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Home > Dictionary of Science Quotations > Scientist Names Index L > Gottfried Wilhelm Leibniz Quotes

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Gottfried Wilhelm Leibniz
(1 Jul 1646 - 14 Nov 1716)

German philosopher, mathematician and political adviser.

Science Quotes by Gottfried Wilhelm Leibniz (25 quotes)

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Nihil est sine ratione.
There is nothing without a reason.
— Gottfried Wilhelm Leibniz
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According to their [Newton and his followers] doctrine, God Almighty wants to wind up his watch from time to time: otherwise it would cease to move. He had not, it seems, sufficient foresight to make it a perpetual motion. Nay, the machine of God's making, so imperfect, according to these gentlemen; that he is obliged to clean it now and then by an extraordinary concourse, and even to mend it, as clockmaker mends his work.
— Gottfried Wilhelm Leibniz
'Mr. Leibniz's First Paper' (1715). In H. G. Alexander (ed.), The Leibniz-Clarke Correspondence (1956), 11-2.
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All the different classes of beings which taken together make up the universe are, in the ideas of God who knows distinctly their essential gradations, only so many ordinates of a single curve so closely united that it would be impossible to place others between any two of them, since that would imply disorder and imperfection. Thus men are linked with the animals, these with the plants and these with the fossils which in turn merge with those bodies which our senses and our imagination represent to us as absolutely inanimate. And, since the law of continuity requires that when the essential attributes of one being approximate those of another all the properties of the one must likewise gradually approximate those of the other, it is necessary that all the orders of natural beings form but a single chain, in which the various classes, like so many rings, are so closely linked one to another that it is impossible for the senses or the imagination to determine precisely the point at which one ends and the next begins?all the species which, so to say, lie near the borderlands being equivocal, at endowed with characters which might equally well be assigned to either of the neighboring species. Thus there is nothing monstrous in the existence zoophytes, or plant-animals, as Budaeus calls them; on the contrary, it is wholly in keeping with the order of nature that they should exist. And so great is the force of the principle of continuity, to my thinking, that not only should I not be surprised to hear that such beings had been discovered?creatures which in some of their properties, such as nutrition or reproduction, might pass equally well for animals or for plants, and which thus overturn the current laws based upon the supposition of a perfect and absolute separation of the different orders of coexistent beings which fill the universe;?not only, I say, should I not be surprised to hear that they had been discovered, but, in fact, I am convinced that there must be such creatures, and that natural history will perhaps some day become acquainted with them, when it has further studied that infinity of living things whose small size conceals them for ordinary observation and which are hidden in the bowels of the earth and the depth of the sea.
— Gottfried Wilhelm Leibniz
Lettre Prétendue de M. De Leibnitz, à M. Hermann dont M. Koenig a Cité le Fragment (1753), cxi-cxii, trans. in A. O. Lovejoy, Great Chain of Being: A Study of the History of an Idea (1936), 144-5.
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Although the whole of this life were said to be nothing but a dream and the physical world nothing but a phantasm, I should call this dream or phantasm real enough, if, using reason well, we were never deceived by it.
— Gottfried Wilhelm Leibniz
Epigraph, without citation, in J.R. Newman (ed.) The World of Mathematics (1956), 1832.
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He who understands Archimedes and Apollonius will admire less the achievements of the foremost men of later times.
— Gottfried Wilhelm Leibniz
Quoted, without citation, in Max Dehn, 'Mathematics, 300 B.C.-200 B.C.', The American Mathematical Monthly (Jan 1944), 51, No. 1, 31.
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Imaginary numbers are a fine and wonderful refuge of the divine spirit almost an amphibian between being and non-being. (1702)
[Alternate translation:] The Divine Spirit found a sublime outlet in that wonder of analysis, that portent of the ideal world, that amphibian between being and not-being, which we call the imaginary root of negative unity.
