Gottfried Wilhelm Leibniz Quotes

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.

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

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

Nothing is necessitated whose opposite is possible.

He who does not act does not exist.

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.)

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

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.

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.

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

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.

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.

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 ?

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.

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.}

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…

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

[...] 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…

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.

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.

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.

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.

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.

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

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.

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.

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?

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.

[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.

[...] 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]

The present state of a single substance is the natural result of its precedent state, so much so that the present is pregnant with the future.

Milovať znamená radovať sa z cudzieho šťastia.

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

Suppose that there be a machine, the structure of which produces thinking, feeling, and perceiving; imagine this machine enlarged but preserving the same proportions, so you could enter it as if it were a mill. This being supposed, you might visit inside; but what would you observe there? Nothing but parts which push and move each other, and never anything that could explain perception. —Gottfried Wilhelm Leibniz

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.

La tranquillité est un degré pour avancer vers la stupidité. . . Il faut toujours trouver quelque chose à faire, penser, projeter, s'intéresser, pour le public et pour le particulier, mais cela d'une manière qui nous réjouisse, si nos souhaits sont accomplis et ne nous chagrine point en cas qu'ils manquent.

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

Copies of Ficino’s translations were owned by Ben Jonson, John Milton, and Samuel Taylor Coleridge in England, by Jean-Jacques Rousseau and Jean Racine in France, by Bishop Berkeley in Ireland and Baruch Spinoza in the Netherlands, and by Gottfried Wilhelm Leibniz and Immanuel Kant in Germany.56 The Ripoli Press’s 1484 edition is recorded at Harvard in 1735, at Yale in 1742, and even, by 1623, in China.57 More than 120 copies have survived into the twenty-first century: thirty-six in Italy, the remainder scattered from Malta, Slovakia, and Sweden to libraries in California, Kansas, Oregon, and the Rare Book Division of the Library of Congress.

This connection of all created things with every single one of them and their adaptation to every single one, as well as the connection and adaptation of every single thing to all others, has the result that every single substance stands in relations which express all the others. Whence every single substance is a perpetual living mirror of the universe.

But in the treasures of divine wisdom, that is, in the hidden God and (which comes to the same) in the universal harmony of the world, a profundity (bathos) is latent, which contains the reasons why the actual series of the universe, comprehending the events we admire and the judgements we worship, has been chosen by God as the best and as preferable to all others.

Base two especially impressed the seventeenth-century religious philosopher and mathematician Gottfried Wilhelm Leibniz. He observed that in this base all numbers were written in terms of the symbols 0 and 1 only. Thus eleven, which equals 1 · 23 + 0 · 22 + 1 · 2 + 1, would be written 1011 in base two. Leibniz saw in this binary arithmetic the image and proof of creation. Unity was God and zero was the void. God drew all objects from the void just as the unity applied to the zero creates all numbers. This conception, over which the reader would do well not to ponder too long, delighted Leibniz so much that he sent it to Grimaldi, the Jesuit president of the Chinese tribunal for mathematics, to be used as an argument for the conversion of the Chinese emperor to Christianity.

Now, since in the divine ideas there is an infinity of possible universes of which only one can exist, the choice made by God must have a sufficient reason which determines him to the one rather than to another. This reason can be found only in fitness, that is, in the degree of perfection contained in these worlds. For each possible has a right to claim existence in proportion to the perfection it involves. Thus nothing is entirely arbitrary.

Of course, this isn’t usually the way historians of ideas tell this story. Not only are we taught to think of intellectual history as something largely produced by individuals writing great books or thinking great thoughts, but these ‘great thinkers’ are assumed to perform both these activities almost exclusively with reference to each other. As a result, even in cases where Enlightenment thinkers openly insisted they were getting their ideas from foreign sources (as the German philosopher Gottfried Wilhelm Leibniz did when he urged his compatriots to adopt Chinese models of statecraft), there’s a tendency for contemporary historians to insist they weren’t really serious; or else that when they said they were embracing Chinese, or Persian, or indigenous American ideas these weren’t really Chinese, Persian or indigenous American ideas at all but ones they themselves had made up and merely attributed to exotic Others.

