Leibniz Quotes

It is not always the most brilliant speculations nor the choice of the most exotic materials that is most profitable. I prefer Monsieur de Reaumur busy exterminating moths by means of an oily fleece; or increasing fowl production by making them hatch without the help of their mothers, than Monsieur Bemouilli absorbed in algebra, or Monsieur Leibniz calculating the various advantages and disadvantages of the possible worlds. ~ Noel-Antoine Pluche

TO LOVE is to find pleasure in the happiness of others. ~ Gottfried Leibniz

The analytical geometry of Descartes and the calculus of Newton and Leibniz have expanded into the marvelous mathematical method-more daring than anything that the history of philosophy records-of Lobachevsky and Riemann, Gauss and Sylvester. Indeed, mathematics, the indispensable tool of the sciences, defying the senses to follow its splendid flights, is demonstrating today, as it never has been demonstrated before, the supremacy of the pure reason. ~ Nicholas Murray Butler

There are also two kinds of truths, those of reasoning and those of fact. Truths of reasoning are necessary and their opposite is impossible: truths of fact are contingent and their opposite is possible. When a truth is necessary, reason can be found by analysis, resolving it into more simple ideas and truths, until we come to those which are primary. ~ Gottfried Leibniz

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. ~ Gottfried Wilhelm Leibniz

It is necessary to believe that the mixture of evil has produced the greatest possible good: otherwise the evil would not have been permitted. ~ Gottfried Leibniz

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. ~ Gottfried Wilhelm Leibniz

I do not conceive of any reality at all as without genuine unity. ~ Gottfried Leibniz

Imaginary numbers are a fine and wonderful refuge of the divine spirit almost an amphibian between being and non-being. ~ Gottfried Leibniz

God makes nothing without order, and everything that forms itself develops imperceptibly out of small parts. ~ Gottfried Leibniz

To love is to be delighted by the happiness of someone, or to experience pleasure upon the happiness of another. I define this as true love. ~ Gottfried Leibniz

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. ~ Bertrand Russell

Nothing is accomplished all at once, and it is one of my great maxims, and one of the most completely verified, that Nature makes no leaps: a maxim which I have called the law of continuity. ~ Gottfried Leibniz

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. ~ Gottfried Wilhelm Leibniz

Taking mathematics from the beginning of the world to the time when Newton lived, what he had done was much the better half. ~ Gottfried Leibniz

It is unworthy of excellent men to lose hours like slaves in the labour of calculation which could safely be relegated to anyone else if machines were used.
(Describing, in 1685, the value to astronomers of the hand-cranked calculating machine he had invented in 1673.) ~ Gottfried Wilhelm Leibniz

From 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. N ~ Samir Okasha

Music is the hidden arithmetical exercise of a mind unconscious that it is calculating. ~ Gottfried Wilhelm Leibniz

Reality cannot be found except in One single source, because of the interconnection of all things with one another. ~ Gottfried Leibniz

Every substance is as a world apart, independent of everything else except God. ~ Gottfried Leibniz

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. ~ Neal Stephenson

[Alternate translation:] The Divine Spirit found a sublime outlet in that wonder of analysis, that portent of the ideal world, that amphibian between being and not-being, which we call the imaginary root of negative unity. ~ Gottfried Leibniz

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

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. ~ Gottfried Wilhelm Leibniz

It's easier to be original and foolish than original and wise. ~ Gottfried Leibniz

I have said more than once, that I hold space to be something purely relative, as time; an order of coexistences, as time is an order of successions. ~ Gottfried Leibniz

Leibniz is proposing a strange inversion of what we normally mean when we describe a man as distinguished, or unique. Normally when we say these things, we mean that the man himself stands out from a crowd in some way. But Leibniz is saying that such a man's uniqueness is rooted in his ability to perceive the rest of the universe with unusual clarity - to distinguish one thing from another more effectively than ordinary souls." Roger ~ Neal Stephenson

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. ~ Gottfried Wilhelm Leibniz

