Leibniz Quotes

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.

This is the best of all possible worlds.

He who hasn't tasted bitter things hasn't earned sweet things.

Nihil est sine ratione. [There is nothing without a reason.]

Reading list (1972 edition)[edit] 1. Homer – Iliad, Odyssey 2. The Old Testament 3. Aeschylus – Tragedies 4. Sophocles – Tragedies 5. Herodotus – Histories 6. Euripides – Tragedies 7. Thucydides – History of the Peloponnesian War 8. Hippocrates – Medical Writings 9. Aristophanes – Comedies 10. Plato – Dialogues 11. Aristotle – Works 12. Epicurus – Letter to Herodotus; Letter to Menoecus 13. Euclid – Elements 14. Archimedes – Works 15. Apollonius of Perga – Conic Sections 16. Cicero – Works 17. Lucretius – On the Nature of Things 18. Virgil – Works 19. Horace – Works 20. Livy – History of Rome 21. Ovid – Works 22. Plutarch – Parallel Lives; Moralia 23. Tacitus – Histories; Annals; Agricola Germania 24. Nicomachus of Gerasa – Introduction to Arithmetic 25. Epictetus – Discourses; Encheiridion 26. Ptolemy – Almagest 27. Lucian – Works 28. Marcus Aurelius – Meditations 29. Galen – On the Natural Faculties 30. The New Testament 31. Plotinus – The Enneads 32. St. Augustine – On the Teacher; Confessions; City of God; On Christian Doctrine 33. The Song of Roland 34. The Nibelungenlied 35. The Saga of Burnt Njál 36. St. Thomas Aquinas – Summa Theologica 37. Dante Alighieri – The Divine Comedy;The New Life; On Monarchy 38. Geoffrey Chaucer – Troilus and Criseyde; The Canterbury Tales 39. Leonardo da Vinci – Notebooks 40. Niccolò Machiavelli – The Prince; Discourses on the First Ten Books of Livy 41. Desiderius Erasmus – The Praise of Folly 42. Nicolaus Copernicus – On the Revolutions of the Heavenly Spheres 43. Thomas More – Utopia 44. Martin Luther – Table Talk; Three Treatises 45. François Rabelais – Gargantua and Pantagruel 46. John Calvin – Institutes of the Christian Religion 47. Michel de Montaigne – Essays 48. William Gilbert – On the Loadstone and Magnetic Bodies 49. Miguel de Cervantes – Don Quixote 50. Edmund Spenser – Prothalamion; The Faerie Queene 51. Francis Bacon – Essays; Advancement of Learning; Novum Organum, New Atlantis 52. William Shakespeare – Poetry and Plays 53. Galileo Galilei – Starry Messenger; Dialogues Concerning Two New Sciences 54. Johannes Kepler – Epitome of Copernican Astronomy; Concerning the Harmonies of the World 55. William Harvey – On the Motion of the Heart and Blood in Animals; On the Circulation of the Blood; On the Generation of Animals 56. Thomas Hobbes – Leviathan 57. René Descartes – Rules for the Direction of the Mind; Discourse on the Method; Geometry; Meditations on First Philosophy 58. John Milton – Works 59. Molière – Comedies 60. Blaise Pascal – The Provincial Letters; Pensees; Scientific Treatises 61. Christiaan Huygens – Treatise on Light 62. Benedict de Spinoza – Ethics 63. John Locke – Letter Concerning Toleration; Of Civil Government; Essay Concerning Human Understanding;Thoughts Concerning Education 64. Jean Baptiste Racine – Tragedies 65. Isaac Newton – Mathematical Principles of Natural Philosophy; Optics 66. Gottfried Wilhelm Leibniz – Discourse on Metaphysics; New Essays Concerning Human Understanding;Monadology 67. Daniel Defoe – Robinson Crusoe 68. Jonathan Swift – A Tale of a Tub; Journal to Stella; Gulliver's Travels; A Modest Proposal 69. William Congreve – The Way of the World 70. George Berkeley – Principles of Human Knowledge 71. Alexander Pope – Essay on Criticism; Rape of the Lock; Essay on Man 72. Charles de Secondat, baron de Montesquieu – Persian Letters; Spirit of Laws 73. Voltaire – Letters on the English; Candide; Philosophical Dictionary 74. Henry Fielding – Joseph Andrews; Tom Jones 75. Samuel Johnson – The Vanity of Human Wishes; Dictionary; Rasselas; The Lives of the Poets

Music is the hidden arithmetical exercise of a mind unconscious that it is calculating.

Why is there something rather than nothing?

There is nothing in the understanding which has not come from the senses, except the understanding itself, or the one who understands.

Nothing is in the intellect that was not first in the senses, except the intellect itself.

The present is big with the future.

…every feeling is the perception of a truth...

Nothing is necessitated whose opposite is possible.

If you could blow the brain up to the size of a mill and walk about inside, you would not find consciousness.

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.