To the possible objection that thus the world would of necessity have long ago turned into a paradise, it is easy to reply: Many substances already may have attained great perfection; yet, the continuum being infinitely divisible, there will always remain in the unfathomable depth of the universe some somnolent elements which are still to be awakened, developed, and improved - in a word, promoted to higher culture. This is why the end of progress can never be attained.

[...] c’est que jamais rien n’arrive, sans qu’il y ail une cause ou du moins une raison déterminante, c’est-à-dire quelque chose qui puisse servir à rendre a priori, pourquoi cela est existant plulôt que de toute autre façon. Ce grand principe a lieu dans tous les événements, et on ne donnera jamais un exemple contraire : et quoique le plus souvent ces raisons déterminantes ne nous soient pas assez connues, nous ne laissons pas d’entrevoir qu’il y en a. Essais de Théodicée, 1.44

In 1714, Gottfried Wilhelm Leibniz argued that matter alone could never produce a mind. Leibniz was a German philosopher, mathematician, and scientist who is sometimes called “the last man who knew everything”. To Leibniz, brain tissue alone could not have an interior life. He suggested a thought experiment, known today as Leibniz’s Mill. Imagine a large mill. If you were to walk around inside of it, you would see its cogs and struts and levers all moving, but it would be preposterous to suggest that the mill is thinking or feeling or perceiving. How could a mill fall in love or enjoy a sunset? A mill is just made of pieces and parts. And so it is with the brain, Leibniz asserted. If you could expand the brain to the size of a mill and stroll around inside it, you would only see pieces and parts. Nothing would obviously correspond to perception. Everything would simply be acting on everything else. If you wrote down every interaction, it wouldn’t be obvious where thinking and feeling and perceiving reside.

Take the case (to use an easy example) of a river, carrying boats and communicating to them its own velocity, yet limited by their own inertia so that, all the rest being equal, the more heavily loaded will be carried more slowly. Hence it can be stated that the speed of the boats comes from the river, the slowness, from the load; the positive, from the force of the propelling agent, the privative, from the inertia of the propelled. Quite in the same manner it may be said that God contributes to the creatures their perfections, yet is limited by their receptivity. Thus all goods are due to the divine force; the evils, to the torpor of the creature.

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.

If my opinion that substance requires a true unity were founded only on a definition I had formulated in opposition to common usage, *then the dispute would be only one of words*. But besides the fact that most philosophers have taken the term in almost the same fashion, distinguishing between a unity in itself and an accidental unity, between substantial and accidental form, and between perfect and imperfect, natural and artificial mixtures, I take things to a much higher level, and setting aside the question of terminology, *I believe that where there are only beings by aggregation, there aren't any real beings*. For every being by aggregation presupposes beings endowed with real unity, because every being derives its reality only from the reality of those beings of which it is composed, so that it will not have any reality at all if each being of which it is composed is itself a being by aggregation, a being for which we must still seek further grounds for its reality, grounds which can never be found in this way, if we must always continue to seek for them. I agree, Sir, that there are only machines (that are often animated) in all of corporeal nature, but I do not agree that *there are only aggregates of substances, there must also be true substances from which all the aggregates result. We must, then, necessarily come down to the atoms of Epicurus and Cordemoy (which are things you reject along with me), or else we must admit that we do not find any reality in bodies; or finally, we must recognize some substances that have a true unity. I have already said in another letter that the composite made up of the diamonds of the Grand Duke and of the Great Mogul can be called a pair of diamonds, but this is only a being of reason. And when they are brought closer to one another, it would be a being of the imagination or perception, that is to say, a phenomenon. For contact, common motion, and participation in a common plan have no effect on substantial unity. It is true that there are sometimes more, sometimes fewer, grounds for supposing that several things constitute a single thing, in proportion to the extent to which these things are connected. But this serves only to abbreviate our thoughts and to represent the phenomena. It also seems that what constitutes the essence of a being by aggregation is only a mode (*maniére d'être*) of the things of which it is composed. For example, what constitutes the essence of an army is only a mode of the men who compose it. This mode therefore presupposes a substance whose essence is not a mode of substance. Every machine also presupposes some substance in the pieces of which it is made, and there is no plurality without true unities. To put it briefly, I hold this identical proposition, differentiated only by the emphasis, to be an axiom, namely, *that what is not truly* one *being is not truly one* being *either*. It has always been thought that one and being are reciprocal things. Being is one thing and beings are another; but the plural presupposes the singular, and where there is no being still less will there be several beings. What could be clearer? [[I therefore believed that I would be allowed to distinguish beings by aggregation from substances, since these beings have their unity in our mind only, a unity founded on the relations or modes [*modes*] of true substances. If a machine is one substance, a circle of men holding hands will also be one substance, and so will an army, and finally, so will every multitude of substances.]]." —from_Letters to Arnauld_

