The earliest generalization in this direction is associated with F.
If there be but one of these uncovered by the generalization, this cannot be sound.
It may be added that we have here no generalization imported from a higher level of culture, but an idea or blend of ideas familiar to primitive thought.
At the beginning is the well-known generalization of Eucl.
The Treaty of Algeciras is essentially a generalization of the Franco-German agreement of the 28th of September 1905.
Granting this is a general truth, it must yet be acknowledged as a special fact, that in fossil birds we have as yet but scanty means of arriving at any precise results which will justify bold generalization in the matter of avine distribution.
We will briefly notice the case of two degrees, which involves an interesting generalization of the method (already explained) of compounding rotations about intersecting axes.
No biological generalization rests on a wider series of observations, or has been subjected to a more critical scrutiny than that every living organism has come into existence from a living portion or portions of a pre-existing organism.
All are contained in the broad generalization that every part of an animal, however minute, has its separate and independent basis in the hereditary substance of the germ cells from which it is derived and may enjoy consequently a separate and independent history.
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.
It was a favourite idea of his that chemical affinity and capillary attraction would eventually be included under the same law, and it was perhaps because of its recalcitrance to this cherished generalization that the undulatory theory of light was distasteful to him.
Relief maps on a small scale necessitate a generalization of the features of the ground, as in the case of ordinary maps, as likewise an exaggeration of the heights.
Their generalization is given by the Euler-Maclaurin formula = I, = 0, = 0, = 0 .
A further generalization was effected by August Kekule, who rejected the hydrochloric acid type as unnecessary, and introduced the methane type and condensed mixed types.
In such a consideration we have to make use not only of the fact just mentioned, but of three important generalizations which serve as it were as implements for the proper estimation of the relationships of any series of organic forms. First of all there is the generalization that the relationships of the various forms of animals (or of plants) to one another is that of the ultimate twigs of a much-branching genealogical tree.
He founded his generalization to a large extent upon the observation that in Gloeosiphonia capillaris two cells completely fuse, and that only one nucleus can be detected in the fused mass.
On the ether hand, a survey of the facts of cellular embryology which were accumulated in regard to a variety of classes within a few years of Kovalevsky's work led to a generalization, independently arrived at by Haeckel and Lankester, to the effect that a lower grade of animals may be distinguished, the Protozoa or Plastidozoa, which consist either of single cells or colonies of equiformal cells, and a higher grade, the Metazoa or Enterozoa, in which the egg-cell by " cell division " gives rise to two layers of cells, the endoderm and the ectoderm, surrounding a primitive digestive chamber, the archenteron.
Their observations on the solid elements led to a remarkable generalization, now known as Dulong and Petit's law.
Materials accumulated far more rapidly, however, than the power of generalization and classification.
Soon after his time, however, this conception was clearly established, and with so large a generalization the mental horizon was widened to conceive of a geography which was a science.
Various chemists had traced numerical sequences among the atomic weights of some of the elements and noted connexions between them and the properties of the different substances; but it was left to him to give a full expression to the generalization, and to treat it not merely as a system of classifying the elements according to certan observed facts, but as a "law of nature" which could be relied upon to predict new facts and to disclose errors in what were supposed to be old facts.
There is no exception to this generalization.
The greatest generalization of this second period, however, was that partly prepared for by d'Orbigny, as will be more fully explained later in this article, and clearly expressed by Agassiz - namely, the law of repetition of ancestral stages of life in the course of the successive stages of individual development.
noticed in their immediate connexion with literary results; but Hallam had little taste for the spacious generalization which such subjects suggest.
However, this is a generalization that does not apply in many specific instances.
Its striated plumage also favours this view, as an evidence of permanent immaturity or generalization of form, since striped feathers are so often the earliest clothing of many of these birds, which only get rid of them at their first moult.
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.
Legendre, in 1783, extended Maclaurin's theorem concerning ellipsoids of revolution to the case of any spheroid of revolution where the attracted point, instead of being limited to the axis or equator, occupied any position in space; and Laplace, in his treatise Theorie du mouvement et de la figure elliptique des planetes (published in 1784), effected a still further generalization by proving, what had been suspected by Legendre, that the theorem was equally true for any confocal ellipsoids.
His genius was one of generalization and abstraction; and the aspirations of the time towards unity and perfection received, by his serene labours, an embodiment denied to them in the troubled world of politics.
Induction is generalization.
Such a generalization will become sounder, if, as is now generally done by anthropologists, the Eskimo with their pyramidal skulls, dull complexion and flat noses are removed into a division by themselves.
Bradley had already perceived, in the case of the two stars previously scrutinized, that the apparent difference of declination from the maximum positions was nearly proportional to the sun's distance from the equinoctial points; and he realized the necessity for more observations before any generalization could be attempted.
Next, he supposes that mind obeys the same law of evolution, and exemplifies integration by generalization, differentiation by the development of the five senses, and determination by the development of the order of consciousness.
A generalization of Galileo's results takes the form that under constant conditions of this kind, force (defined in terms of motion) is constant, and that the superposition of two sets of conditions, if their independence can be secured, results in superposition of the forces associated with them separately.