— Gottfried Wilhelm Leibniz
Quoted in Félix Klein, Elementary Mathematics From an Advanced Standpoint: Arithmetic, Algebra, Analysis (1924), 56. Alternate translation as quoted in Tobias Dantzig, Number, the Language of Science: a Critical Survey Written for the Cultured Non-Mathematician (1930), 204
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In symbols one observes an advantage in discovery which is greatest when they express the exact nature of a thing briefly and, as it were, picture it; then indeed the labor of thought is wonderfully diminished.
— Gottfried Wilhelm Leibniz
In letter to Tschirnhaus. As quoted in George F. Simmons Calculus Gems (1992), 156, citing Dirk Jan Struik, 281-282.
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It follows from the supreme perfection of God, that in creating the universe has chosen the best possible plan, in which there is the greatest variety together with the greatest order; the best arranged ground, place, time; the most results produced in the most simple ways; the most of power, knowledge, happiness and goodness the creatures that the universe could permit. For since all the possibles in I understanding of God laid claim to existence in proportion to their perfections, the actual world, as the resultant of all these claims, must be the most perfect possible. And without this it would not be possible to give a reason why things have turned out so rather than otherwise.
— Gottfried Wilhelm Leibniz
The Principles of Nature and Grace (1714), The Philosophical Works of Leibnitz (1890), ed. G. M. Duncan, 213-4.
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It is God who is the ultimate reason things, and the Knowledge of God is no less the beginning of science than his essence and will are the beginning of things.
— Gottfried Wilhelm Leibniz
Letter on a General Principle Useful in Explaining the Laws of Nature (1687).
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It is unworthy of excellent men to lose hours like slaves in the labour of calculation which could safely be relegated to anyone else if machines were used.
Describing, in 1685, the value to astronomers of the hand-cranked calculating machine he had invented in 1673.
— Gottfried Wilhelm Leibniz
From 'Machina Arithmetica in qua non Aditio tantum Subtractio', as translated by Mark Kormes in David Eugene Smith, A Source Book in Mathematics (1929), 181.
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It is worth noting that the notation facilitates discovery. This, in a most wonderful way, reduces the mind's labour.
— Gottfried Wilhelm Leibniz
In Eberhard Zeidler, Applied Functional Analysis: main principles and their applications (1995), 225.
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Music is the pleasure the human soul experiences from counting without being aware that it is counting.
— Gottfried Wilhelm Leibniz
As quoted, without citation, in William L. Schaaf, 'The Highest Rung', National Mathematics Magazine (May 1942), 16, 8, 395.
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Nothing is accomplished all at once, and it is one of my great maxims, and one of the most completely verified, that Nature makes no leaps: a maxim which I have called the law of continuity.
[Referring to the gradual nature of all change from an initial state, through a continuous series of intermediate stages, to a final state.]
— Gottfried Wilhelm Leibniz
Letter to de Volder, in Nouveaux Essais, New Essays (1703) translated by A. G. Langley (3rd ed. 1949). In Frederick Copleston, A History of Philosophy (1999), 292.
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Nothing is more important than to see the sources of invention which are, in my opinion more interesting than the inventions themselves.
— Gottfried Wilhelm Leibniz
Epigraph, without citation, in R.P. Watkins, Computer Problem Solving (1980). Webmaster has not yet been able to find a primary source. Can you help?
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Now this supreme wisdom, united to goodness that is no less infinite, cannot but have chosen the best. For as a lesser evil is a kind of good, even so a lesser good is a kind of evil if it stands in the way of a greater good; and the would be something to correct in the actions of God if it were possible to the better. As in mathematics, when there is no maximum nor minimum, in short nothing distinguished, everything is done equally, or when that is not nothing at all is done: so it may be said likewise in respect of perfect wisdom, which is no less orderly than mathematics, that if there were not the best (optimum) among all possible worlds, God would not have produced any.
— Gottfried Wilhelm Leibniz
Theodicy: Essays on the Goodness of God and Freedom of Man and the Origin of Evil (1710), 128.
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One cannot explain words without making incursions into the sciences themselves, as is evident from dictionaries; and, conversely, one cannot present a science without at the same time defining its terms.
— Gottfried Wilhelm Leibniz
'Of the Division of the Sciences' (1765), Book 4, Chap. 21, in New Essays on Human Understanding, trans. and ed. Peter Remnal (1981), 522.