...as far as we are capable of knowledge we sin in neglecting to acquire it...

Leibniz is at the disadvantage of not having seen it. Or perhaps we should count this as an advantage, for anyone who sees it is dumbfounded by the brilliance of the geometry, and it is difficult to criticize a man’s work when you are down on your knees shielding your eyes.

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.)

He who does not act does not exist.

...it is the knowledge of necessary and eternal truths that distinguishes us from the mere animals and gives us Reason and the sciences, raising us to the knowledge of ourselves and of God...

Leibniz was somewhat mean about money. When any young lady at the court of Hanover married, he used to give her what he called a "wedding present," consisting of useful maxims, ending up with the advice not to give up washing now that she had secured a husband. History does not record whether the brides were grateful.

Perceptions which are at present insensible may grow some day: nothing is useless, and eternity provides great scope for change.

The means of obtaining as much variety as possible, but with the greatest possible order...is the means of obtaining as much perfection as possible.

This interconnection or accommodation of all created things to each other, and each to all the others, brings it about that each simple substance has relations that express all the others, and consequently, that each simple substance is a perpetual, living mirror of the universe.

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.

For all bodies are in perpetual flux like rivers, and parts are passing in and out of them continually.

imaginary numbers are a fine and wonderful resource of the divine intellect, almost an amphibian between being and non-being.

that each ejaculation contains several billion sperm cells –or roughly the same number as there are people in the world– which means that, in himself, each man holds the potential of an entire world. And what would happen, could it happen, is the full range of possibilities: a spawn of idiots and geniuses, of the beautiful and the deformed, of saints, catatonics, thieves, stock brokers, and high-wire artists. Each man, therefore, is the entire world, bearing within his genes a memory of all mankind. Or, as Leibniz put it: “Every living substance is a perpetual living mirror of the universe.

Rien n'est plus troublant que les mouvements incessants de ce qui semble immobile. p214 (Minuit)

And yet viewing several depictions of even an imaginary city, is enlightening in a way," Leibniz said. "Each painter can view the city from only one standpoint at a time, so he will move about the place, and paint it from a hilltop on one side, then a tower on the other, then from a grand intersection in the middle--all in the same canvas. When we look at the canvas, then, we glimpse in a small way how God understands the universe--for he sees it from every point of view at once. By populating the world with so many different minds, each with its own point of view, God gives us a suggestion of what it means to be omniscient.

The city seems to be a labyrinth that can be ordered. The world is an infinite series of curvatures or inflections, and the entire world is enclosed in the soul from one point of view.

I have so many ideas that may perhaps be of some use in time if others more penetrating than I go deeply into them someday and join the beauty of their minds to the labour of mine.

Pourquoi y a-t-il quelque chose plutôt que rien ?

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.

Shut up about Leibniz for a moment, Rudy, because look here: You—Rudy—and I are on a train, as it were, sitting in the dining car, having a nice conversation, and that train is being pulled along at a terrific clip by certain locomotives named The Bertrand Russell and Riemann and Euler and others. And our friend Lawrence is running alongside the train, trying to keep up with us—it’s not that we’re smarter than he is, necessarily, but that he’s a farmer who didn’t get a ticket. And I, Rudy, am simply reaching out through the open window here, trying to pull him onto the fucking train with us so that the three of us can have a nice little chat about mathematics without having to listen to him panting and gasping for breath the whole way.

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.}

And just as the same town, when looked at from different sides, appears quite different and is, as it were, multiplied in perspective, so also it happens that because of the infinite number of simple substances, it is as if there were as many different universes, which are however but different perspective representations of a single universe form the different point of view of each monad.

For I hold that it is only when we can prove everything we assert that we understand perfectly the thing under consideration.

It is true that the more we see some connection in what happens to us, the more we are confirmed in the opinion we have about the reality of our appearances; and it is also true that the more we examine our appearances closely, the more we find them well-sequenced, as microscopes and other aids in making experiments have shown us.

The mind is not only capable of knowing [innate ideas], but further of finding them in itself; and if it had only the simple capacity to receive knowledge…it would not be the source of necessary truths…

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.

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?

Leibniz had a vision of a world in which everything lives not in space but immersed in a network of relationships.

In the century of Kepler, Galileo, Descartes, Pascal, and Newton,” one historian wrote, “the most versatile genius of all was Gottfried Wilhelm Leibniz.

Leibniz's machine was designed to automate the dreary task of solving moral problems

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

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?

[...] we can find no true or existent fact, no true assertion, without there being a sufficient reason why it is thus and not otherwise, although most of the time these reasons cannot be known to us.

…if geometry were as much opposed to our passions and present interests as is ethics, we should contest it and violate I but little less, notwithstanding all the demonstrations of Euclid and Archimedes…

But as the late- seventeenth-century philosopher Gottfried Wilhelm Leibniz said, 'To be neutral is rather like someone who lives in the middle of a house and is smoked out from below and drenched with urine from above.

