Leibniz Quotes

Quotes tagged as "leibniz" Showing 1-30 of 31
G.K. Chesterton
“Because children have abounding vitality, because they are in spirit fierce and free, therefore they want things repeated and unchanged. They always say, "Do it again"; and the grown-up person does it again until he is nearly dead. For grown-up people are not strong enough to exult in monotony. But perhaps God is strong enough to exult in monotony. It is possible that God says every morning, "Do it again" to the sun; and every evening, "Do it again" to the moon. It may not be automatic necessity that makes all daisies alike; it may be that God makes every daisy separately, but has never got tired of making them. It may be that He has the eternal appetite of infancy; for we have sinned and grown old, and our Father is younger than we.”
G. K. Chesterton, Orthodoxy

Gottfried Wilhelm Leibniz
“Nihil est sine ratione.
[There is nothing without a reason.]”
Gottfried Wilhelm Leibniz

Robert G. Ingersoll
“Is it possible that the Pentateuch could not have been written by uninspired men? that the assistance of God was necessary to produce these books? Is it possible that Galilei ascertained the mechanical principles of 'Virtual Velocity,' the laws of falling bodies and of all motion; that Copernicus ascertained the true position of the earth and accounted for all celestial phenomena; that Kepler discovered his three laws—discoveries of such importance that the 8th of May, 1618, may be called the birth-day of modern science; that Newton gave to the world the Method of Fluxions, the Theory of Universal Gravitation, and the Decomposition of Light; that Euclid, Cavalieri, Descartes, and Leibniz, almost completed the science of mathematics; that all the discoveries in optics, hydrostatics, pneumatics and chemistry, the experiments, discoveries, and inventions of Galvani, Volta, Franklin and Morse, of Trevithick, Watt and Fulton and of all the pioneers of progress—that all this was accomplished by uninspired men, while the writer of the Pentateuch was directed and inspired by an infinite God? Is it possible that the codes of China, India, Egypt, Greece and Rome were made by man, and that the laws recorded in the Pentateuch were alone given by God? Is it possible that Æschylus and Shakespeare, Burns, and Beranger, Goethe and Schiller, and all the poets of the world, and all their wondrous tragedies and songs are but the work of men, while no intelligence except the infinite God could be the author of the Pentateuch? Is it possible that of all the books that crowd the libraries of the world, the books of science, fiction, history and song, that all save only one, have been produced by man? Is it possible that of all these, the bible only is the work of God?”
Robert G. Ingersoll, Some Mistakes of Moses

Gottfried Wilhelm Leibniz
“Nature has established patterns originating in the return of events, but only for the most part. New illnesses flood the human race, so that no matter how many experiments you have done on corpses, you have not thereby immposd a limit on the nature of events so that in the future they could not vary.”
Gottfried Leibniz

Benjamin Franklin
“We hold these truths to be self-evident.

{Franklin's edit to the assertion 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 Wilhelm 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.}”
Benjamin Franklin

Nicholas Murray Butler
“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.”
Nicholas Murray Butler

“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.”
Hans Reichenbach

Samir Okasha
“From a philosophical point of view, Leibniz's most interesting argument was that absolute space conflicted with what he called the principle of the identity of indiscernibles (PII). PII says that if two objects are indiscernible, then they are identical, i.e. they are really one and the same object. What does it mean to call two objects indiscernible? It means that no difference at all can be found between them--they have exactly the same attributes. So if PII is true, then any two genuinely distinct objects must differ in at least one of their attributes--otherwise they would be one, not two. PII is intuitively quite compelling. It certainly is not easy to find an example of two distinct objects that share all their attributes. Even two mass-produced factory goods will normally differ in innumerable ways, even if the differences cannot be detected with the naked eye.