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Our reasonings are grounded upon two great principles, that of contradiction, in virtue of which we judge false that which involves a contradiction, and true that which is opposed or contradictory to the false.
— Gottfried Wilhelm Leibniz
The Monadology and Other Philosophical Writings (1714), trans. Robert Latta (1898) 235.
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Taking mathematics from the beginning of the world to the time when Newton lived, what he had done was much the better half.
— Gottfried Wilhelm Leibniz
As quoted in Edmund Fillingham King, A Biographical Sketch of Sir Isaac Newton (1858), 97, stating this was Leibniz's reply “when asked at the royal table in Berlin his opinion of Newton.” No source citation was given, although all the next quotes that followed had footnotes. The lack of citation leaves the accuracy of the quote unverified. If you know a primary source, please contact the Webmaster.
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The art of discovering the causes of phenomena, or true hypothesis, is like the art of deciphering, in which an ingenious conjecture greatly shortens the road.
— Gottfried Wilhelm Leibniz
In Gottfried Leibniz and Alfred Fideon Langley (trans.), 'Leibniz’s Critique of Locke', New Essays Concerning Human Understanding (1896), Book 4, Chap. 12, 526.
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The knowledge we have aquired ought not to resemble a great shop without order, and without inventory; we ought to know what we possess, and be able to make it serve us in our need.
— Gottfried Wilhelm Leibniz
In Hialmer Day Gould, New Practical Spelling (1905), 27
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The order, the symmetry, the harmony enchant us ... God is pure order. He is the originator of universal harmony
— Gottfried Wilhelm Leibniz
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The soul [is a] mirror of an indestructible universe.
— Gottfried Wilhelm Leibniz
In Gottfried von Leibniz and ‎Robert Latta (trans.), The Monadology and Other Philosophical Writings (1898), 262.
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There are also two kinds of truths, those of reasoning and those of fact. Truths of reasoning are necessary and their opposite is impossible: truths of fact are contingent and their opposite is possible. When a truth is necessary, reason can be found by analysis, resolving it into more simple ideas and truths, until we come to those which are primary.
— Gottfried Wilhelm Leibniz
The Monadology and Other Philosophical Writings (1714), trans. Robert Latta (1898), 235-6.
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These principles have given me a way of explaining naturally the union or rather the mutual agreement [conformité] of the soul and the organic body. The soul follows its own laws, and the body likewise follows its own laws; and they agree with each other in virtue of the pre-established harmony between all substances, since they are all representations of one and the same universe.
— Gottfried Wilhelm Leibniz
The Monadology and Other Philosophical Writings (1714), trans. Robert Latta (1898), 262.
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We should like Nature to go no further; we should like it to be finite, like our mind; but this is to ignore the greatness and majesty of the Author of things.
— Gottfried Wilhelm Leibniz
Letter to S. Clarke, 1715. Trans. M. Morris and G. H. R. Parkinson, Leibniz: PhilosophicalWritings (1973), 220.
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Quotes by others about Gottfried Wilhelm Leibniz (13)

I see no good reason why the views given this volume [The Origin of Species] should shock the religious feelings of any one. It is satisfactory, as showing how transient such impressions are, to remember that the greatest discovery ever made by man, namely, the law of attraction of gravity, was also attacked by Leibnitz, “as subversive of natural, and inferentially of revealed, religion.”
The Origin of Species (1909), 520.
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The stone that Dr. Johnson once kicked to demonstrate the reality of matter has become dissipated in a diffuse distribution of mathematical probabilities. The ladder that Descartes, Galileo, Newton, and Leibniz erected in order to scale the heavens rests upon a continually shifting, unstable foundation.
Mathematics in Western Culture (1953), 382.
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Laplace would have found it child's-play to fix a ratio of progression in mathematical science between Descartes, Leibnitz, Newton and himself
The Education of Henry Adams: An Autobiography? (1918), 491.