The mind leans on [innate] principles every moment, but it does not come so easily to distinguish them and to represent them distinctly and separately, because that demands great attention to its acts, and the majority of people, little accustomed to think, has little of it.

Leibniz used to discourse to Queen Sophia Charlotte of Prussia concerning the infinitely little, and how she would reply that on that subject she needed no instruction—the behaviour of courtiers had made her thoroughly familiar with it.

It is true that as the empty voids and the dismal wilderness belong to zero, so the spirit of God and His light belong to the all-powerful One.

He who understands Archimedes and Apollonius will admire less the achievements of the foremost men of later times.

We actually inhabit not a scientific world but a perfect Cartesian arena of pure mathematics. We really are inside a flawless mathematical matrix. Yet this is not a physical matrix. Points in the Singularity do not physically move anywhere or have any physicality. Coordinates are simply how you provide an internal structure for the Singularity; how you arrange points WITHIN the Singularity. There is no material world at all: only a mental plenum of monads, just as Leibniz said three hundred years ago. And the final key point is that the natural mathematics of zero and infinity is nothing other than HOLOGRAPHY. We are individual holograms within a collective hologram. THAT is God’s secret!

For the [innate] general principles enter into our thoughts, of which they form the soul and the connection. They are as necessary thereto as the muscles and sinews are for walking, although we do not at all think of them.

If we were magically shrunk and put into someone’s brain while she was thinking, we would see all the pumps, pistons, gears and levers working away, and we would be able to describe their workings completely, in mechanical terms, thereby completely describing the thought processes of the brain. But that description would nowhere contain any mention of thought! It would contain nothing but descriptions of pumps, pistons, levers! —G. W. LEIBNIZ (1646–1716)

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.

If Bartleby is a new Messiah, he comes not, like Jesus, to redeem what was, but to save what was not. The Tartarus into which Bartleby, the new savior, descends is the deepest level of the Palace of Destinies, that whose sight Leibniz cannot tolerate, the world in which nothing is compossible with anything else, where "nothing exists rather than something.

When the origin of remote peoples goes beyond history, our languages show themselves their oldest monuments

At the higher realms of rationality, even reason can begin to appear irrational.

La idea del principio en Leibniz у la evolución de la teoría deductiva.

Kabbalah profoundly influenced the greatest thinkers of history, including Abraham, Moses, Jesus, Mohammed, Pythagoras, Plato, Newton, Leibniz, Shakespeare, and Jung.

Gottfried Wilhelm Leibniz, Letter to Christian Goldbach, April 17, 1712: “Music is the occulted arithmetic exercise of a soul that does not know it is counting.

A philosopher who was not sufficiently modern for her, Leibniz, has said that the journey from the intellect to the heart is a long one.

I have often been struck in Britain by this sort of thing - by how mysteriously well educated people from unprivileged background so often are, how the most unlikely people will tell you plant names in Latin or turn out to be experts on the politics of ancient Thrace or irrigation techniques at Glanum. This is a country, after all, where the grand final of a programme like Mastermind is frequently won by cab drivers and footplatemen. I have never been able to decide whether that is deeply impressive or just appalling - whether this is a country where engine drivers know about Tintoretto and Leibniz or a country where people who know about Tintoretto and Leibniz end up driving engines. All I know is that it exists more here than anywhere else.

And as every present state of a simple substance is naturally a consequence of its preceding state, so its present is pregnant with its future. —Gottfried Leibniz, Discourse on Metaphysics and Other Writings

Music, Schopenhauer wrote, is not unconscious arithmetic, as Leibniz had claimed, but unconscious philosophy, since in music the inner essence of the world, which is will, is made directly present to the mind.

G. W. Leibniz, codiscoverer of calculus and a towering intellect of eighteenth-century Europe, wrote: “The first question which should rightly be asked is: Why is there something rather than nothing?”[1] In other words, why does anything at all exist? This, for Leibniz, is the most basic question that anyone can ask. Like me, Leibniz came to the conclusion that the answer is to be found, not in the universe of created things, but in God. God

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.

Galileo essentially started out from where Archimedes left off, proceeding in the same direction as defined by his Greek predecessor. This is true not only of Galileo but also of the other great figures of the so-called “scientific revolution,” such as Leibniz, Huygens, Fermat, Descartes, and Newton. All of them were Archimedes’ children. With Newton, the science of the scientific revolution reached its perfection in a perfectly Archimedean form. Based on pure, elegant first principles and applying pure geometry, Newton deduced the rules governing the universe. All of later science is a consequence of the desire to generalize Newtonian, that is, Archimedean methods.

[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.