Leibniz asks us to imagine two different universes, both containing exactly the same objects. In Universe One, each object occupies a particular location in absolute space.In Universe Two, each object has been shifted to a different location in absolute space, two miles to the east (for example). There would be no way of telling these two universes apart. For we cannot observe the position of an object in absolute space, as Newton himself admitted. All we can observe are the positions of objects relative to each other, and these would remain unchanged--for all objects are shifted by the same amount. No observations or experiments could ever reveal whether we lived in universe One or Two.”
Samir Okasha, Philosophy of Science: A Very Short Introduction

Thomas Henry Huxley
“The careful observations and the acute reasonings of the Italian geologists of the seventeenth and eighteenth centuries; the speculations of Leibnitz in the 'Protogaea' and of Buffon in his 'Théorie de la Terre;' the sober and profound reasonings of Hutton, in the latter part of the eighteenth century; all these tended to show that the fabric of the earth itself implied the continuance of processes of natural causation for a period of time as great, in relation to human history, as the distances of the heavenly bodies from us are, in relation to terrestrial standards of measurement. The abyss of time began to loom as large as the abyss of space. And this revelation to sight and touch, of a link here and a link there of a practically infinite chain of natural causes and effects, prepared the way, as perhaps nothing else has done, for the modern form of the ancient theory of evolution.”
Thomas Henry Huxley, The Advance of Science in the Last Half-Century

Gilles Deleuze
“Morality consists in this for each individual: to attempt each time to extend its region of clear expression, to try to augment its amplitude, so as to produce a free act that expresses the most possible in one given condition or another. -- Gilles Deleuze, The Fold: Leibniz and the Baroque, 73”
Gilles Deleuze

“[On Gottfried Wilhelm Leibniz]

The answer is unknowable, but it may not be unreasonable to see him, at least in theological terms, as essentially a deist. He is a determinist: there are no miracles (the events so called being merely instances of infrequently occurring natural laws); Christ has no real role in the system; we live forever, and hence we carry on after our deaths, but then everything — every individual substance — carries on forever.”
Peter Loptson

“Consistent with the liberal views of the Enlightenment, Leibniz was an optimist with respect to human reasoning and scientific progress. Although he was a great reader and admirer of Spinoza, Leibniz, being a confirmed deist, rejected emphatically Spinoza's pantheism.”
Shelby D. Hunt, Marketing Theory: Foundations, Controversy, Strategy, and Resource-Advantage Theory

René Guénon
“Du reste, la majorité des orientalistes ne sont et ne veulent être que des érudits ; tant qu’ils se bornent à des travaux historiques ou philologiques, cela n’a pas grande importance ; il est évident que des ouvrages de ce genre ne peuvent servir de rien pour atteindre le but que nous envisageons ici, mais leur seul danger, en somme, est celui qui est commun à tous les abus de l’érudition, nous voulons dire la propagation de cette « myopie intellectuelle » qui borne tout savoir à des recherches de détail, et le gaspillage d’efforts qui pourraient être mieux employés dans bien des cas. Mais ce qui est beaucoup plus grave à nos yeux, c’est l’action exercée par ceux des orientalistes qui ont la prétention de comprendre et d’interpréter les doctrines, et qui les travestissent de la façon la plus incroyable, tout en assurant parfois qu’ils les comprennent mieux que les Orientaux eux-mêmes (comme Leibnitz s’imaginait avoir retrouvé le vrai sens des caractères de Fo-hi), et sans jamais songer à prendre l’avis des représentants autorisés des civilisations qu’ils veulent étudier, ce qui serait pourtant la première chose à faire, au lieu de se comporter comme s’il s’agirait de reconstituer des civilisations disparues.”
René Guénon, East and West

“Can you really believe that a drop of urine is an infinity of monads, and that each of these has ideas, however obscure, of the universe as a whole?”
Voltaire, Œuvres complètes - 109 titres et annexes

Gottfried Wilhelm Leibniz
“... for although people can be made worse off by all other gifts, correct reasoning alone can only be for the good.”
Gottfried Wilhelm Leibniz

“Gödel, the great mathematical logician, was the champion of rational religion. In many ways, we seek to establish a Leibniz-Gödel hyperrationalist alternative to science. We want to refute the idea that science is just one monolith of materialism and empiricism. You can be a much better scientist by choosing a much better, more rational science, namely that of idealism and rationalism.”
Thomas Stark, God Is Mathematics: The Proofs of the Eternal Existence of Mathematics