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The analytical geometry of Descartes and the calculus of Newton and Leibniz have expanded into the marvelous mathematical method—more daring than anything that the history of philosophy records—of Lobachevsky and Riemann, Gauss and Sylvester. Indeed, mathematics, the indispensable tool of the sciences, defying the senses to follow its splendid flights, is demonstrating today, as it never has been demonstrated before, the supremacy of the pure reason.
'What Knowledge is of Most Worth?', Presidential address to the National Education Association, Denver, Colorado (9 Jul 1895). In Educational Review (Sep 1895), 10, 109.
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We hold these truths to be self-evident.
Franklin's edit to the assertion of religion in Thomas Jefferson's original wording, “We hold these truths to be sacred and undeniable” in a draft of the Declaration of Independence changes it instead into an assertion of rationality. The scientific mind of Franklin drew on the scientific determinism of Isaac Newton and the analytic empiricism of David Hume and Gottfried Leibniz. In what became known as “Hume's Fork” the latters' theory distinguished between synthetic truths that describe matters of fact, and analytic truths that are self-evident by virtue of reason and definition.
As explained by Walter Isaacson in Benjamin Franklin: An American Life (2004), 312.
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It is not always the most brilliant speculations nor the choice of the most exotic materials that is most profitable. I prefer Monsieur de Reaumur busy exterminating moths by means of an oily fleece; or increasing fowl production by making them hatch without the help of their mothers, than Monsieur Bemouilli absorbed in algebra, or Monsieur Leibniz calculating the various advantages and disadvantages of the possible worlds.
Spectacle, 1, 475. Quoted in Camille Limoges, 'Noel-Antoine Pluche', in C. C. Gillispie (ed.), Dictionary of Scientific Biography (1974 ), Vol. 11, 43.
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It appears that the solution of the problem of time and space is reserved to philosophers who, like Leibniz, are mathematicians, or to mathematicians who, like Einstein, are philosophers.
Collected in Paul Arthur Schilpp (ed.), Albert Einstein: Philosopher-Scientist (1959), Vol. 1, 307. Also, in James Louis Jarrett and Sterling M. McMurrin (eds.), Contemporary Philosophy: A Book of Readings (1954), 71.
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Libraries will in the end become cities, said Leibniz.
Aphorism 29 in Notebook C (1772-1773), as translated by R.J. Hollingdale in Aphorisms (1990). Reprinted as The Waste Books (2000), 37.
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[Isaac Newton] regarded the Universe as a cryptogram set by the Almighty—just as he himself wrapt the discovery of the calculus in a cryptogram when he communicated with Leibniz. By pure thought, by concentration of mind, the riddle, he believed, would be revealed to the initiate.
In 'Newton, the Man' (1946). In Geoffrey Keynes (ed.), Essays in Biography, 2nd edition (1951), 314.
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Notable enough, however, are the controversies over the series 1 – 1 + 1 – 1 + 1 – … whose sum was given by Leibniz as 1/2, although others disagree. … Understanding of this question is to be sought in the word “sum”; this idea, if thus conceived—namely, the sum of a series is said to be that quantity to which it is brought closer as more terms of the series are taken—has relevance only for convergent series, and we should in general give up the idea of sum for divergent series.
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Leibniz never married; he had considered it at the age of fifty; but the person he had in mind asked for time to reflect. This gave Leibniz time to reflect, too, and so he never married.
From the original French, “Leibnitz ne s'était point marié ; il y avait pensé à l'âge de cinquante ans; mais la personne qu’il avait en vue voulut avoir le temps de faire ses réflexions. Cela donna à Leibnitz le loisir de faire aussi les siennes, et il ne se maria point.” In 'Éloge de Leibniz' (1768), in Éloges de Fontenelle (1883), 132.
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Marly 30 July 1705. From all I hear of Leibniz he must be very intelligent, and pleasant company in consequence. It is rare to find learned men who are clean, do not stink and have a sense of humour.
