There must be a God who can miraculously endow the irrational mind of man with truth - so runs the new.
It wasn't the money he objected to so much as the irrational logic.
The real numbers, which include irrational numbers, have now to be defined.
In this work, which is one of the most valuable contributions to the literature of algebra, Cardan shows that he was familiar with both real positive and negative roots of equations whether rational or irrational, but of imaginary roots he was quite ignorant, and he admits his inability to resolve the so-called lation of Arabic manuscripts.
Graphic methods also enter into the consideration of irrational numbers (ï¿½ 65).
We are forced to fall back on fatalism as an explanation of irrational events (that is to say, events the reasonableness of which we do not understand).
1892), are more suitable for revision purposes; the second of these deals rather fully with irrational numbers.
Would Dean ever make such irrational and illogical decisions if faced with a test of his love?
The irrational discords of Strauss are also real phenomena in musical aesthetics.
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.
The number of questions which Calvin failed to ask or eluded by absolutely irrational expedients frees him from any taint of modern rationalism.
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).
Do) that acting according to right reason is when the irrational part of the soul does not hinder the rational part of intellect from doing its work.
There must be a God, who could compel irrational matter to serve rational ends - so ran the old argument.
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.
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 ?
Sents an irrational quantity.
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.
The universe is merely blind Will, not thought; this Will is irrational, purposeless and therefore unhappy.
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.
Atoms swerved as they fell endlessly downwards, and thus introduced an indeterminate or irrational element into the processes of the world.
Strauss makes a steadily increasing use of avowedly irrational discords, in order to produce an emotionally apt physical sensation.
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.
But now the irrational real numbers have all made their appearance.
These are isolated cases of irrational numbers.
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.
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.
The soul is partly irrational, partly rational; and therefore there are two kinds of virtue.
Moral virtue, which is that of the irrational desires so far as they are obedient to reason, is a purposive habit in the mean.
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.
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.
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.
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.
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.
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.
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.
Good fortune it divides into two kinds, both irrational; one divine, according to impulse, and more continuous; the other contrary to impulse and not continuous.
When he found himself confronted with the blind forces of Nature he was obliged to divest irrational will of feeling.
This passion or emotion, according to those who deny her attachment to Bothwell, was simply terror - the blind and irrational prostration of an abject spirit before the cruel force of circumstances and the crafty wickedness of men.
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.
Their attacks on infant baptism seemed to him not altogether irrational, and in regard to their claim to personal inspiration he said "Luther alone can decide; on the one hand let us beware of quenching the Spirit of God, and on the other of being led astray by the spirit of Satan."
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.
The Irrational Knot, written in 1880, and Love among the Artists (written in 1881) first appeared as serials in Our Corner, a monthly edited by Mrs Annie Besant; Cashel Byron's Profession (reprinted in 1901 in the series of "Novels of his Nonage") and An Unsocial Socialist first appeared in a Socialist magazine To-day, which no longer exists.
In crystallography, the regular or ordinary dodecahedron is an impossible form since the faces cut the axes in irrational ratios; the "pentagonal dodecahedron" of crystallographers has irregular pentagons for faces, while the geometrical solid, on the other hand, has regular ones.
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.
Her commercial policy was one of most irrational and intolerable restriction and repression; and till the end of Spanish rule on the American continent, the whole political power was retained by the court at Madrid, and administered in the colonies by an oligarchy of home-bred Spaniards.
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.
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."
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.
P. Manning, Irrational Numbers (1906); J.
Since they have sinned in consequence of Adam's fall, their fate is considered worse than that of the irrational creation.