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Who said: “God does not care about our mathematical difficulties. He integrates empirically.”
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Whatsoever Quotes (41 quotes)

In primis, hominis est propria VERI inquisitio atque investigato. Itaque cum sumus negotiis necessariis, curisque vacui, tum avemus aliquid videre, audire, ac dicere, cognitionemque rerum, aut occultarum aut admirabilium, ad benè beatéque vivendum necessariam ducimus; —ex quo intelligitur, quod VERUM, simplex, sincerumque sit, id esse naturæ hominis aptissimum. Huic veri videndi cupiditati adjuncta est appetitio quædam principatûs, ut nemini parere animus benè a naturâ informatus velit, nisi præcipienti, aut docenti, aut utilitatis causâ justè et legitimè imperanti: ex quo animi magnitudo existit, et humanarum rerum contemtio.
Before all other things, man is distinguished by his pursuit and investigation of TRUTH. And hence, when free from needful business and cares, we delight to see, to hear, and to communicate, and consider a knowledge of many admirable and abstruse things necessary to the good conduct and happiness of our lives: whence it is clear that whatsoever is TRUE, simple, and direct, the same is most congenial to our nature as men. Closely allied with this earnest longing to see and know the truth, is a kind of dignified and princely sentiment which forbids a mind, naturally well constituted, to submit its faculties to any but those who announce it in precept or in doctrine, or to yield obedience to any orders but such as are at once just, lawful, and founded on utility. From this source spring greatness of mind and contempt of worldly advantages and troubles.
In De Officiis, Book 1. Sect. 13. As given in epigraph to John Frederick William Herschel, A Preliminary Discourse on the Study of Natural Philosophy (1830), viii.
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A few days afterwards, I went to him [the same actuary referred to in another quote] and very gravely told him that I had discovered the law of human mortality in the Carlisle Table, of which he thought very highly. I told him that the law was involved in this circumstance. Take the table of the expectation of life, choose any age, take its expectation and make the nearest integer a new age, do the same with that, and so on; begin at what age you like, you are sure to end at the place where the age past is equal, or most nearly equal, to the expectation to come. “You don’t mean that this always happens?”—“Try it.” He did try, again and again; and found it as I said. “This is, indeed, a curious thing; this is a discovery!” I might have sent him about trumpeting the law of life: but I contented myself with informing him that the same thing would happen with any table whatsoever in which the first column goes up and the second goes down.
In Budget of Paradoxes (1872), 172.
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All animals whatsoever, whether they fly or swim or walk upon dry land, whether they bring forth their young alive or in the egg, develop in the same way.
Aristotle
In The Works of Aristotle: Historia Animalium (350 BC), (The History of Animals), Book VII, Part 7, 586a21 translated in William David Ross and John Alexander Smith (eds.), D’Arcy Wentworth Thompson (trans.), (1910), Vol. 4, 27.
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As regards railways, it is certain that nothing is so profitable, because nothing is so cheaply transported, as passenger traffic. Goods traffic, of whatsoever description, must be more or less costly. Every article conveyed by railway requires handling and conveyance beyond the limit of the railway stations; but passengers take care of themselves, and find their own way.
From 'Railway System and its Results' (Jan 1856) read to the Institution of Civil Engineers, reprinted in Samuel Smiles, Life of George Stephenson (1857), 520.
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At the age of eleven, I began Euclid, with my brother as my tutor. ... I had not imagined that there was anything so delicious in the world. After I had learned the fifth proposition, my brother told me that it was generally considered difficult, but I had found no difficulty whatsoever. This was the first time it had dawned on me that I might have some intelligence.
In Autobiography: 1872-1914 (1967), Vol. 1, 37-38.
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But let your communication be Yea, yea; Nay, nay: for whatsoever is more than these cometh of evil.
Bible
[Reminiscent of binary code!] Matthew 5:37. In Gary William Flake, The Computational Beauty of Nature (2000), 23.