Why is there anything at all rather than nothing whatsoever? ~ Gottfried Leibniz

It can have its effect only through the intervention of God, inasmuch as in the ideas of God a monad rightly demands that God, in regulating the rest from the beginning of things, should have regard to itself. ~ Gottfried Leibniz

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

It is a good thing to proceed in order and to establish propositions. This is the way to gain ground and to progress with certainty. ~ Gottfried Leibniz

Every present state of a simple substance is the natural consequence of its preceding state, in such a way that its present is big with its future. ~ Gottfried Leibniz

"We hold these truths to be sacred and undeniable" in a draft of the Declaration of Independence changes it instead into an assertion of rationality. The scientific mind of Franklin drew on the scientific determinism of Isaac Newton and the analytic empiricism of David Hume and Gottfried Leibniz. In what became known as "Hume's Fork" the latters' theory distinguished between synthetic truths that describe matters of fact, and analytic truths that are self-evident by virtue of reason and definition. ~ Benjamin Franklin

Music is a secret and unconscious mathematical problem of the soul. ~ Gottfried Leibniz

if Newton is the finger, Leibniz is the stone, and they press against each other with equal and opposite force, a little bit harder every day. RAVENSCAR: ~ Neal Stephenson

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 i ~ Huston Smith

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. ~ Gottfried Wilhelm Leibniz

Nihil est sine ratione. There is nothing without a reason. ~ Gottfried Leibniz

It appears that the solution of the problem of time and space is reserved to philosophers who, like Leibniz, are mathematicians, or to mathematicians who, like Einstein, are philosophers. ~ Hans Reichenbach

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. ~ Reviel Netz

The words 'Here you can find perfect peace' can be written only over the gates of a cemetery. ~ Gottfried Leibniz

If we could sufficiently understand the order of the universe, we should find that it exceeds all the desires of the wisest men, and that it is impossible to make it better than it is, not only as a whole and in general but also for ourselves in particular, if we are attached, as we ought to be, to the Author of all, not only as to the architect and efficient cause of our being, but as to our master and to the final cause, which ought to be the whole aim of our will, and which can alone make our happiness. ~ Gottfried Leibniz

The present is big with the future. ~ Gottfried Wilhelm Leibniz

All things in God are spontaneous. ~ Gottfried Leibniz

For things remain possible, even if God does not choose them. Indeed, even if God does not will something to exist, it is possible for it to exist, since, by its nature, it could exist if God were to will it to exist. ~ Gottfried Leibniz

The present is big with the future, the future might be read in the past, the distant is expressed in the near. ~ Gottfried Leibniz

Leibniz dedicated his life to efforts to educate people to understand that true happiness is found by locating their identity in benefitting mankind and their posterity. ~ Robert Trout

Once the characteristic numbers of most notions are determined, the human race will have a new kind of tool, a tool that will increase the power of the mind much more than optical lenses helped our eyes, a tool that will be as far superior to microscopes or telescopes as reason is to vision. - LEIBNIZ, Philosophical Essays, TRANS. BY ARLEW AND GARBER ~ Neal Stephenson

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

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. ~ Giorgio Agamben

Navarette, a Chinese missionary, agrees with Leibniz and says that It is the special providence of God that the Chinese did not know what was done in Christendom; for if they did, there would be never a man among them, but would spit in our faces. ~ Matthew Tindal

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

A great doctor kills more people than a great general. ~ Gottfried Leibniz

God's relation to spirits is not like that of a craftsman to his work, but also like that of a prince to his subjects. ~ Gottfried Leibniz

There are also two kinds of truths: truth of reasoning and truths of fact. Truths of reasoning are necessary and their opposite is impossible; those of fact are contingent and their opposite is possible. ~ Gottfried Leibniz

I also take it as granted that every created thing, and consequently the created monad also, is subject to change, and indeed that this change is continual in each one. ~ Gottfried Leibniz

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 ... ~ Gottfried Wilhelm Leibniz

