derived, by an unbroken sequence of deduction, from one radical principle; and analytical mechanics assumed the clear and complete form of logical perfection which it now wears.
The five processes of deduction then reduce to four, which may be described as (i.) subtraction, (ii.) division, (iii.) (a) taking a root, (iii.) (b) taking logarithms. It will be found that these (and particularly the first three) cover practically all the processes legitimately adopted in the elementary theory of the solution of equations; other processes being sometimes liable to introduce roots which do not satisfy the original equation.
The middle element alone contributes without deduction; the effect of every other must be found by introduction of a resolving factor, equal to cos 0, if 0 represent the difference of phase between this element and the resultant.
All units of thought) are (1) analysable only by abstraction, and (2) are compound of deduction and induction, i.e.
Per standard ounce troy, no deduction being made for wastage, seigniorage, the purchase of alloy metal, or the expense of manufacture.
Modern theory accepts the deduction, but ascribes the momentum to the revolving ions in the molecules of matter traversed by the light; for the magneto-optic effect is present only in material media.
Money, "the great wheel of circulation," is altogether different from the goods which are circulated by means of it; it is a costly instrument by means of which all that each individual receives is distributed to him; and the expenditure required, first to provide it, and afterwards to maintain it, is a deduction from the net revenue of the society.
From 1796 date the Briefe Ã¼ber Dogmatismus and Kriticismus, an admirably written critique of the ultimate issues of the Kantian system; from 1797 the essay entitled Neue Deduction des Naturrechts, which to some extent anticipated Fichte's treatment in the Grundlage des Naturrechts, published in 1796, but not before Schelling's essay had been received by the editors of the Journal.'
When, however, he had succeeded in extracting from the sources a general idea that seemed to him clear and simple, he attached himself to it as if to the truth itself, employing dialectic of the most penetrating, subtle and even paradoxical character in his deduction of the logical consequences.
We have seen how its utilization in the " structure theory " permitted great clarification, and attempts were not wanting for the deduction of analogies or a periodicity between elements.
But on the assumption that "mathematics" is to denote a science well marked out by its subject matter and its methods from other topics of thought, and that at least it is to include all topics habitually assigned to it, there is now no option but to employ "mathematics" in the general sense' of the "science concerned with the logical deduction of consequences from the general premisses of all reasoning."
The foregoing account of the nature of mathematics necessitates a strict deduction of the general properties ' The first unqualified explicit statement of part of this definition seems to be by B.
When once the fixed conditions which any hypothetical group of entities are to satisfy have been precisely formulated, the deduction of the further propositions, which also will hold respecting them, can proceed in complete independence of the question as to whether or no any such group of entities can be found in the world of phenomena.
Mechanics (including dynamical astronomy) is that subject among those traditionally classed as "applied" which has been most completely transfused by mathematics - that is to say, which is studied with the deductive spirit of the pure mathematician, and not with the covert inductive intention overlaid with the superficial forms of deduction, characteristic of the applied mathematician.
We may generalize these statements in the following theorem, which is an important deduction from a wider theorem due to G.
Amongst the brilliant group of mathematicians whose magnanimous rivalry contributed to accomplish the task of generalization and deduction reserved for the 18th century, Lagrange occupies an eminent place.
In one case the hysteresis loss per cubic centimetre per cycle was 16,100 ergs for B =1 5,900, and only 1200 ergs for B = 20,200, the highest induction obtained in the experiment; possibly it would have vanished before B had reached 21,000.2 These experiments prove that actual friction must be almost entirely absent, and, as Baily remarks, the agreement of the results with the previously suggested deduction affords a strong verification of Ewing's form of the molecular theory.
Special attention was called by the minister to the fact that the system of contributions of officials to the pension funds has been modified, the deduction from salaries being now To °A instead of 5%, and the contributions to the funds being made as to one-third by the treasury, and two-thirds by the officials, instead of the reverse as formerly: the economy effected is about £T30o,000.
Four-fifths of the net product of the revenues, after deduction of the first charge of £T590,000, was to be applied.to the service of the interest on the new reduced debt, and provided that the four-fifths were sufficient to allow the distribution of 1% interest, one-fifth was to be devoted to sinking fund; but this latter fifth was to be reduced, if necessary, by an amount sufficient to maintain the rate of interest at i %.