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Confined to its true domain, mathematical reasoning is admirably adapted to perform the universal office of sound logic: to induce in order to deduce, in order to construct. … It contents itself to furnish, in the most favorable domain, a model of clearness, of precision, and consistency, the close contemplation of which is alone able to prepare the mind to render other conceptions also as perfect as their nature permits. Its general reaction, more negative than positive, must consist, above all, in inspiring us everywhere with an invincible aversion for vagueness, inconsistency, and obscurity, which may always be really avoided in any reasoning whatsoever, if we make sufficient effort.
In Synthèse Subjective (1856), 98. As translated in Robert Édouard Moritz, Memorabilia Mathematica; Or, The Philomath’s Quotation-Book (1914), 202-203. From the original French, “Bornée à son vrai domaine, la raison mathématique y peut admirablement remplir l’office universel de la saine logique: induire pour déduire, afin de construire. … Elle se contente de former, dans le domaine le plus favorable, un type de clarté, de précision, et de consistance, dont la contemplation familière peut seule disposer l’esprit à rendre les autres conceptions aussi parfaites que le comporte leur nature. Sa réaction générale, plus négative que positive, doit surtout consister à nous inspirer partout une invincible répugnance pour le vague, l’incohérence, et l’obscurité, que nous pouvons réellement éviter envers des pensées quelconques, si nous y faisons assez d’efforts.”
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During the time of the Deluge, whilst the Water was out upon, and covered the Terrestrial Globe, … all Fossils whatever that had before obtained any Solidity, were totally dissolved, and their constituent Corpuscles all disjoyned, their Cohesion perfectly ceasing … [A]nd, to be short, all Bodies whatsoever that were either upon the Earth, or that constituted the Mass of it, if not quite down to the Abyss, yet at least to the greatest depth we ever dig: I say all these were assumed up promiscuously into the Water, and sustained in it, in such a manner that the Water, and Bodies in it, together made up one common confused Mass. That at length all the Mass that was thus borne up in the Water, was again precipitated and subsided towards the bottom. That this subsidence happened generally, and as near as possibly could be expected in so great a Confusion, according to the laws of Gravity.
In An Essay Toward A Natural History of the Earth (1695), 74-75.
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For between true Science, and erroneous Doctrines, Ignorance is in the middle. Naturall sense and imagination, are not subject to absurdity. Nature it selfe cannot erre: and as men abound in copiousnesses of language; so they become more wise, or more mad than ordinary. Nor is it possible without Letters for any man to become either excellently wise, or (unless his memory be hurt by disease, or ill constitution of organs) excellently foolish. For words are wise men's counters, they do but reckon by them; but they are the money of fools that value them by the authority of an Aristotle, a Cicero, or a Thomas, or any other Doctor whatsoever, if but a man.
Leviathan (1651), ed. C. B. Macpherson (1968), Part 1, Chapter 4, 106.
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Given any domain of thought in which the fundamental objective is a knowledge that transcends mere induction or mere empiricism, it seems quite inevitable that its processes should be made to conform closely to the pattern of a system free of ambiguous terms, symbols, operations, deductions; a system whose implications and assumptions are unique and consistent; a system whose logic confounds not the necessary with the sufficient where these are distinct; a system whose materials are abstract elements interpretable as reality or unreality in any forms whatsoever provided only that these forms mirror a thought that is pure. To such a system is universally given the name MATHEMATICS.
In 'Mathematics', National Mathematics Magazine (Nov 1937), 12, No. 2, 62.
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I am by heritage a Jew, by citizenship a Swiss, and by makeup a human being, and only a human being, without any special attachment to any state or national entity whatsoever.
…...