You sometimes hear people say, with a certain pride in their clerical resistance to the myth, that the nineteenth century really ended not in 1900 but in 1914. But there are different ways of measuring an epoch. 1914 has obvious qualifications; but if you wanted to defend the neater, more mythical date, you could do very well. In 1900 Nietzsche died; Freud published The Interpretation of Dreams; 1900 was the date of Husserl Logic, and of Russell's Critical Exposition of the Philosophy of Leibniz. With an exquisite sense of timing Planck published his quantum hypothesis in the very last days of the century, December 1900. Thus, within a few months, were published works which transformed or transvalued spirituality, the relation of language to knowing, and the very locus of human uncertainty, henceforth to be thought of not as an imperfection of the human apparatus but part of the nature of things, a condition of what we may know. 1900, like 1400 and 1600 and 1000, has the look of a year that ends a saeculum. The mood of fin de siècle is confronted by a harsh historical finis saeculi. There is something satisfying about it, some confirmation of the rightness of the patterns we impose. But as Focillon observed, the anxiety reflected by the fin de siècle is perpetual, and people don't wait for centuries to end before they express it. Any date can be justified on some calculation or other. And of course we have it now, the sense of an ending. It has not diminished, and is as endemic to what we call modernism as apocalyptic utopianism is to political revolution. When we live in the mood of end-dominated crisis, certain now-familiar patterns of assumption become evident. Yeats will help me to illustrate them. For Yeats, an age would end in 1927; the year passed without apocalypse, as end-years do; but this is hardly material. 'When I was writing A Vision,' he said, 'I had constantly the word "terror" impressed upon me, and once the old Stoic prophecy of earthquake, fire and flood at the end of an age, but this I did not take literally.' Yeats is certainly an apocalyptic poet, but he does not take it literally, and this, I think, is characteristic of the attitude not only of modern poets but of the modern literary public to the apocalyptic elements. All the same, like us, he believed them in some fashion, and associated apocalypse with war. At the turning point of time he filled his poems with images of decadence, and praised war because he saw in it, ignorantly we may think, the means of renewal. 'The danger is that there will be no war.... Love war because of its horror, that belief may be changed, civilization renewed.' He saw his time as a time of transition, the last moment before a new annunciation, a new gyre. There was horror to come: 'thunder of feet, tumult of images.' But out of a desolate reality would come renewal. In short, we can find in Yeats all the elements of the apocalyptic paradigm that concern us.

Leibniz’s most fundamental assumption, namely that the universe makes sense and that the human has the power to make sense of it and that, consequently, pure metaphysics is no waste of time, remains perhaps the central question of all science.

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.

Leibniz raised his eyebrows and spent a few moments staring at the clutter of pots and cups on the table. “This is one of the two great labyrinths into which human minds are drawn: the question of free will versus predestination. You were raised to believe in the latter. You have rejected it—which must have been a great spiritual struggle—and become a thinker. You have adopted a modern, mechanical philosophy. But that very philosophy now seems to be leading you back towards predestination. It is most difficult.

I don't really eliminate body, but reduce it to what it is. For I show that corporeal mass, which is thought to have something over and above simple substances, is not a substance, but a phenomenon resulting from simple substances, which alone have unity and absolute reality.

Our work is rejected because we are actually interested in the truth. Not a good look! People are “ashamed and embarrassed” by our work because, like Nietzsche’s work, it’s full of “difficult” material. Nietzsche was totally ignored during his sane life. Even today, the common herd don’t have a clue who he is. Leibniz, humanity’s greatest genius, is more or less unknown. That’s the way it goes. Our work is suffering the same fate. Well, it’s no surprise. We refused to play the Mandarin game. We refused to comply with the herd. Like true philosophers, we prefer to be Sages and Gadflies. The masses killed Socrates. Everyone that refuses to share our work is passing us the hemlock. So be it! We have total contempt for people that claim to like our work, but wouldn’t be seen dead sharing it on social media. You must be able to stand with those making difficult arguments that the herd don’t like. We disagree with Nietzsche on all manner of things, but we would certainly stand shoulder to shoulder with him against the herd. It’s essential for Gadflies to exist to shake the masses out of their complacency. Yet the Gadflies are always hated and, in the end, they are always handed the hemlock. They are the true heroes of our world, the ones that never get any credit.

[...] Et celui de la raison suffisante, en vertu duquel nous considérons qu’aucun fait ne saurait se trouver vrai, ou existant, aucune énonciation véritable, sans qu’il y ait une raison suffisante pourquoi il en soit ainsi et non pas autrement. Quoique ces raisons le plus souvent ne puissent point nous être connues. [sect. 32]

And so now, today, one cannot think of the greats—Kant, Hegel, Spinoza, Marx, Fichte, Freud, Nietzsche, Einstein, Schopenhauer, Leibniz, Schelling—the whole Germanic sphere—without thinking, at some point, of Auschwitz and Treblinka, Sobibor and Dachau, Bergen-Belsen and Chelmno. My God, they have names, as if they were human.