From Letter (30 Jul 1705), in Maria Kroll (trans.), Letters from Liselotte: Elisabeth-Charlotte, Princess Palatine and Duchess of Orléans, "Madame" 1652-1722 (1970), 131. Also seen in Alan L. MacKay, A Dictionary of Scientific Quotations (1991), 175. Also seen attributed to Charles-Louis de Secondat Montesquieu, in Alan L. MacKay, Dictionary of Scientific Quotations (1977), 175, citing Letter LXVI (30 Jul 1705) in Les Lettres Persanes. However, Webmaster does not find this quote when looking at Letter LXVI in Les Lettres Persanes (1721), text prepared by André Lefèvre (1873). (Can you help).
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It would be difficult and perhaps foolhardy to analyze the chances of further progress in almost every part of mathematics one is stopped by unsurmountable difficulties, improvements in the details seem to be the only possibilities which are left… All these difficulties seem to announce that the power of our analysis is almost exhausted, even as the power of ordinary algebra with regard to transcendental geometry in the time of Leibniz and Newton, and that there is a need of combinations opening a new field to the calculation of transcendental quantities and to the solution of the equations including them.
From Rapport historique sur les progrès des sciences mathématiques depuis 1789, et sur leur état actuel (1810), 131. As translated in George Sarton, The Study of the History of Mathematics (1936), 13. In the original French: “Il seroit difficile et peut-être téméraire d’analyser les chances que l’avenir offre à l’avancement des mathématiques: dans presque toutes les parties, on est arrêté par des difficultés insurmontables; des perfectionnements de détail semblent la seule chose qui reste à faire… Toutes ces difficultés semblent annoncer que la puissance de notre analyse est à-peu-près épuisée, comme celle de l’algèbre ordinaire l’étoit par rapport à la géométrie transcendante au temps de Leibnitz et de Newton, et qu’il faut des combinaisons qui ouvrent un nouveau champ au calcul des transcendantes et à la résolution des équations qui les contiennent.” Sarton states this comes from “the report on mathematical progress prepared for the French Academy of Sciences at Napoleon’s request”.
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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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- 100 -
Sophie Germain
Gertrude Elion
Ernest Rutherford
James Chadwick
Marcel Proust
William Harvey
Johann Goethe
John Keynes
Carl Gauss
Paul Feyerabend
- 90 -
Antoine Lavoisier
Lise Meitner
Charles Babbage
Ibn Khaldun
Ralph Emerson
Robert Bunsen
Frederick Banting
Andre Ampere
Winston Churchill
- 80 -
John Locke
Bronislaw Malinowski
Thomas Huxley
Alessandro Volta
Erwin Schrodinger
Wilhelm Roentgen
Louis Pasteur
Bertrand Russell
Jean Lamarck
- 70 -
Samuel Morse
John Wheeler
Nicolaus Copernicus
Robert Fulton
Pierre Laplace
Humphry Davy
Thomas Edison
Lord Kelvin
Theodore Roosevelt
Carolus Linnaeus
- 60 -
Francis Galton
Linus Pauling
Immanuel Kant
Martin Fischer
Robert Boyle
Karl Popper
Paul Dirac
James Watson
William Shakespeare
- 50 -
Stephen Hawking
Niels Bohr
Nikola Tesla
Rachel Carson
Max Planck
Henry Adams
Richard Dawkins
Werner Heisenberg
Alfred Wegener
John Dalton
- 40 -
Pierre Fermat
Edward Wilson
Johannes Kepler
Gustave Eiffel
Giordano Bruno
JJ Thomson
Thomas Kuhn
Leonardo DaVinci
David Hume
- 30 -
Andreas Vesalius
Rudolf Virchow
Richard Feynman
James Hutton
Alexander Fleming
Emile Durkheim
Benjamin Franklin
Robert Oppenheimer
Robert Hooke
Charles Kettering
- 20 -
Carl Sagan
James Maxwell
Marie Curie
Rene Descartes
Francis Crick
Michael Faraday
Srinivasa Ramanujan
Francis Bacon
Galileo Galilei
- 10 -
John Watson
Rosalind Franklin
Michio Kaku
Isaac Asimov
Charles Darwin
Sigmund Freud
Albert Einstein
Florence Nightingale
Isaac Newton

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