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I shall explain a System of the World differing in many particulars from any yet known, answering in all things to the common Rules of Mechanical Motions: This depends upon three Suppositions. First, That all Cœlestial Bodies whatsoever, have an attraction or gravitating power towards their own Centers, whereby they attract not only their own parts, and keep them from flying from them, as we may observe the Earth to do, but that they do also attract all the other Cœlestial bodies that are within the sphere of their activity; and consequently that not only the Sun and Moon have an influence upon the body and motion the Earth, and the Earth upon them, but that Mercury also Venus, Mars, Saturn and Jupiter by their attractive powers, have a considerable influence upon its motion in the same manner the corresponding attractive power of the Earth hath a considerable influence upon every one of their motions also. The second supposition is this, That all bodies whatsoever that are put into a direct and simple motion, will continue to move forward in a streight line, till they are by some other effectual powers deflected and bent into a Motion, describing a Circle, Ellipse, or some other more compounded Curve Line. The third supposition is, That these attractive powers are so much the more powerful in operating, by how much the nearer the body wrought upon is to their own Centers. Now what these several degrees are I have not yet experimentally verified; but it is a notion, which if fully prosecuted as it ought to be, will mightily assist the Astronomer to reduce all the Cœlestial Motions to a certain rule, which I doubt will never be done true without it. He that understands the nature of the Circular Pendulum and Circular Motion, will easily understand the whole ground of this Principle, and will know where to find direction in Nature for the true stating thereof. This I only hint at present to such as have ability and opportunity of prosecuting this Inquiry, and are not wanting of Industry for observing and calculating, wishing heartily such may be found, having myself many other things in hand which I would first compleat and therefore cannot so well attend it. But this I durst promise the Undertaker, that he will find all the Great Motions of the World to be influenced by this Principle, and that the true understanding thereof will be the true perfection of Astronomy.
An Attempt to Prove the Motion of the Earth from Observations (1674), 27-8. Based on a Cutlerian Lecture delivered by Hooke at the Royal Society four years earlier.
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I use the word “attraction” here in a general sense for any endeavor whatever of bodies to approach one another, whether that endeavor occurs as a result of the action of the bodies either drawn toward one other or acting on one another by means of spirits emitted or whether it arises from the action of aether or of air or of any medium whatsoever—whether corporeal or incorporeal—in any way impelling toward one another the bodies floating therein. I use the word “impulse” in the same general sense, considering in this treatise not the species of forces and their physical qualities but their quantities and mathematical proportions, as I have explained in the definitions.
The Principia: Mathematical Principles of Natural Philosophy (1687), 3rd edition (1726), trans. I. Bernard Cohen and Anne Whitman (1999), Book I, Section II, Scholium, 588.
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If one of these elements, heat, becomes predominant in any body whatsoever, it destroys and dissolves all the others with its violence. …Again if too much moisture enters the channels of a body, and thus introduces disproportion, the other elements, adulterated by the liquid, are impaired, and the virtues of the mixture dissolved. This defect, in turn, may arise from the cooling properties of moist winds and breezes blowing upon the body. In the same way, increase or diminution of the proportion of air or of the earthy which is natural to the body may enfeeble the other elements.
Vitruvius
In De Architectura, Book 1, Chap 4, Sec. 6. As translated in Morris Hicky Morgan (trans.), Vitruvius: The Ten Books on Architecture (1914), 18-19.
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Into whatsoever houses I enter, I will enter to help the sick, and I will abstain from all intentional wrong-doing and harm, especially from abusing the bodies of man or woman, bond or free. And whatsoever I shall see or hear in the course of my profession, as well as outside my profession in my intercourse with men, if it be what should not be published abroad, I will never divulge, holding such things to be holy secrets.
Oath, in Hippocrates, trans. W. H. S. Jones (1923), Vol. 1, 301.
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It seems plain and self-evident, yet it needs to be said: the isolated knowledge obtained by a group of specialists in a narrow field has in itself no value whatsoever, but only in its synthesis with all the rest of knowledge and only inasmuch as it really contributes in this synthesis toward answering the demand, ‘Who are we?’
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It seems to me that your Reverence and Signor Galileo act prudently when you content yourselves with speaking hypothetically and not absolutely, as I have always understood that Copernicus spoke. To say that on the supposition of the Earth’s movement and the Sun's quiescence all the celestial appearances are explained better than by the theory of eccentrics and epicycles is to speak with excellent good sense and to run no risk whatsoever. Such a manner of speaking is enough for a mathematician. But to want to affirm that the Sun, in very truth, is at the center of the universe and only rotates on its axis without going from east to west, is a very dangerous attitude and one calculated not only to arouse all Scholastic philosophers and theologians but also to injure our holy faith by contradicting the Scriptures.
Letter to Paolo Antonio Foscarini, 12 April 1615. Quoted in Giorgio De Santillana, The Crime of Galileo (1955), 99.