If my opinion that substance requires a true unity were founded only on a definition I had formulated in opposition to common usage, *then the dispute would be only one of words*. But besides the fact that most philosophers have taken the term in almost the same fashion, distinguishing between a unity in itself and an accidental unity, between substantial and accidental form, and between perfect and imperfect, natural and artificial mixtures, I take things to a much higher level, and setting aside the question of terminology, *I believe that where there are only beings by aggregation, there aren't any real beings*. For every being by aggregation presupposes beings endowed with real unity, because every being derives its reality only from the reality of those beings of which it is composed, so that it will not have any reality at all if each being of which it is composed is itself a being by aggregation, a being for which we must still seek further grounds for its reality, grounds which can never be found in this way, if we must always continue to seek for them. I agree, Sir, that there are only machines (that are often animated) in all of corporeal nature, but I do not agree that *there are only aggregates of substances, there must also be true substances from which all the aggregates result. We must, then, necessarily come down to the atoms of Epicurus and Cordemoy (which are things you reject along with me), or else we must admit that we do not find any reality in bodies; or finally, we must recognize some substances that have a true unity. I have already said in another letter that the composite made up of the diamonds of the Grand Duke and of the Great Mogul can be called a pair of diamonds, but this is only a being of reason. And when they are brought closer to one another, it would be a being of the imagination or perception, that is to say, a phenomenon. For contact, common motion, and participation in a common plan have no effect on substantial unity. It is true that there are sometimes more, sometimes fewer, grounds for supposing that several things constitute a single thing, in proportion to the extent to which these things are connected. But this serves only to abbreviate our thoughts and to represent the phenomena. It also seems that what constitutes the essence of a being by aggregation is only a mode (*maniére d'être*) of the things of which it is composed. For example, what constitutes the essence of an army is only a mode of the men who compose it. This mode therefore presupposes a substance whose essence is not a mode of substance. Every machine also presupposes some substance in the pieces of which it is made, and there is no plurality without true unities. To put it briefly, I hold this identical proposition, differentiated only by the emphasis, to be an axiom, namely, *that what is not truly* one *being is not truly one* being *either*. It has always been thought that one and being are reciprocal things. Being is one thing and beings are another; but the plural presupposes the singular, and where there is no being still less will there be several beings. What could be clearer? [[I therefore believed that I would be allowed to distinguish beings by aggregation from substances, since these beings have their unity in our mind only, a unity founded on the relations or modes [*modes*] of true substances. If a machine is one substance, a circle of men holding hands will also be one substance, and so will an army, and finally, so will every multitude of substances.]]." —from_Letters to Arnauld_

[Was gibt es besseres für uns, als] wenn wir uns pflichtgemäß an den Urheber des Alls anschließen, an ihn, nicht nur als den Baumeister der Welt und Urgrund unseres Daseins, sondern als unsern Herrn und Endzweck, der das Ziel unseres Wollens bleiben soll und der einzige Urheber unsrer Glückseligkeit. [Absatz 90]

Gustavo Solivellas dice: "Vivimos en el mejor de los mundos posibles" (Gottfried Wilhelm Leibniz)

67. Chaque portion de la matière peut être conçue comme un jardin plein de plantes, et comme un étang plein de poissons. Mais chaque rameau de la plante, chaque membre de l'animal, chaque goutte de ses humeurs est encore un tel jardin ou un tel étang. 68. Et quoique la terre et l'air interceptés entre les plantes du jardin, ou l'eau interceptée entre les poissons de l'étang, ne soient point plante ni poisson, ils en contiennent pourtant encore, mais le plus souvent d'une subtilité à nous imperceptible.