The Industrial Revolution was based on two grand concepts that were profound in their simplicity. Innovators came up with ways to simplify endeavors by breaking them into easy, small tasks that could be accomplished on assembly lines. Then, beginning in the textile industry, inventors found ways to mechanize steps so that they could be performed by machines, many of them powered by steam engines. Babbage, building on ideas from Pascal and Leibniz, tried to apply these two processes to the production of computations, creating a mechanical precursor to the modern computer. His most significant conceptual leap was that such machines did not have to be set to do only one process, but instead could be programmed and reprogrammed through the use of punch cards. Ada saw the beauty and significance of that enchanting notion, and she also described an even more exciting idea that derived from it: such machines could process not only numbers but anything that could be notated in symbols.

Milovať znamená radovať sa z cudzieho šťastia.

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.

We assert now that Being is the proper and sole theme of philosophy. This is not our own invention; it is a way of putting the theme which comes to life at the beginning of philosophy in antiquity, and it assumes its most grandiose form in Hegel's logic. At present we are merely asserting that Being is the proper and sole theme of philosophy. Negatively, this means that philosophy is not a science of beings but of Being or, as the Greek expression goes, ontology. We take this expression in the widest possible sense and not in the narrower one it has, say, in Scholasticism or in modern philosophy in Descartes and Leibniz. A discussion of the basic problems of phenomenology then is tantamount to providing fundamental substantiation for this assertion that philosophy is the science of Being and establishing how it is such. The discussion should show the possibility and necessity of the absolute science of Being and demonstrate its character in the very process of the inquiry. Philosophy is the theoretical conceptual interpretation of Being, of Being's structure and its possibilities. Philosophy is ontological." ―from_The Basic Problems of Phenomenology_

Starting from Descartes’ commitment to a few absolutely certain innate ideas and reason’s ability to determine some facts about reality a priori, Leibniz ended up making all ideas innate and deducing how God must have set up the universe. On the other side, Hume continued Locke’s emptying out of the mind until there was no longer a there there, that is, not even a substantial mind to be emptied.

If pure philosophy took any of its ideas from Christian revelation, if anything in the Bible and the Gospel has passed into metaphysics, if, in short, it is inconceivable that the system of Descartes, Malebranche, and Leibniz would be what in fact they are had they been altogether withdrawn from Christian influence, then it becomes, highly probable that since the influence of Christianity on philosophy was a reality, the concept of Christian philosophy is not without a real meaning.

Thinking is what angels do—it is a property given to Man by God.” “How do you suppose God gives it to us?” “I do not pretend to know, sir!” “If you take a man’s brain and distill him, can you extract a mysterious essence—the divine presence of God on Earth?” “That is called the Philosophick Mercury by Alchemists.” “Or, if Hooke were to peer into a man’s brain with a good enough microscope, would he see tiny meshings of gears?” Daniel said nothing. Leibniz had imploded his skull. The gears were jammed, the Philosophick Mercury dribbling out his ear-holes.

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.

The mind cannot be a blank slate, because blank slates don’t do anything. As long as people had only the haziest concept of what a mind was or how it might work, the metaphor of a blank slate inscribed by the environment did not seem too outrageous. But as soon as one starts to think seriously about what kind of computation enables a system to see, think, speak, and plan, the problem with blank slates becomes all too obvious: they don’t do anything. The inscriptions will sit there forever unless something notices patterns in them, combines them with patterns learned at other times, uses the combinations to scribble new thoughts onto the slate, and reads the results to guide behavior toward goals. Locke recognized this problem and alluded to something called “the understanding,” which looked at the inscriptions on the white paper and carried out the recognizing, reflecting, and associating. But of course explaining how the mind understands by invoking something called “the understanding” is circular. This argument against the Blank Slate was stated pithily by Gottfried Wilhelm Leibniz (1646-1716) in a reply to Locke. Leibniz repeated the empiricist motto “There is nothing in the intellect that was not first in the senses,” then added, “except the intellect itself.”8

It is not difficult to imagine the Catholic Church adopting, after a Tychonic transition, the Copernican cosmology some 200 years earlier than she eventually did. The Galileo affair was an isolated episode in the history of relations between science and theology. But its dramatic circumstances, magnified out of all proportion, created a popular belief that science stood for freedom, the Church for oppression of thought. Some historians wish to make us believe that the decline of science in Italy was due to the "terror" caused by the trial of Galileo. But the next generation saw the rise of Toricelli, Cavallieri, Borelli, whose contributions to science were more substantial than those of any generation before or during Galileo's lifetime. The contemporary divorce between faith and reason is not the result of a contest for power or intellectual monopoly, but of a progressive estrangement. This becomes evident if we shift our attention from Italy to the Protestant countries of Europe, and to France. Kepler, Descartes, Barrow, Leibniz, Gilbert, Boyle and Newton himself, the generation of pioneers contemporary with and succeeding Galileo, were all deeply and genuinely religious thinkers. The pioneers of the new cosmology, from Kepler to Newton and beyond, based their search into nature on the mystic conviction that there must exist laws behind the confusing phenomena; that the world was a completely rational, ordered, harmonic creation.