It must, however, be remembered that so important a generalization is as yet supported upon a somewhat narrow base of observation.
They have much acuteness of perception for the relations of individual objects, but little power of generalization.
al-jebr wa'l-mugabala, transposition and removal (of terms of an equation), the name of a treatise by Mahommed ben Musa al-Khwarizmi), a branch of mathematics which may be defined as the generalization and extension of arithmetic.
Altogether this work is rich in suggestion to the philosophic historian and the anthropologist, though marked by much vagueness of conception and hastiness of generalization.
Moreover, causal induction is itself both synthetic and analytic: according as experiment combines elements into a compound, or resolves a compound into elements, it is the origin of a synthetic or an analytic generalization.
Its terse, epigrammatic phrases sink into the fibre of the mind, and are a healthy warning against crude, immature generalization.
These processes are conceivable only as " modes " of mind, changes in the soul's substance, and the same is true of the higher conceptions, the products of generalization.
The generalization of a class is not, as the conceptual logic assumes, the abstraction of a general idea, but an inference from the analogy of a whole individual thing, e.g.
The perception of its inadequacy in this respect, and the consequent generalization of Hume's problem, are the essential features of the new critical method.
Kant, indeed, was mainly influenced by his strong opposition to the Leibnitzian rationalism, and therefore assigns the categories to understanding, the logical faculty, without consideration of the question, - which might have been suggested by the previous statements of the Dissertation, - what relation these categories held to the empirical notions formed by comparison, abstraction and generalization when directed upon representations of objects.
differential equation known as the Schrodinger equation (or a generalization thereof ).
In fact, it obeys a differential equation known as the Schrodinger equation (or a generalization thereof ).
generalization of the traditional notion of a serial publication.
generalization of the concept of abstraction in that a module is permitted to contain a collection of definitions.
generalization of information theory, but also forms its foundation.
generalization based on feelings of superiority.
Some implications of these results are provided, including a generalization of the CAPM.
This, I pointed out, was just a sweeping generalization.
This is a signal that the text is using the rule of logic called " universal generalization " .
A natural generalization of the problem is: Let M be a von Neumann algebra on a Hilbert space H.
generalization error is very narrow minded.
generalization performance using the number of support vectors.
These agents also engender stimulus generalization gradients similar to those of exteroceptive stimuli as a function of modifications of their chemical composition.
Then the question is: which feature space's maximal margin hyperplane gives the best generalization guarantee?
This maybe a grossly exaggerated generalization of black men's infidelity and perhaps all black men shouldn't be painted with the same brush.
Our results are in keeping with the assumption that generalization, indicated by myeloid metaplasia, has a prodigious impact on prognosis in IMF.
The process of demonization includes generalization, hyperbole, lies and outright slander at times.
torus method can be seen as a direct generalization of methods for periodic orbit continuation and it is extensible to tori of arbitrary dimension.
uncalled-for generalization " .
We must content ourselves by referring to the progress of physical (including chemical) theory, which has led to the great generalization of the conservation of energy; to the discovery of the fundamental chemical identity of the matter of our planet and of other celestial bodies, and of the chemical relations of organic and inorganic bodies; to the advance of astronomical speculation respecting the origin of the solar system, &c.; to the growth of the science of geology which has necessitated the conception of vast and unimaginable periods of time in the past history of our globe, and to the rapid march of the biological sciences which has made us familiar with the simplest types and elements of organism; finally, to the development of the science of anthropology (including comparative psychology, philology, &c.), and to the vast extension and improvement of all branches of historical study.
Von Baer thus prepared the way for Herbert Spencer's generalization of the law of organic evolution as the law of all evolution.
When we come to phenomena such as proliferations, vivipary, the development of Lammas shoots, adventitious buds, epicormic branches, and to those malformations of flowers known as peloria, phyllody, virescence, &c. while assured that definite, and in many cases recognizable, physiological disturbances are,at work, we find ourselves on the borderland between patho~gical and physiological variation, where each case must be examined with dtie regard to all the circumstances, and no generalization seems possible beyond what has been sketched.
The division of the sphere into parallel zones and some of the consequences of this generalization seem to have presented themselves to Parmenides (c. 450 B.C.); but these ideas did not influence the Ionian school of philosophers, who in their treatment of geography preferred to deal with facts demonstrable by flecataeus .
Their quantitative experiments were, however, too rough to permit of accurate generalization; and although Lavoisier and Laplace stated the principle that the same amount of heat must be supplied to decompose a compound as would be produced on its formation, the statement was not based on exact experiment, and only received experimental confirmation much later.
Thomsen and Berthelot independently enunciated a generalization (commonly known as Berthelot's Third Principle, or Principle of Maximum Work), which may be stated in brief as follows: - Every pure chemical reaction is accompanied by evolution of heat.
An explanation of this unwarrantable generalization may be found in the fact that the incident is derived from a source which was unfavourable to the Pharisees: they are described as a Jewish section of men who pretend to set great store by the exactitude of the ancestral tradition and the laws in which the deity delights - as dominant over women-folk - and as sudden and quick in quarrel.
He permits himself a sweeping generalization (vii.