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Knowledge is a matter of science, and no dishonesty or conceit whatsoever is permissible. What is required is definitely the reverse—honesty and modesty.
In Quotations from Chairman Mao Tsetung (1966, 1972), 310.
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Nature has but one plan of operation, invariably the same in the smallest things as well as in the largest, and so often do we see the smallest masses selected for use in Nature, that even enormous ones are built up solely by fitting these together. Indeed, all Nature’s efforts are devoted to uniting the smallest parts of our bodies in such a way that all things whatsoever, however diverse they may be, which coalesce in the structure of living things construct the parts by means of a sort of compendium.
'On the Developmental Process', in H. B. Adelmann (ed.), Marcello Malpighi and the Evolution of Embryology (1966), Vol. 2, 843.
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Not that we may not, to explain any Phenomena of Nature, make use of any probable Hypothesis whatsoever: Hypotheses, if they are well made, are at least great helps to the Memory, and often direct us to new discoveries. But my Meaning is, that we should not take up anyone too hastily, (which the Mind, that would always penetrate into the Causes of Things, and have Principles to rest on, is very apt to do,) till we have very well examined Particulars, and made several Experiments, in that thing which we would explain by our Hypothesis, and see whether it will agree to them all; whether our Principles will carry us quite through, and not be as inconsistent with one Phenomenon of Nature, as they seem to accommodate and explain another.
An Essay Concerning Human Understanding (1690). Edited by Peter Nidditch (1975), Book 4, Chapter 12, Section 13, 648.
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Now this is the peculiarity of scientific method, that when once it has become a habit of mind, that mind converts all facts whatsoever into science.
From The Grammar of Science (1892), 15.
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One could not by any experience whatsoever demonstrate that the heavens, and not the earth, are moved with a diurnal motion.
In Livre du ciel et du monde (On the Book of the Heavens and the World of Aristotle) (completed 1377), Book 2, Chap 25. Translated by Menut and Denomy (1968), as excerpted in Marshall Clagett, The Science of Mechanics in the Middle Ages, 600. Also found translated as, “No experience whatsoever could prove that the heavens rotate daily and not the earth.”
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One must believe that every living thing whatsoever must change insensibly in its organization and in its form... One must therefore never expect to find among living species all those which are found in the fossil state, and yet one may not assume that any species has really been lost or rendered extinct.
Système des Animaux sans Vertébres, (1801) trans. D. R. Newth, in Annals of Science (1952), 5, 253-4.
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Scientific discovery and scientific knowledge have been achieved only by those who have gone in pursuit of them without any practical purpose whatsoever in view.
The New Science (1959), 93.
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Scientific truth, like puristic truth, must come about by controversy. Personally this view is abhorrent to me. It seems to mean that scientific truth must transcend the individual, that the best hope of science lies in its greatest minds being often brilliantly and determinedly wrong, but in opposition, with some third, eclectically minded, middle-of-the-road nonentity seizing the prize while the great fight for it, running off with it, and sticking it into a textbook for sophomores written from no point of view and in defense of nothing whatsoever. I hate this view, for it is not dramatic and it is not fair; and yet I believe that it is the verdict of the history of science.
From Address of the President before the American Psychological Association at New York (28 Dec 1928) 'The Psychology of Controversy', Psychological Review (1929), 36, 97. Collected in Robert I. Watson and Donald T. Campbell (eds.), History, Psychology and Science: Selected Papers by Edwin Boring (1963), 68.
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So, then, the Tincture of the Philosophers is a universal medicine, and consumes all diseases, by whatsoever name they are called, just like an invisible fire. The dose is very small, but its effect is most powerful. By means thereof I have cured the leprosy, venereal disease, dropsy, the falling sickness, colic, scab, and similar afflictions; also lupus, cancer, noli-metangere, fistulas, and the whole race of internal diseases, more surely than one could believe.
Quoted in Paracelsus and Arthur Edward Waite (ed.), The Hermetic and Alchemical Writings of Paracelsus (1894), Vol. 1, 29.
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The divergent series are the invention of the devil, and it is a shame to base on them any demonstration whatsoever. By using them, one may draw any conclusion he pleases and that is why these series have produced so many fallacies and so many paradoxes.