As was foreshadowed in Paragraphs 1 and 4, Cantor, and Dedekind's near-simultaneous appearance in math is more or less the Newton + Leibniz thing all over again, a sure sign that the Time Was Right for (Infinity)-type sets. Just as striking is the Escherian way the two men's work dovetails. Cantor is able to define and ground the concepts of 'infinite set' and 'transfinite number,' and to establish rigorous techniques for combining and comparing different types of (Infinity)s, which is just where Dedekind's def. of irrationals needs shoring up. Pro quo, the schnitt technique demonstrates that actually-infinite sets can have real utility in analysis. That, in other words, as sensuously and cognitively abstract as they must remain, (Infinity)s can nevertheless function in math as practical abstractions rather than as just weird paradoxical flights of fancy.

Philosophy is the theory of multiplicities, each of which is composed of actual and virtual elements. Purely actual objects do not exist. Every actual surrounds itself with a cloud of virtual images. This cloud is composed of a series of more or less extensive coexisting circuits, along which the virtual images are distributed, and around which they run. These virtuals vary in kind as well as in their degree of proximity from the actual particles by which they are both emitted and absorbed. They are called virtual in so far as their emission and absorption, creation and destruction, occur in a period of time shorter than the shortest continuous period imaginable; it is this very brevity that keeps them subject to a principle of uncertainty or indetermination. The virtuals, encircling the actual, perpetually renew themselves by emitting yet others, with which they are in turn surrounded and which go on in turn to react upon the actual: ‘in the heart of the cloud of the virtual there is a virtual of a yet higher order ... every virtual particle surrounds itself with a virtual cosmos and each in its turn does likewise indefinitely.’ It is the dramatic identity of their dynamics that makes a perception resemble a particle: an actual perception surrounds itself with a cloud of virtual images, distributed on increasingly remote, increasingly large, moving circuits, which both make and unmake each other. These are memories of different sorts, but they are still called virtual images in that their speed or brevity subjects them too to a principle of the unconsciousness. It is by virtue of their mutual inextricability that virtual images are able to react upon actual objects. From this perspective, the virtual images delimit a continuum, whether one takes all of the circles together or each individually, a spatium determined in each case by the maximum of time imaginable. The varyingly dense layers of the actual object correspond to these, more or less extensive, circles of virtual images. These layers, whilst themselves virtual, and upon which the actual object becomes itself virtual, constitute the total impetus of the object. The plane of immanence, upon which the dissolution of the actual object itself occurs, is itself constituted when both object and image are virtual. But the process of actualization undergone by the actual is one which has as great an effect on the image as it does on the object. The continuum of virtual images is fragmented and the spatium cut up according to whether the temporal decompositions are regular or irregular. The total impetus of the virtual object splits into forces corresponding to the partial continuum, and the speeds traversing the cut-up spatium. The virtual is never independent of the singularities which cut it up and divide it out on the plane of immanence. As Leibniz has shown, force is as much a virtual in the process of being actualized as the space through which it travels. The plane is therefore divided into a multiplicity of planes according to the cuts in the continuum, and to the divisions of force which mark the actualization of the virtual. But all the planes merge into one following the path which leads to the actual. The plane of immanence includes both the virtual and its actualization simultaneously, without there being any assignable limit between the two. The actual is the complement or the product, the object of actualization, which has nothing but virtual as its subject. Actualization belongs to the virtual. The actualization of the virtual is singularity whereas the actual itself is individuality constituted. The actual falls from the plane like a fruit, whist the actualization relates it back to the plane as if to that which turns the object back into a subject.

A radical alternative put forward by Newton's rival Leibniz provides my central idea. The world is to be understood, not in the dualistic terms of atoms (things of one kind) that move in the framework and container of space and time (another quite different kind of thing), but in terms of more fundamental entities that fuse space and matter into the single notion of a possible arrangement, or configuration, of the entire universe. Such configurations, which can be fabulously richly structured, are the ultimate things. There are infinitely many of them; they are all different instances of a common principle of construction; and they are all, in my view, the different instants of time. In fact, many people who have written about time have conceived of instants of time in a somewhat similar way, and have called them 'nows'. Since I make the concept more precise and put it at the heart of my theory of time, I shall call them Nows. The world is made of Nows.

The three greatest metaphysicians who ever existed - Plato, Aristotle and St.Thomas Aquinas - had no system in the idealistic sense of the word. Their ambition was not to achieve philosophy once and for all, but to maintain it and to serve it in ours. For us, as for them, the great thing is not to achieve a system of the world as if being could be deduced from thought, but to relate reality, as we know it, to the permanent principles in whose light all the changing problems of science, of ethics and of art have to be solved. A metaphysics of existence cannot be a system wherewith to get rid of philosophy, it is an always open inquiry, whose conclusions are both always the same and always new, because it is conducted under the guidance of immutable principles, which will never exhaust experience, or be themselves exhausted by it. For even though, as is impossible, all that which exists were known to us, existence itself would still remain a mystery. Why, asked Leibniz, is there something rather than nothing ?

