In thus reverting to the crudities of certain Pythagoreans, he laid himself open to the criticisms of Aristotle, who, in his Metaphysics, recognizing amongst contemporary Platonists three principal groups - (1) those who, like Plato, distinguished mathematical and ideal numbers; (2) those who, like Xenocrates, identified them; and (3) those who, like Speusippus, postulated mathematical numbers only - has much to say against the Xenocratean interpretation of the theory, and in particular points out that, if the ideas are numbers made up of arithmetical units, they not only cease to be principles, but also become subject to arithmetical operations.
For the world as a whole, however, he postulated a beginning in time (whence his use of the word creation), and further supposed that the impulse of organization which was conveyed to chaotic matter by the Creator issued from a central point in the infinite space spreading gradually outwards.
Though again in the Transcendental Dialect he spoke of pure reason conceiving " ideals " of noumena, he did not mean that a noumenon is nothing but a thought arising only through thinking, or projected by reason, but meant that pure reason can only conceive the " ideal " while, over and above the " ideal " of pure reason, a noumenon is a real thing, a thing in itself, which is not indeed known, but whose existence is postulated by practical reason in the three instances of God, freedom, and immortality.
This Barlaam held to be polytheistic, inasmuch as it postulated two eternal substances, a visible and an invisible God.
Cuenot, in order to explain certain features in the hereditary transmission of coat colour in mice, postulated the hypothesis that the grey colour of the wild mouse (which is known to be a compound of black, chocolate and yellow pigments) may be due either to the interaction of a single ferment and three chromogens, or vice versa, to one chromogenic substance and three ferments.
The assertion preserved by Stobaeus that Thales recognized, together with the material element " water," " mind," which penetrates it and sets it in motion, is refuted by the precise testimony of Aristotle, who declares that the early physicists did not distinguish the moving cause from the material cause, and that before Hermotimus and Anaxagoras no one postulated a creative intelligence.
If this view be, rejected and it is necessary to fall back on the choice between 64 and 67, the problem is perhaps insoluble, but 64 has somewhat more intrinsic probability, and 67 can be explained as due to an artificial system of chronology which postulated for Peter an episcopate of Rome of twenty-five years - a number which comes so often in the early episcopal lists that it seems to mean little more than "a long time," just as "forty years" does in the Old Testament.
Behind the great natural phen.omena that they 0th ceived all around them, the Egyptians, like other primitive cha :, postulated the existence of divine wills not dissimilar the dnd to their own, though vastly superior in power.
The casual concept, as given by experience, expresses not a necessary objective order of things, but an ordered scheme of perception; it is subjective and cannot be postulated as a concrete law apart from consciousness.
Most inductions are made without any assumption of the uniformity of nature; for, whether it is itself induced, or a priori or postulated, this like every assumption is a judgment, and most men are incapable of judgment on so universal a scale, when they are quite capable of induction.
But the one in the many, the identity in difference, is so far only postulated, not established.
Thus the suggestion preserved by Stobaeus that he conceived water to be endowed with mind is discredited by the specific statement of Aristotle that the earlier physicists (physiologi) did not distinguish the material from the moving cause, and that before Anaxagoras no one postulated creative intelligence.
Anaximander postulated a corporeal substance intermediate between air and fire on the one hand, and between earth and water on the other hand.
Like the early Ionians he postulated a primary substance, fire, out of which all things have emerged and into which all must return.
No alphabet corresponds exactly to the ideal which we have postulated, nor if it did, would it continue long so to do, as the sounds of most languages are continually changing.
He postulated primitive Matter, identical with air and mingled with Mind, thus avoiding the dualism of Anaxagoras.
Both these writers, more particularly the latter, had postulated in controverting Hobbes the existence of a moral sense to explain the fact that we approve benevolent actions, done either by ourselves or by others, which bring no advantage to ourselves.
Two other conditions may also be postulated: one is always the elimination of the aberration on the axis; the second either the " Herschel " or " Fraunhofer condition," the latter being the best (vide supra, " Monochromatic Aberration ").
Posidonius, unable to explain the emotions as " judgments " or the effects of judgments, postulated, like Plato, an irrational principle (including a concupiscent and a spirited element) to account for them, although he subordinated all these as faculties to the one substance of the soul lodged in the heart.
But although the possibility of such a philosophy seems implied in the postulated nationality of the universe, many would hold that it remains as yet an unachieved ideal.