From letter (Jan 1828) to his former teacher Berndt Holmböe. In Morris Kline, Mathematics: The Loss of Certainty (1982), 170.
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The domain of mathematics is the sole domain of certainty. There and there alone prevail the standards by which every hypothesis respecting the external universe and all observation and all experiment must be finally judged. It is the realm to which all speculation and thought must repair for chastening and sanitation, the court of last resort, I say it reverently, for all intellection whatsoever, whether of demon, or man, or deity. It is there that mind as mind attains its highest estate.
In 'The Universe and Beyond', Hibbert Journal (1904-1906), 3, 314.
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The Excellence of Modern Geometry is in nothing more evident, than in those full and adequate Solutions it gives to Problems; representing all possible Cases in one view, and in one general Theorem many times comprehending whole Sciences; which deduced at length into Propositions, and demonstrated after the manner of the Ancients, might well become the subjects of large Treatises: For whatsoever Theorem solves the most complicated Problem of the kind, does with a due Reduction reach all the subordinate Cases.
In 'An Instance of the Excellence of Modern Algebra, etc', Philosophical Transactions, 1694, 960.
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The first question which you will ask and which I must try to answer is this, “What is the use of climbing Mount Everest ?” and my answer must at once be, “It is no use.” There is not the slightest prospect of any gain whatsoever. Oh, we may learn a little about the behavior of the human body at high altitudes, and possibly medical men may turn our observation to some account for the purposes of aviation. But otherwise nothing will come of it. We shall not bring back a single bit of gold or silver, not a gem, nor any coal or iron. We shall not find a single foot of earth that can be planted with crops to raise food. It’s no use. So, if you cannot understand that there is something in man which responds to the challenge of this mountain and goes out to meet it, that the struggle is the struggle of life itself upward and forever upward, then you won’t see why we go. What we get from this adventure is just sheer joy. And joy is, after all, the end of life. We do not live to eat and make money. We eat and make money to be able to enjoy life. That is what life means and what life is for.
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The genotypic constitution of a gamete or a zygote may be parallelized with a complicated chemico-physical structure. This reacts exclusively in consequence of its realized state, but not in consequence of the history of its creation. So it may be with the genotypical constitution of gametes and zygotes: its history is without influence upon its reactions, which are determined exclusively by its actual nature. The genotype-conception is thus an 'ahistoric' view of the reactions of living beings—of course only as far as true heredity is concerned. This view is an analog to the chemical view, as already pointed out; chemical compounds have no compromising ante-act, H2O is always H2O, and reacts always in the same manner, whatsoever may be the 'history' of its formation or the earlier states of its elements. I suggest that it is useful to emphasize this 'radical' ahistoric genotype-conception of heredity in its strict antagonism to the transmission—or phenotype-view.
'The Genotype Conception of Heredity', The American Naturalist (1911), 45, 129.
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The object of pure mathematics is those relations which may be conceptually established among any conceived elements whatsoever by assuming them contained in some ordered manifold; the law of order of this manifold must be subject to our choice; the latter is the case in both of the only conceivable kinds of manifolds, in the discrete as well as in the continuous.
In Über das System der rein mathematischen Wissenschaften, Jahresbericht der Deutschen Mathematiker-Vereinigung, Bd. 1, 36. As quoted and cited in Robert Édouard Moritz, Memorabilia Mathematica; Or, The Philomath’s Quotation-book (1914), 3.
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The observer is never entirely replaced by instruments; for if he were, he could obviously obtain no knowledge whatsoever ... They must be read! The observer’s senses have to step in eventuality. The most careful record, when not inspected, tells us nothing.
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The qualities of bodies, which admit neither intension nor remission of degrees, and which are found to belong to fill bodies within the reach of our experiments, are to be esteemed the universal qualities of all bodies whatsoever.
From Isaac Newton, Rules of Reasoning in Philosophy, Rule 3, as translated by Andrew Motte in The Mathematical Principles of Natural Philosophy (1803), Vol. 2, 160.