If my opinion that substance requires a true unity were founded only on a definition I had formulated in opposition to common usage, *then the dispute would be only one of words*. But besides the fact that most philosophers have taken the term in almost the same fashion, distinguishing between a unity in itself and an accidental unity, between substantial and accidental form, and between perfect and imperfect, natural and artificial mixtures, I take things to a much higher level, and setting aside the question of terminology, *I believe that where there are only beings by aggregation, there aren't any real beings*. For every being by aggregation presupposes beings endowed with real unity, because every being derives its reality only from the reality of those beings of which it is composed, so that it will not have any reality at all if each being of which it is composed is itself a being by aggregation, a being for which we must still seek further grounds for its reality, grounds which can never be found in this way, if we must always continue to seek for them. I agree, Sir, that there are only machines (that are often animated) in all of corporeal nature, but I do not agree that *there are only aggregates of substances, there must also be true substances from which all the aggregates result. We must, then, necessarily come down to the atoms of Epicurus and Cordemoy (which are things you reject along with me), or else we must admit that we do not find any reality in bodies; or finally, we must recognize some substances that have a true unity. I have already said in another letter that the composite made up of the diamonds of the Grand Duke and of the Great Mogul can be called a pair of diamonds, but this is only a being of reason. And when they are brought closer to one another, it would be a being of the imagination or perception, that is to say, a phenomenon. For contact, common motion, and participation in a common plan have no effect on substantial unity. It is true that there are sometimes more, sometimes fewer, grounds for supposing that several things constitute a single thing, in proportion to the extent to which these things are connected. But this serves only to abbreviate our thoughts and to represent the phenomena. It also seems that what constitutes the essence of a being by aggregation is only a mode (*maniére d'être*) of the things of which it is composed. For example, what constitutes the essence of an army is only a mode of the men who compose it. This mode therefore presupposes a substance whose essence is not a mode of substance. Every machine also presupposes some substance in the pieces of which it is made, and there is no plurality without true unities. To put it briefly, I hold this identical proposition, differentiated only by the emphasis, to be an axiom, namely, *that what is not truly* one *being is not truly one* being *either*. It has always been thought that one and being are reciprocal things. Being is one thing and beings are another; but the plural presupposes the singular, and where there is no being still less will there be several beings. What could be clearer? [[I therefore believed that I would be allowed to distinguish beings by aggregation from substances, since these beings have their unity in our mind only, a unity founded on the relations or modes [*modes*] of true substances. If a machine is one substance, a circle of men holding hands will also be one substance, and so will an army, and finally, so will every multitude of substances.]]." —from_Letters to Arnauld_

Los misterios se pueden explicar hasta donde es necesario para creerlos, pero no se les puede comprender, ni hacer entender cómo se verifican, a la manera que en la misma física explicamos hasta cierto punto muchas cualidades sensibles, pero de una manera imperfecta, porque no las comprendemos.

Fuit in Cartesio major librorum usus quam ipse videri volebat: hoc stylus et res ipsae docent.

Alles studiren und lesen soll künfftig meistentheils in teutschen büchern geschehen, auch was man schreibt, teutsch antworten. Im reden und schreiben muß man sich zu kurzen wohl geschlossenen periodis gewöhnen, die flickwörter meiden, denen worthen liecht und krafft geben. Allezeit also reden, wie es gleich zu papier gebracht werden könte. Die gebreuchlichsten formeln und redensarten sich wohl einbilden, damit sie ungezwungen und von selbsten fließen.

That zero and one were sufficient for logic as well as arithmetic was established by Gottfried Wilhelm Leibniz in 1679, following the lead given by Thomas Hobbes in his Computation, or Logique of 1656.