The three greatest metaphysicians who ever existed - Plato, Aristotle and St.Thomas Aquinas - had no system in the idealistic sense of the word. Their ambition was not to achieve philosophy once and for all, but to maintain it and to serve it in their own times, as we have to maintain it and to serve it in ours. For us, as for them, the great thing is not to achieve a system of the world as if being could be deduced from thought, but to relate reality, as we know it, to the permanent principles in whose light all the changing problems of science, of ethics and of art have to be solved. A metaphysics of existence cannot be a system wherewith to get rid of philosophy, it is an always open inquiry, whose conclusions are both always the same and always new, because it is conducted under the guidance of immutable principles, which will never exhaust experience, or be themselves exhausted by it. For even though, as is impossible, all that which exists were known to us, existence itself would still remain a mystery. Why, asked Leibniz, is there something rather than nothing ?

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.

So it happens that we must ask ourselves, with regard to truth, not for a new criterion for it, which will be better polished than earlier ones, but, peremptorily and seizing it by the lapels, "what is truth as such," and with regard to reality, not what things are or what and how is that which is, but for what reason that X which we call Being is in the Universe, and with regard to knowledge we must not ask for its bases and limits—as Plato, Aristotle Descartes, Kant did—but for something which comes before all this: for what reason we concern ourselves with trying to know.

Starting from Descartes’ commitment to a few absolutely certain innate ideas and reason’s ability to determine some facts about reality a priori, Leibniz ended up making all ideas innate and deducing how God must have set up the universe. On the other side, Hume continued Locke’s emptying out of the mind until there was no longer a there there, that is, not even a substantial mind to be emptied. Far from being rationally justifiable, Hume demonstrated that most of our beliefs are determined by an arational reflex, a process that has roughly the epistemological status of digestion. Perhaps Kant’s greatest accomplishment was reconciling these deeply heterogeneous schools, weaving a seamless system out of ideas taken from both sides. The linchpin of this synthesis was what he called his Copernican Revolution: the epoch-making claim that the mind actively processes or organizes experience in constructing knowledge, rather than passively reflecting an independent reality. To speak metaphorically, the mind is more like a factory than a mirror or soft wax. It is this idea that enabled Kant to incorporate the empiricist dependence on experience into the rationalist ideal of universal and necessary knowledge.

Definiţia durerii poate fi sistematizată astfel: 1. Prin ea se exteriorizează o judecată, în care s-a acumulat experienţa; 2. specificul ei este un şoc în sistemul nervos, care provoacă un dezechilibru; 3. este ea însăşi o reacţie, nu este cauza unei alte reacţii. 1. «În sine nu există durere. Nu rana este cea care doare; experienţa cu privire la consecinţele nefaste pe care le poate avea o rană» provoacă durerea. Cu alte cuvinte, obişnuinţa, prin care am învăţat să percepem durerea, este cea care judecă. Rana este secundară, exerciţiul durerii este cel care îşi spune cuvântul. Analiza lui Nietzsche este inventivă: mai degrabă comportamentul nostru (prin habitudini, dezvoltate din experienţă) transmite senzaţia de durere (nu rana efectivă). Ar fi interesant de investigat cum am reacţiona efectiv la durere, dacă obişnuinţa şi comportamentul nu ne-ar dicta că trebuie să plângem, să ne contorsionăm, să tremurăm atunci când ne-am lovit. 2. «Specificul autentic al durerii este întotdeauna îndelunga cutremurare, vibraţia ulterioară – determinată de un şoc înspăimântător. [...] De fapt nu suferim datorită cauzei durerii (a unei leziuni oarecare, de pildă), ci datorită dezechilibrului îndelungat ce apare ca urmare a acelui şoc.» Din acest fragment, putem izola elementul ştiinţific de cel biografic, deşi ele sunt complementare. «Cutremurarea» şi «vibraţia» (angoasa este subliniată auditiv), pe scurt «dezechilibrul» este consecinţa unui «şoc». Nici acum rana nu impune durerea, ci dezechilibrul provocat de şoc induce suferinţa. 3. «Dacă se observă corect, reacţia apare în mod vădit anterior senzaţiei de durere. [...] Mai degrabă eu disting cât se poate de clar că întâi apare reacţia piciorului spre a evita căderea, iar apoi, la un interval de timp apreciabil, devine subit perceptibilă un fel de undă dureroasă în regiunea frontală.» Nietzsche demontează o veche prejudecată, prin care se afirma că durerea este cauza unei reacţii. Analizând retardul dintre o reacţie de autoconservare şi senzaţia de durere, filosoful respinge o interpretare de tip cauză/efect. Mai degrabă durerea este o «reacţie», mişcarea contrară constând într-o altă reacţie (cele două avându-şi «sursa în două locuri diferite.»). În concluzie, «diminuarea sentimentului de putere» nu ţine de «esenţa durerii». Se ajunge la distincţia dintre plăcere şi durere, de la care s-a început. Rezumând, durerea este o «maladie» (plăcerea – nu), cele două stări nu sunt dialectice, durerea este un obstacol care asigură prin contrast creşterea puterii (la fel cum plăcerea însoţeşte sentimentul predominant al puterii). Înţeleg necesitatea respingerii durerii ca epifenomen în contextul unei teorii a voinţei de putere, dar nu ştiu dacă ea este justificată. Schopenhauer, atunci când îl parodiază pe Leibniz, spunând că trăim în cea mai rea din lumile posibile, chiar dacă este agresiv şi excesiv, are dreptatea de partea lui. Din punctul de vedere al lui Schopenhauer, durerea este de netrecut: nu poate fi negată şi nu poate fi transcesă. Nietzsche demonstrează că există stări în care durerea, dacă nu dispare, poate fi amânată. Cu alte cuvinte, semnalul indus de şoc – întârzie. Cazul durerii predormale îi dă dreptate. În cazul unei răni sau în cazul unei altercaţii violente excesul de adrenalină mută conştiinţa pe o altă frecvenţă. Durerea este diluată, este înşelată, doar pentru a reveni în forţă, atunci când este momentul ei. Ceva asemănător voinţei de putere, dacă putem folosi această metonimie pentru un proces neurologic se exprimă în locul durerii. Durerea este astfel transgresată, temporar. Cu toate acestea, durerea efectivă (în tortură, de exemplu) are imediatul ei. Nu este necesar să-l citim pe Cioran să actualizăm ramificaţiile culturale ale unei teorii ale durerii – judecata empirică poate să suplinească cunoştinţa durerii, care este universală.