(A) In regard to his theory of being: (1) whereas Plato postulated as the basis of his system a cause which should be at once Unity, Good, and Mind, Speusippus distinguished Unity, the origin of things, from Good, their end, and both Unity and Good from controlling Mind or Reason; (2) whereas Plato recognized three kinds of numbers - firstly, ideal numbers, i.e.
In his ontology Xenocrates built upon Plato's foundations: that is to say, with Plato he postulated ideas or numbers to be the causes of nature's organic products, and derived these ideas or numbers from unity (which is active) and plurality (which is passive).
14, the use of the altar as an asylum is postulated, though denied to the wilful murderer.
But while the theologian incessantly postulated the agency of that God whose nature he deemed beyond the pale of science, the philosopher, following a purely human and natural aim, directed his efforts to the gradual elevation of his part of reason from its unformed state, and to its final union with the controlling intellect which moves and draws to itself the spirits of those who prepare themselves for its influences.
Conceiving that the simplest principle is the most likely to be true, he assumed as a postulate that bodies falling freely towards the earth descend with a uniformly accelerated motion, and deduced thence that the velocities acquired are in the direct, and the spaces traversed in the duplicate ratio of the times, counted from the beginning of motion; finally, he proved, by observing the times of descent of bodies falling down inclined planes, that the postulated law was the true law.
23-26, &c. The religious views are so varied that a single writer or even a single age cannot be postulated; note especially I Sam.
A short summary may here be given of the grounds on which the present writer has postulated a diversity of authorship. If the letter to the tribes in captivity (lxxviii.
Just as we have evidence of a former mild climate in the arctic regions, so a similar mild climate has been postulated for Antarctica.
He also postulated, with Regnault, the existence of " molecular or mechanical types " containing substances which, although having the same number of equivalents, are essentially different in characters.
Taking as types hydrogen, hydrochloric acid, water and ammonia, he postulated that all organic compounds were referable to these four forms: the hydrogen type included hydrocarbons, aldehydes and ketones; the hydrochloric acid type, the chlorides, bromides and iodides; the water type, the alcohols, ethers, monobasic acids, acid anhydrides, and the analogous sulphur compounds; and the ammonia type, the amines, acid-amides, and the analogous phosphorus and arsenic compounds.
Postulated the existence of one common indivisible state of which mutilated Hungary 2 formed an important section.
Against this Dr Wekerle had protested, as opposed to general Hungarian opinion and ruinous to the national credit, pointing out that whenever it was a question of raising a loan, the maintenance of the financial community between Hungary and Austria was always postulated as a preliminary condition.
According to Aristotle, "the first of Eleatic unitarians was not careful to say whether the unity which he postulated was finite or infinite, but, contemplating the whole firmament, declared that the One is God."
The righteousness of God postulated according to the law the temporal prosperity of the righteous and the temporal prosperity of necessity; for as yet there was no.
Opposition to the " hydrogen-acid " theory centred mainly about the hypothetical radicals which it postulated; moreover, the electrochemical theory of Berzelius exerted a stultifying influence on the correct views of Davy and Dulong.
As a technical term in theology, it has various shades of meaning according to the degree of authority which is postulated and the nature of the evidence on which it is based.
With reference to all such further refinements of theory, it is to be borne in mind that the perfect fluid of hydrodynamic analysis is not a merely passive inert plenum; it is also a continuum with the property that no finite internal slip or discontinuity of motion can ever arise in it through any kind of disturbance; and this property must be postulated, as it cannot be explained.
Among his happy conjectures may be mentioned that of the sun's axial rotation, postulated by him as the physical cause of the revolutions of the planets, and soon after confirmed by the discovery of sun-spots; the suggestion of a periodical variation in the obliquity of the ecliptic; and the explanation as a solar atmospheric effect of the radiance observed to surround the totally eclipsed sun.
The original one, made by Newton and Pullan, is obviously in error in many respects; and that of Oldfield, though to be preferred for its lightness (the Mausoleum was said anciently to be "suspended in mid-air"), does not satisfy the conditions postulated by the remains.
While Leucippus's notion of Being agreed generally with that of the Eleatics, he postulated its plurality (atoms) and motion, and the reality of not-Being (the void) in which his atoms moved.
They rightly revolted against the inconsistencies of Kant's third and fourth positions about the existence of unknown but postulated things in themselves, hidden from theoretical, but revealed to practical, reason.
Both philosophers appeal to the English love of experience, and Kant had these advantages over Hume: that within the narrow circle of sensible phenomena his theory of understanding gave to experience a fuller content, and that beyond phenomena, however inconsistently, his theory of reason postulated the reality of God, freedom and immortality.