Determined by increasing generality as by increasing speciality.
The flight from a cursory survey of facts to wide so-called principles must give way to a gradual progress upward from propositions of minimum to those of medium generality, and in these consists the fruitfulness of science.
For The Sake Of Greater Generality, The Days Of The Week Are Denoted By The First Seven Letters Of The Alphabet, A, B, C, D, E, F, G, Which Are Placed In The Calendar Beside The Days Of The Year, So That A Stands Opposite The First Day Of January, B Opposite The Second, And So On To G, Which Stands Opposite The Seventh; After Which A Returns To The Eighth, And So On Through The 365 Days Of The Year.
That teaches us what we ought to believe in history as it is compiled according to ostensible events and results known to the generality of people."
But inferences of this class have hardly attained to sufficient certainty and generality to be set down in the form of rules.
Cherries and the generality of plums succeed very well either on an east or a west aspect.
Yet Burke threw such breadth and generality over all he wrote that even these propositions, relative as they were, form a short manual of statesmanship.
This selection of one market for detailed examination does not rob our sketch of generality, as might at first be thought, since broadly the history of the development of one market is the history of the development of all, and on the whole the economic explanation of the evolution that has taken place may be universalized.
However, it is made clear as the result of an elaborate examination that the generality of these correspondences cannot be affirmed.'
Isomorphism is most clearly discerned between elements of analogous chemical properties; and from the wide generality of such observations attempts have been made to form a classification of elements based on isomorphous replacements.
Without astonishment," even to himself, regard being had to the great generality of the differential equations, he reached a result so wide as to include, as a particular case, the solution of the planetary problem recently obtained by him.
To this entire branch of knowledge, in short, he successfully imparted that character of generality and completeness towards which his labours invariably tended.
In the limiting case in which the medium is regarded as absolutely incompressible S vanishes; but, in order that equations (2) may preserve their generality, we must suppose a at the same time to become infinite, and replace a 2 3 by a new function of the co-ordinates.
The law of gravitation is unique among the laws of nature, not only in its wide generality, taking the whole universe in its scope, but in the fact that, so far as yet known, it is absolutely unmodified by any condition or cause whatever.
Or spirit or generality hitherto confined to philosophy, and to give to philosophy the rigour and solidity of science.
Spencer's two chief points are these: (i) He denies that the principle of Criticism the development of the sciences is the principle of on Comte's decreasing generality; he asserts that there are as classifica= many examples of the advent of a science being tion.
In formulating these facts Liebig at first retained the dualistic conception of the structure of acids; but he shortly afterwards perceived that this view lacked generality since the halogen acids, which contained no oxygen but yet formed salts exactly similar in properties to those containing oxygen, could not be so regarded.
Napoleon in like case refused, at the risk of enforced resignation, but so did Moreau; the generality of lesser men have obeyed, but so did Suvarov.
The mild rule of Ferdinand, his solicitude for the welfare of his subjects, his enlightened patronage of art and science, his encouragement of commerce, and his toleration render him an honourable exception to the generality of Italian princes.
The generality of treatment is indeed remarkable; he gives as the fundamental property of all the conics the equivalent of the Cartesian equation referred to oblique axes (consisting of a diameter and the tangent at its extremity) obtained by cutting an oblique circular cone in any manner, and the axes appear only as a particular case after he has shown that the property of the conic can be expressed in the same form with reference to any new diameter and the tangent at its extremity.
He means that a sophist like Protagoras will teach superficially anything as wisdom for money; and that even a dialectician like Plato will write a dialogue, such as the Republic, nominally about justice, but really about all things from the generality of the form of good, instead of from appropriate moral principles; but that a primary philosopher selects as a definite subject all things as such without interfering with the special sciences of different things each in its kind (Met.
This law cannot be maintained in its generality, but nevertheless highly dispersive substances like carbon bisulphide are always found to produce a greater shift than liquids of smaller dispersion like water and alcohol.
Both parties put themselves in the wrong, the province by refusing its quota to the federal war-sheet, the generality by dealing with individual towns instead of with the states of the province.
By comparing England with other countries we may be able in the distant future to reach conclusions of some generality as to the laws of growth, maturity and decay of industrial nations.
Moreover, he compared dialectic and sophistry, on account of their generality, with primary philosophy in the Metaphysics (P 2, 1004 b 17-26); to the effect that all three concern themselves with all things, but that about everything metaphysics is scientific, dialectic tentative, sophistry apparent, not real.
On the theoretical side the question is open until we introduce some limitation upon the generality of the functions.