Queen Anne of England established the Longitude Act in 1714, and offered a monetary prize of over a million in today’s dollars to anyone who invented a method to accurately calculate longitude at sea. Longitude is about determining one’s point in space. So one might ask what it has to do with clocks? Mathematically speaking, space (distance) is the child of time and speed (distance equals time multiplied by speed). Thus, anything that moves at a constant speed can be used to calculate distance, provided one knows for how long it has been moving. Many things have constant speeds, including light, sound, and the rotation of the Earth. Your brain uses the near constancy of the speed of sound to calculate where sounds are coming from. As we have seen, you know someone is to your left or right because the sound of her voice takes approximately 0.6 milliseconds to travel from your left to your right ear. Using the delays it takes any given sound to arrive to your left and right ears allows the brain to figure out if the voice is coming directly from the left, the right, or somewhere in between. The Earth is rotating at a constant speed—one that results in a full rotation (360 degrees) every 24 hours. Thus there is a direct correspondence between degrees of longitude and time. Knowing how much time has elapsed is equivalent to knowing how much the Earth has turned: if you sit and read this book for one hour (1/24 of a day), the Earth has rotated 15 degrees (360/24). Thus, if you are sitting in the middle of the ocean at local noon, and you know it is 16:00 in Greenwich, then you are “4 hours from Greenwich”—exactly 60 degrees longitude from Greenwich. Problem solved. All one needs is a really good marine chronometer. The greatest minds of the seventeenth and eighteenth centuries could not overlook the longitude problem: Galileo Galilei, Blaise Pascal, Robert Hooke, Christiaan Huygens, Gottfried Leibniz, and Isaac Newton all devoted their attention to it. In the end, however, it was not a great scientist but one of the world’s foremost craftsman who ultimately was awarded the Longitude Prize. John Harrison (1693–1776) was a self-educated clockmaker who took obsessive dedication to the extreme.

Que as meditações dos teólogos e dos filósofos conhecidos por escolásticos não são inteiramente desprezíveis Sei que enuncio um grande paradoxo ao pretender reabilitar de certo modo a antiga filosofia, e recordar postlimino as formas substanciais já quase banidas; mas, talvez não me condenem levianamente quando se souber que meditei bastante sobre a filosofia moderna, que dediquei muito tempo às experiências da física e às demonstrações da geometria, que estive muito tempo persuadido da fragilidade desses entes, que fui, enfim, obrigado a retomar contra a própria vontade e como que à força, depois de eu próprio ter feito investigações que me levaram a reconhecer que os nossos modernos não fazem suficientemente justiça a S. Tomás de Aquino e a outros grandes homens desse tempo, e que há, nas opiniões dos filósofos e teólogos escolásticos, muito mais solidez do que se imagina, contando que delas nos sirvamos a propósito e no seu lugar. Estou mesmo persuadido de que, se algum espírito exacto e meditativo se desse ao trabalho de esclarecer e digerir o pensamento deles à maneira dos geómetras analíticos, encontraria aí um tesouro de grande quantidade de verdades importantíssimas e absolutamente demonstrativas.