Christianity claims that the supernatural is as reasonable as the natural, that man himself is supernatural as truly as he is natural, and that the Bible is so clearly the word of God by proofs that are unanswerable, that it is unreasonable to disbelieve its divine truths.
Though our own hearts break, we cannot flinch; these are new times, sir. There is a misty plot afoot so subtle we should be criminal to cling to old respect and ancient friendships. I have seen too many frightful proofs in court the Devil is alive in Salem, and we dare not quail to follow wherever the accusing finger points!Arthur Miller
Would you convey my compliments to the purist who reads your proofs and tell him or her that I write in a sort of broken-downpatoiswhichissomething likethewaya Swiss waiter talks, and that when I split an infinitive,God damn it, I split it so it will stay split.Raymond Chandler
Variant translation: A poet must leave traces of his passage, not proofs. Only traces bring about dreams.rené char
As Eisenstein shows, his method for constructing elliptic functions applies beautifully to the simpler case of trigonometric functions. Moreover, this case provides not merely an illuminating introduction to his theory, but also the simplest proofs for a series of results, originally discussed by Euler.ferdinand eisenstein
The establishment of formal standards for proofs about programs [...] and the proposal that the semantics of a programming language may be defined independently of all processors for that language, by establishing standards of rigor for proofs about programs in the language, appears to be novel.robert w floyd
I HAVE no patience with the hypothesis occasionally expressed, and often implied, especially in tales written to teach children to be good, that babies are born pretty much alike, and that the sole agencies in creating differences between boy and boy, and man and man, are steady application and moral effort. It is in the most unqualified manner that I object to pretensions of natural equality. The experiences of the nursery, the school, the University, and of professional careers, are a chain of proofs to the contrary.francis galton
I mean the word proof not in the sense of the lawyers, who set two half proofs equal to a whole one, but in the sense of a mathematician, where ½ proof = 0, and it is demanded for proof that every doubt becomes impossible.carl friedrich gauss
It is not particularly satisfactory to see equations set forth as direct results of observation and experiment, where we used to get long mathematical deductions as apparent proofs of them. Nevertheless, I believe that we cannot, without deceiving ourselves, extract much more from known facts than is asserted in the papers referred to. If we wish to lend more color to the theory, there is nothing to prevent us from supplementing all this and aiding our powers of imagination by concrete representations of the various conceptions as to the nature of electric polarisation, the electric current, etc.heinrich hertz
On the whole, however, the conclusions I have drawn from the proofs quoted may, I believe, safely be relied on. Assuredly they will not be disturbed either by the lays of a poet displaying the exaggeration of his craft, or by the compositions of the chroniclers that are attractive at truth's expense; the subjects they treat of being out of the reach of evidence, and time having robbed most of them of historical value by enthroning them in the region of legend.Thucydides
Since fresh examples and proofs could always be found of the alleged relation between guilt and punishment: if you behave in such and such a way, it will go badly with you. Now, as it generally does go badly, the allegation was constantly confirmed; and thus popular morality, a pseudo- science on a level with popular medicine, continually gained ground.georg brandes
It has been observed before that images, however beautiful, though faithfully copied from nature, and as accurately represented in words, do not of themselves characterize the poet. They become proofs of original genius only as far as they are modified by a predominant passion; or by associated thoughts or images awakened by that passion; or when they have the effect of reducing multitude to unity, or succession to an instant; or lastly, when a human and intellectual life is transferred to them from the poet's spirit.Samuel Taylor Coleridge
No body wishes more than I do to see such proofs as you exhibit, that nature has given to our black brethren, talents equal to those of the other colors of men, and that the appearance of a want of them is owing merely to the degraded condition of their existence, both in Africa & America.thomas jefferson
I see too many proofs of the imperfection of human reason, to entertain wonder or intolerance at any difference of opinion on any subject; and acquiesce in that difference as easily as on a difference of feature or form; experience having long taught me the reasonableness of mutual sacrifices of opinion among those who are to act together for any common object, and the expediency of doing what good we can, when we cannot do all we would wish.thomas jefferson
I hate the world and almost all the people in it. I hate the Labour Congress and the journalists who send men to be slaughtered, and the fathers who feel a smug pride when their sons are killed, and even the pacifists who keep saying human nature is essentially good, in spite of all the daily proofs to the contrary. I hate the planet and the human race – I am ashamed to belong to such a species.bertrand russell
So many really divine individuals humanity has not already produced:;! Heros in the moral sense, who never got tired to practice renouncement and charity; bright intelligences who opened to the mind new ways and horizons; poets and wonderful artists, who created for him the image of an ideal world, the reflect of perfection. These are as many proofs of the presence of the absolu in the midst of humanity, for him that does not discover the immediate proof of that in himself.african spir
Closely related to the problem of the parallel postulate is the problem of whether physical space is infinite. Euclid assumes in Postulate 2 that a straight-line segment can be extended as far as necessary; he uses this fact, but only to find a larger finite length for example in Book I, Propositions 11, 16, and 20. For these proofs Heron gave new proofs that avoided extending the lines, in order to meet the objection of anyone who would deny that the space was available for the extension.
Algorithms are the computational content of proofs.
If I shall be condemn'd Upon surmises, all proofs sleeping else But what your jealousies awake, I tell you, 'Tis rigour, and not law.william shakespeare
The belief in a certain idea gives to the researcher the support for his work. Without this belief he would be lost in a sea of doubts and insufficiently verified proofs.
It is worthy of notice that Apollonius nowhere introduces the notion of directrix for a conic, and that, though he incidentally discovered the focus of an ellipse and hyperbola, he did not discover the focus of a parabola. Conspicuous in his geometry is also the absence of technical terms and symbols, which renders the proofs long and cumbrous.Florian Cajori
The analytic method is not conclusive, unless all operations involved in it are known to be reversible. To remove all doubt, the Greeks, as a rule added to the analytic process a synthetic one, consisting of a reversion of all operations occurring in the analysis. Thus the aim of analysis was to aid in the discovery of synthetic proofs or solutions.
A poet should leave traces of his passage, not proofs. Traces alone engender dreams.
... that what is proved, by impossibility proofs, is lack of imagination.
Comparatively few of the propositions and proofs in the Elements are his [Euclid's] own discoveries. In fact, the proof of the "Theorem of Pythagoras" is the only one directly ascribed to him.
On the whole, however, the conclusions I have drawn from the proofs quoted may, I believe, safely be relied on. Assuredly they will not be disturbed either by the lays of a poet displaying the exaggeration of his craft, or by the compositions of the chroniclers that are attractive at truth's expense; the subjects they treat of being out of the reach of evidence, and time having robbed most of them of historical value by enthroning them in the region of legend.
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