Not only are we taught to think of intellectual history as something largely produced by individuals writing great books or thinking great thoughts, but these ‘great thinkers’ are assumed to perform both these activities almost exclusively with reference to each other. As a result, even in cases where Enlightenment thinkers openly insisted they were getting their ideas from foreign sources (as the German philosopher Gottfried Wilhelm Leibniz did when he urged his compatriots to adopt Chinese models of statecraft), there’s a tendency for contemporary historians to insist they weren’t really serious; or else that when they said they were embracing Chinese, or Persian, or indigenous American ideas these weren’t really Chinese, Persian or indigenous American ideas at all but ones they themselves had made up and merely attributed to exotic Others.

If there is reality in essences or possibles, or indeed, in eternal truths, this reality must be grounded in something existent and actual, and consequently, it must be grounded in the existence of the necessary being...

The world had become Newton’s family, with a few notable exceptions. Having laid Robert Hooke to rest, literally, Newton had become involved in an all-out feud with a German philosopher named Gottfried Wilhelm Leibniz, who had claimed credit for discovering the calculus. (See “Between a Rock and a Hard Life.”)

Wer seine Schüler das Abc gelehrt, hat eine größere Tat vollbracht als der Feldherr, der eine Schlacht geschlagen.

Alles wat mogelijk is, vraagt erom te bestaan en zou bij gevolg ook bestaan, als niet iets anders dat er ook om vraagt te bestaan en dat niet tegelijk met het eerste kan bestaan, dat tegenhield. - Gottfried Wilhelm Leibniz

Gott sah unendlich viele Welten als möglich vor sich; aber aus diesen unendlich vielen wählte er die wirkliche als die beste.

Lieben heißt, unser Glück in das Glück eines anderen zu legen.

Nature does not make leaps. ― Gottfried Wilhelm Leibniz Nature makes every birth a leap, and it also manifests itself in weather, rain, storms, and other natural forms; human creation is a leap of a semen drop. ― Ehsan Sehgal

The immediate catalyst for the emergence of the Enlightenment in the eighteenth century was the scientific revolution of the sixteenth and seventeenth centuries, which included three momentous discoveries in astronomy: Johannes Kepler delineated the rules that govern the movement of the planets, Galileo Galilei placed the sun at the center of the universe, and Isaac Newton discovered the force of gravity, invented calculus (Gottfried Wilhelm Leibniz independently discovered it at the same time), and used it to describe the three laws of motion. In so doing, Newton joined physics and astronomy and illustrated that even the deepest truths in the universe could be revealed by the methods of science. These contributions were celebrated in 1660 with the formation of the first scientific society in the world: the Royal Society of London for Improving Natural Knowledge, which elected Isaac Newton as its president in 1703. The founders of the Royal Society thought of God as a mathematician who had designed the universe to function according to logical and mathematical principles. The role of the scientist—the natural philosopher—was to employ the scientific method to discover the physical principles underlying the universe and thereby decipher the codebook that God had used in creating the cosmos. Success in the realm of science led eighteenth-century thinkers to assume that other aspects of human action, including political behavior, creativity, and art, could be improved by the application of reason, leading ultimately to an improved society and better conditions for all humankind. This confidence in reason and science affected all aspects of political and social life in Europe and soon spread to the North American colonies. There, the Enlightenment ideas that society can be improved through reason and that rational people have a natural right to the pursuit of happiness are thought to have contributed to the Jeffersonian democracy that we enjoy today in the United States.

Dust shows that space, traversed by barely noticeable vibrations and morsels of things, is not empty and warns us against equating it to a vacuum. It substantiates the philosophical position of Gottfried Wilhelm Leibniz, who ridiculed the thesis that a void existed in nature and who held that even microscopic units of water and air contained intricate worlds lodged within worlds within worlds. But, instead of focusing our gazes on itself, on the uncanny microcosms it houses, dust foregrounds the space it occupies. In the state of maximum exposure, it retreats from our grasp. In spite of being noticed and seen, it functions as a sign that points toward a reality outside it.

Just as the same city viewed from different directions appears entirely different.. there are, as it were, just as many different universes, which are, nevertheless, only perspectives on a single one, corresponding to the different point of view.

In 1673 an esteemed German lawyer and philosopher visited London. His name was Gottfried Wilhelm Leibniz. He and Newton would tear the scientific world asunder, though neither would solve the problem of the zeros that suffused calculus.

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