“Leibniz’s brilliant monadic system naturally gives rise to calculus (the main tool of mathematics and science). But it was not Leibniz who linked the energy of monads to waves – that was done later following the work of the French genius Jean Baptiste Joseph Fourier on Fourier series and Fourier transforms. Nevertheless, Leibniz’s idea of energy originating from countless mathematical points and flowing across a plenum is indeed the first glimpse in the modern age of “field theory” that now underpins contemporary physics. Leibniz was centuries ahead of his time. Leibniz’s system is entirely mathematical. It brings mathematics to life. The infinite collection of monads constitutes an evolving cosmic organism, unfolding according to mathematical laws.”
Mike Hockney, The Last Man Who Knew Everything

Neal Stephenson
“Now walking out onto the upper deck to find Minerva sailing steadily eastward on calm seas, Daniel is appalled that anyone ever doubted these matters. The horizon is a perfect line. The sun a red circle tracing a neat path through the sky and proceeding through an orderly series of color changes: red, yellow, white. Thus nature.

Minerva, the human world, is a family of curves. There are no straight lines here. The decks are slightly arched, to shed water and supply greater strength. The masts flexed, impelled by the thrust of the sails, but restrained by webs of rigging, curved grids like Isaac’s sundial lines. Of course, wherever wind collects in a sail or water skims around the hull, it follows rules that Bernoulli has set down using the calculus, Leibniz’s version. Minerva is a congregation of Leibniz curves, navigating according to Bernoulli rules, across a vast mostly water-covered sphere whose size, precise shape, trajectory through the heavens and destiny were all laid down by Newton.”
Neal Stephenson

Charles Taylor
“Leibniz combines Aristotelian teleology in the notion that the nature of a thing provides for its unfolding in a certain fashion with the modern idea that the nature of a thing is within it. Because the forms are internal in the way that they are not with Aristotle, the harmony of the world has to be pre-established by God.”
Charles Taylor, Sources of the Self: The Making of the Modern Identity

René Guénon
“La première de toutes les difficultés auxquelles il donne lieu à cet égard, c’est précisément la conception des quantités négatives comme « moindres que zéro », que Leibnitz rangeait parmi les affirmations qui ne sont que « toleranter verae », mais qui, en réalité, est, comme nous le disions tout à l’heure, entièrement dépourvue de toute signification. « Avancer qu’une quantité négative isolée est moindre que zéro, a dit Carnot, c’est couvrir la science des mathématiques, qui doit être celle de l’évidence, d’un nuage impénétrable, et s’engager dans un labyrinthe de paradoxes tous plus bizarres les uns que les autres ». Sur ce point, nous pouvons nous en tenir à ce jugement, qui n’est pas suspect et n’a certainement rien d’exagéré ; on ne devrait d’ailleurs jamais oublier, dans l’usage qu’on fait de cette notation des nombres négatifs, qu’il ne s’agit là de rien de plus que d’une simple convention.”
René Guénon, The Metaphysical Principles of the Infinitesimal Calculus

Kevin R.D. Shepherd
“The subject of 'perennial philosophy' is currently one of the many misleading themes employed in vulgar mysticism. Emanating from enthusiasts of traditional religion, this topic has been appropriated by new age communities and figureheads, to the extent that even Huxley can appear profound by comparison. The Latin phrase is often associated with Leibniz, who may be credited with a more genuine attitude, though it is clear that he did not resolve the issue involved. The term philosophy is currently so confused in application that it can mean anything saleable or novelistic.”
Kevin R.D. Shepherd, Some Philosophical Critiques and Appraisals: An Investigation of Perennial Philosophy, Cults, Occultism, Psychotherapy, and Postmodernism

Arthur Schopenhauer
“Că însă un patron absolut ticălos precum Hegel, a cărui întreagă pseudofilozofare a fost de fapt o amplificare monstruoasă a argumentului ontologic, a căutat să-I apere pe acesta împotriva criticii lui Kant constituie o alianţă de care însuşi argumentului ontologic i s-ar face ruşine, oricât de puţin are el de-a face cu ruşinea.”
Arthur Schopenhauer, On the Fourfold Root of the Principle of Sufficient Reason