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There is no area in our minds reserved for superstition, such as the Greeks had in their mythology; and superstition, under cover of an abstract vocabulary, has revenged itself by invading the entire realm of thought. Our science is like a store filled with the most subtle intellectual devices for solving the most complex problems, and yet we are almost incapable of applying the elementary principles of rational thought. In every sphere, we seem to have lost the very elements of intelligence: the ideas of limit, measure, degree, proportion, relation, comparison, contingency, interdependence, interrelation of means and ends. To keep to the social level, our political universe is peopled exclusively by myths and monsters; all it contains is absolutes and abstract entities. This is illustrated by all the words of our political and social vocabulary: nation, security, capitalism, communism, fascism, order, authority, property, democracy. We never use them in phrases such as: There is democracy to the extent that… or: There is capitalism in so far as… The use of expressions like “to the extent that” is beyond our intellectual capacity. Each of these words seems to represent for us an absolute reality, unaffected by conditions, or an absolute objective, independent of methods of action, or an absolute evil; and at the same time we make all these words mean, successively or simultaneously, anything whatsoever. Our lives are lived, in actual fact, among changing, varying realities, subject to the casual play of external necessities, and modifying themselves according to specific conditions within specific limits; and yet we act and strive and sacrifice ourselves and others by reference to fixed and isolated abstractions which cannot possibly be related either to one another or to any concrete facts. In this so-called age of technicians, the only battles we know how to fight are battles against windmills.
From 'The Power of Words', collected in Siân Miles (ed.), Simone Weil: An Anthology (2000), 222-223.
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Through purely logical thinking we can attain no knowledge whatsoever of the empirical world.
In Francis Crick, The Astonishing Hypothesis: the Scientific Search for the Soul (1995), 215.
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We, however, maintain … that all animals whatsoever, even the viviparous, and man himself not excepted, are produced from ova; that the first conception, from which the foetus proceeds in all, is an ovum of one description or another, as well as the seeds of all kinds of plants.
As translated by Robert Willis in The Works of William Harvey (1847), Vol. 7, 170. Harvey’s doctrine, given herein, has been summarized in later literature as: omne vivum ex ovo omnia, (all life from an egg). Also see the quote “Ex ova omnia,” elsewhere on this webpage.
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Whatsoever accidents Or qualities our sense make us think there be in the world, they are not there, but are seemings and apparitions only. The things that really are in the world without us, are those motions by which these seemings are caused. And this is the great deception of sense, which also is by sense to be corrected. For as sense telleth me, when I see directly, that the colour seemeth to be in the object; so also sense telleth me, when I see by reflection, that colour is not in the object.
The Elements of Law: Natural and Politic (1640), Ferdinand Tonnies edn. (1928), Part 1, Chapter 2, 6.
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Whatsoever therefore is consequent to a time of Warre, where every man is Enemy to every man; the same is consequent to the time, wherein men live without other security, than what their own strength, and their own invention shall furnish them withall. In such condition, there is no place for Industry; because the fruit thereof is uncertain: and consequently no Culture of the Earth; no Navigation, nor use of the commodities that may be imported by Sea; no commodious Building; no Instruments of moving, and removing, such things as require much force; no Knowledge of the face of the Earth; no account of Time; no Arts; no Letters; no Society; and which is worst of all, continual fear, and danger of violent death; And the life of man, solitary, poore, nasty, brutish, and short.
Leviathan (1651), ed. C. B. Macpherson (1968), Part 1, Chapter 13, 186.
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Whatsoever thy hand findeth to do, do it with all thy might.
Quoted as Carroll’s “rule of life” in Stuart Dodgson Collingwood, The Life and Letters of Lewis Carroll (1898), 292.
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When I was a boy, I read with great interest but skepticism about a magic lamp which was used with success by a certain Aladdin. Today I have no skepticism whatsoever about the magic of the xenon flash lamp which we use so effectively for many purposes.
In Electronic Flash, Strobe (1970), v.
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Carl Sagan Thumbnail In science it often happens that scientists say, 'You know that's a really good argument; my position is mistaken,' and then they would actually change their minds and you never hear that old view from them again. They really do it. It doesn't happen as often as it should, because scientists are human and change is sometimes painful. But it happens every day. I cannot recall the last time something like that happened in politics or religion. (1987) -- Carl Sagan
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- 90 -
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- 40 -
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