When this fundamental truth had been fully grasped, mathematicians began to inquire whether algebras might not be discovered which obeyed laws different from those obtained by the generalization of arithmetic. The answer to this question has been so manifold as to be almost embarrassing.
The old doctrine of types, which was used by the philosophically minded zoologists (and botanists) of the first half 1 A very subtle and important qualification of this generalization has to be recognized (and was recognized by Darwin) in the fact that owing to the interdependence of the parts of the bodies of living things and their profound chemical interactions and peculiar structural balance (what is called organic polarity) the variation of one single part (a spot of colour, a tooth, a claw, a leaflet) may, and demonstrably does in many cases entail variation of other parts - what are called correlated variations.
Yet, although, as Andral and other French physicians proved, it was extravagant to say that all fevers take their origin from some local inflammation, it was true and most useful to insist, as Broussais vehemently insisted, that "fever" is no substance, but a generalization drawn from symptoms common to many and various diseases springing from many various and often local causes; from causes agreeing perhaps only in the factor of elevation of the temperature of the body.
In illustration of this tendency, he pointed out that mind tends to assimilate a new impression to a previous content, and by generalization to bring as many impressions under as few general conceptions as possible, and succeeds so far as it generalizes from pure experience of the given.
This is a deeper generalization than that which says, "A man is born to trouble as the sparks fly upward."
de Chim., 1805), which contained the germ of his most important generalization, the authors noting that when oxygen and hydrogen combine together by volume, it is in the proportion of one volume of the former to two volumes of the latter.
Yet they are alike in requiring the generalization of the universal and the belief that there are classes which are whole numbers of similars.
Universal inference thus requires particular and universal conceptions as its condition; but, so far as it arises from sense, memory, experience, and involves generalization, it consists of judgments which do not consist of conceptions, but are beliefs in things existing beyond conception.
Bacon seems indeed to have been a lawyer of the first order, with a keen scientific insight into the bearings of isolated facts and a power of generalization which admirably fitted him for the self-imposed task, unfortunately never completed, of digesting or codifying the chaotic mass of the English law.
The details of the logical method on which its author laid the greatest stress have not been found of practical service; 5 yet the fundamental ideas on which the theory rested, the need for rejecting rash generalization, and the necessity for a critical analysis of experience, are as true and valuable now as they were then.
The initial mutations, then, are as follows: The initial mutation of any word depends upon its position in the sentence, and is determined by a grammatical rule which can ordinarily be traced to a generalization of the original phonetic conditions.
"Jethart or Jeddart justice," according to which a man was hanged first and tried afterwards, seems to have been a hasty generalization from a solitary fact - the summary execution in James VI.'s reign of a gang of rogues at the instance of Sir George Home, but has nevertheless passed into a proverb.
He combined the power of patient and minute investigation with a singular faculty for bold generalization and the capacity for tracing out the effects of thoughts and ideas on political and social life.
Having accepted these two conclusions, we formulate the generalization that tracheae can be independently acquired by various branches of Arthropod descent in adaptation to a terrestrial as opposed to an aquatic mode of life.
The discovery by improved optical means, and especially by photography, of new bodies of our system so small that they evaded all scrutiny in former times, is still going on, but does not at present promise any important generalization, unless we regard as such the conclusion that our solar system is a more complex organism than was formerly supposed.
" All men must die " is a generalization which he has scarcely reached; in his philosophy the proposition is more like this - " all men who die die by violence."
The title is of later origin, and rendered possible only by the generalization of the name Maccabee so as to embrace all who suffered for the ancestral faith.
The importance of this generalization cannot be overestimated; it is of more than historical interest, for it remains the basis upon which certain authorities introduce the study of these curves.
An important generalization of the conic sections was developed about the beginning of the 17th century by Girard Desargues and Blaise Pascal.
to describe a circle touching three given circles, which he discovered in 1805, his generalization of Euler's theorem on polyhedra in 1811, and in several other elegant problems. More important is his memoir on wave-propagation which obtained the Grand Prix of the Institut in 1816.
Our method can be seen as a direct generalization of methods for periodic orbit continuation and it is extensible to tori of arbitrary dimension.
You should have stopped at " uncalled-for generalization ".
In the 1970s and 1980s, anorexia was regarded as a disorder of upper- and middle-class women, but that generalization is as of 2004 also changing.
This is in contrast to the normal child's development, where incidental learning and generalization are the hallmarks of language acquisition.
This is in decided contrast to the normal child's case, where incidental learning and generalization are the hallmarks of language acquisition.
Rather than a specific picture of a certain part of you, your zodiac sign gives a great generalization of major characteristics.
However, the tide is changing, and while the common theory is that two parents are still better than one parent, psychologists and other professionals are starting to decry the all or nothing generalization.
Holding that chemistry had not attained the rank of a science - his lectures dealt with the "effects of heat and mixture" - he had an almost morbid horror of hasty generalization or of anything that had the pretensions of a fully fledged system.
He was wanting in mathematical ability, and never displayed in any remarkable degree the still more important power of scientific generalization, which, whether accompanied by mathematical skill or not, never fails to mark the highest genius in physical science.
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