“The temporal, contingent world is, as Leibniz said, a “collection of finite things.” It is possible only because it is underpinned by an eternal, necessary world, comprising a collection of zero-infinity things, i.e. monads.”
Thomas Stark, God Is Mathematics: The Proofs of the Eternal Existence of Mathematics

“Leibniz’s assertion that we live in the best of all possible worlds is, no matter what present appearances suggest, absolutely true – because the issue has to be considered over an entire cosmic Age, not just one snapshot in time. All the horrors of today are necessary for the glories of tomorrow. They provide the dialectical obstacles we must overcome, and we do so by becoming more and more perfect ourselves.”
Mike Hockney, The Last Man Who Knew Everything

“No one need ever again be embarrassed when they mention religion. It’s not some mad, deluded flight from reality. On the contrary it is ABSOLUTE reality, thanks to mathematics. Had mathematics not had any religious elements, we would be atheists. That’s not how it turned out. The soul is the basis of mathematics – exactly as Leibniz, one of the greatest mathematicians of all time, stated. Descartes, Plato and Pythagoras – three other towering mathematicians and philosophers – would have had no difficulty in agreeing with him. Join Team Logos, Team Mathematics. Mathematics is the one, true, divine subject.”
Mike Hockney, The Last Man Who Knew Everything

“Feynman said, “If, in some cataclysm, all of scientific knowledge were to be destroyed, and only one sentence passed on to the next generations of creatures, what statement would contain the most information in the fewest words? In that one sentence, you will see, there is an enormous amount of information about the world, if just a little imagination and thinking are applied”

Our sentence would be: “The Monadology asserts that the fundamental units of existence are INFINITE, dimensionless, living, thinking points – monads, ZEROS, souls – each of which has INFINITE energy content, all controlled by a single equation – Euler’s Formula – and the collective energy of this universe of mathematical points creates a physical universe of which every objective value is ZERO, but, through a self-solving, self-optimizing, dialectical, evolving process, the universe generates a final, subjective value of INFINITY – divinity, perfection, the ABSOLUTE.”

For ours is the religion of zero and infinity, the two numbers that define the soul and the whole of existence. As above, so below.”
Mike Hockney, The God Equation

“Science should have been about reason, but, instead, it chose to be a crude reaction and retort to religion, and that drove it down a catastrophic atheistic path. Had it not been for religion, science would have become what Leibniz always thought it should be: a union of the empirical and rational, of the physical and metaphysical, with the rational and metaphysical being the dominant partners.”
Mike Hockney, Richard Dawkins: The Pope of Unreason

“Leibniz’s system is compatible with infinite divisibility,
culminating – at infinity – with the indivisible monadic singularity. Materialism has no compatibility with singularities. The laws of physics are explicitly said to break down at singularities. That’s because singularities are mental frequency domains and science religiously believes only in spacetime and matter. Singularities are beyond science’s Meta Paradigm and ideology.”
Mike Hockney, The Forbidden History of Science

Salman Rushdie
“Earthquakes, I point out, have always made men eager to placate the gods. After the great Lisbon earthquake of November 1, 1755—that catastrophe which Voltaire saw as an irrefutable argument for the tragic view of life and against Leibnizian optimism—the locals decided on a propitiatory auto-da-fé.”
Salman Rushdie, The Ground Beneath Her Feet

“Why is there something rather than nothing?” was the supremely profound question posed by Leibniz. The answer is that there is something and nothing – they are two sides of the same coin, two perspectives of the same thing. Zero, ontologically, is also infinity. It contains infinite elements that all balance each other out (they sum to zero). Zero and infinity cannot be found separately. Where you get “nothing” you always get “everything too”. They are inseparable twins. So, Leibniz answered his own question with the most consummate skill. A new question replaced it: “Why are something and nothing the same?” And the answer is that it’s because zero and infinity are the same: two sides of one coin.”
Mark Romel, Strange World: Why People Are Getting Weirder

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