8), after recognizing the necessity of external goods to happiness, it denies that fortune is due to divine grace, and simply defines it as irrational nature (&Xoyos 060-Ls).
On the whole, his voluntarism, though like that of Schopenhauer and Hartmann, is not the same; not Schopenhauer's, because the ideating will of Wundt's philosophy is not a universal irrational will; and not Hartmann's, because, although ideating will, according to Wundt's phenomenalism, is supposed to extend through the world of organisms, the whole inorganic world remains a mere object of unitary experience.
There must be a God who can miraculously endow the irrational mind of man with truth - so runs the new.
The workings of this Will are irrational primarily, but, as in its evolution it becomes more rationalized and understands the whole meaning of the Weltschmerz, it ultimately reaches the point at which the desire for existence is gone.
The Stoic regarded the condition of freedom or slavery as an external accident, indifferent in the eye of wisdom; to him it was irrational to see in liberty a ground of pride or in slavery a subject of complaint; from intolerable indignity suicide was an ever-open means of escape.
Under the general heading "Algebra and Theory of Numbers" occur the subheadings "Elements of Algebra," with the topics rational polynomials, permutations, &c., partitions, probabilities; "Linear Substitutions," with the topics determinants, &c., linear substitutions, general theory of quantics; "Theory of Algebraic Equations," with the topics existence of roots, separation of and approximation to, theory of Galois, &c. "Theory of Numbers," with the topics congruences, quadratic residues, prime numbers, particular irrational and transcendental numbers.
The harmony between arithmetical and geometrical measurement, which was disturbed by the Greek geometers on the discovery of irrational numbers, is restored by an unlimited supply of the causes of disturbance.
On the other hand, this new series is not continuous; for we know that there are some points on the line which represent surds and other irrational numbers, and these numbers are not contained in our series.
The development of the theory of equations leads to the amplification of real numbers, rational and irrational, positive and negative, by imaginary and complex numbers.
But the world will take what is available in Comte, while forgetting that in his work which is as irrational in one way as Hegel is in another.
But could Christians sufficiently numerous to deserve a long discussion by St Epiphanius in 374-377, who upheld the Synoptists, stoutly opposed the Gnostics and Montanists, and had escaped every special designation till the bishop nicknamed them the " Alogoi " (irrational rejectors of the Logos-Gospel), dare, in such a time and country, to hold such views, had the apostolic origin been incontestable ?
Scepticism with regard to reason, on the other hand, depends on an insight into the irrational character of the relation which we chiefly employ, viz.
The soul is partly irrational, partly rational; and therefore there are two kinds of virtue.
1218 b 34); (5) that in them appeared the division of soul into irrational and rational, used by Aristotle (E.N.
The earliest of these works was Custom and Myth (1884); in Myth, Literature and Religion (2 vols., 1887, French trans., 1896) he explained the irrational elements of mythology as survivals from earlier savagery; in The Making of Religion (an idealization of savage animism) he maintained the existence of high spiritual ideas among savage races, and instituted comparisons between savage practices and the occult phenomena among civilized races; he dealt with the origins of totemism in Social Origins, printed (1903) together with J.
He was for five years a clerk in the office of an Irish land-agent, but came to London with his family in 1876, and in 1879 was, according to his own account in the preface to The Irrational Knot, in the offices of the Edison telephone company.
In irrational creatures the particular will or greed of the individual is controlled by external forces, and thus used as an instrument of the universal.
There must be a God, who could compel irrational matter to serve rational ends - so ran the old argument.
But now the irrational real numbers have all made their appearance.
For example, if it should turn out that the mass of a body is to be estimated by counting the number of corpuscles (whatever they may be) which go to form it, then a body with an irrational measure of mass is intrinsically impossible.
Consideration of the binomial theorem for fractional index, or of the continued fraction representing a surd, or of theorems such as Wallis's theorem (ï¿½ 64), shows that a sequence, every term of which is rational, may have as its limit an irrational number, i.e.
This insertion of irrational numbers (with corresponding negative numbers) requires for its exact treatment certain special methods, which form part of the algebraic theory of number, and are dealt with under Number.
Evolution and involution are usually regarded as operations of ordinary algebra; this leads to a notation for powers and roots, and a theory of irrational algebraic quantities analogous to that of irrational numbers.
Although this transition from the discontinuous to continuous is not truly scientific, yet it materially augmented the development of algebra, and Hankel affirms that if we define algebra as the application of arithmetical operations to both rational and irrational numbers or magnitudes, then the Brahmans are the real inventors of algebra.
The Treatise is a reductio ad absurdum of the principles of Lockianism, inasmuch as these principles, when consistently applied, leave the structure of experience entirely " loosened " (to use Hume's own expression), or cemented together only by the irrational force of custom.
That they are in some cases produced by physical or sensory stimuli does not constitute them irrational, and it is purely arbitrary to confine the word pleasure to those cases in which such stimuli are the proximate causes.
Sents an irrational quantity.
If this be applied to the right-hand side of the identity m m m 2 m2 tan-=- - n n -3n-5n" it follows that the tangent of every arc commensurable with the radius is irrational, so that, as a particular case, an arc of 45 having its tangent rational, must be incommensurable with the radius; that is to say, 3r/4 is an incommensurable number."
8-9), where the Nicomachean Ethics places the speculative and the practical life; but it omits the theological element by denying that good fortune is divine grace, and by submitting gentlemanliness to no standard but that of right reason, when the irrational part of the soul does not hinder the rational part, or intellect (vows), from doing its work.
When he found himself confronted with the blind forces of Nature he was obliged to divest irrational will of feeling.
Lastly, by " ` will " he does not mean " rational desire," which is its proper meaning, but inapplicable to Nature; nor unconscious irrational will, which is Schopenhauer's forced meaning; nor unconscious intelligent will, which is Hartmann's more correct meaning, though inapplicable to Nature.