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. ~ Neal Stephenson

God, possessing supreme and infinite wisdom, acts in the most perfect manner, not only metaphysically, but also morally speaking, and ... with respect to ourselves, we can say that the more enlightened and informed we are about God's works, the more we will be disposed to find them excellent and in complete conformity with what we might have desired. ~ Gottfried Leibniz

When one compares the talents one has with those of a Leibniz , one is tempted to throw away one's books and go die quietly in the dark of some forgotten corner. ~ Denis Diderot

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. ~ Neal Stephenson

With an absurd oversimplification, the 'invention' of the calculus is sometimes ascribed to two men, Newton and Leibniz. In reality, the calculus is the product of a long evolution that was neither initiated nor terminated by Newton and Leibniz, but in which both played a decisive part. ~ Richard Courant

I hold that the mark of a genuine idea is that its possibility can be proved, either a priori by conceiving its cause or reason, or a posteriori when experience teaches us that it is in fact in nature. ~ Gottfried Leibniz

Now where there are no parts, there neither extension, nor shape, nor divisibility is possible. And these monads are the true atoms of nature and, in a word, the elements of things. ~ Gottfried Leibniz

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. ~ Gottfried Wilhelm Leibniz

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

In whatever manner God created the world, it would always have been regular and in a certain general order. God, however, has chosen the most perfect, that is to say, the one which is at the same time the simplest in hypothesis and the richest in phenomena. ~ Gottfried Leibniz

... every feeling is the perception of a truth ... ~ Gottfried Wilhelm Leibniz

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. ~ Roger Scruton

I also readily admit that there are animals, taken in the ordinary sense, that are incomparably larger than those we know of, and I have sometimes said in jest that there might be a system like ours which is the pocketwatch of some enormous giant. ~ Gottfried Leibniz

There is nothing without reason. ~ Gottfried Leibniz

Now, as there is an infinity of possible universes in the Ideas of God, and as only one of them can exist, there must be a sufficient reason for God's choice, which determines him toward one rather than another. And this reason can be found only in the fitness, or the degrees of perfection, that these worlds contain, since each possible thing has the right to claim existence in proportion to the perfection it involves. ~ Gottfried Leibniz

Ultimately, Leibniz argued, there are only two absolutely simple concepts, God and Nothingness. From these, all other concepts may be constructed, the world, and everything within it, arising from some primordial argument between the deity and nothing whatsoever. And then, by some inscrutable incandescent insight, Leibniz came to see that what is crucial in what he had written is the alternation between God and Nothingness. And for this, the numbers 0 and 1 suffice. ~ David Berlinski

The dot was introduced as a symbol for multiplication by Leibniz. On July 29, 1698, he wrote in a letter to Johann Bernoulli: I do not like X as a symbol for multiplication, as it is easily confounded with x ... ~ Gottfried Leibniz

Notable enough, however, are the controversies over the series 1 - 1 + 1 - 1 + 1 - ... whose sum was given by Leibniz as 1/2, although others disagree ... Understanding of this question is to be sought in the word "sum"; this idea, if thus conceived - namely, the sum of a series is said to be that quantity to which it is brought closer as more terms of the series are taken - has relevance only for convergent series, and we should in general give up the idea of sum for divergent series. ~ Leonhard Euler

There is a certain destiny of everything, regulated by the foreknowledge and providence of God in His works. ~ Gottfried Leibniz

There never is absolute birth nor complete death, in the strict sense, consisting in the separation of the soul from the body. What we call births are developments and growths, while what we call deaths are envelopments and diminutions. ~ Gottfried Leibniz

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. ~ Etienne Gilson

Music is a hidden arithmetic exercise of the soul, which does not know that it is counting. ~ Gottfried Leibniz

To love is to place happiness in the heart of another ... ~ Gottfried Leibniz

The knowledge which we have acquired ought not to resemble a great shop without order, and without an inventory; we ought to know what we possess, and be able to make it serve us in need. ~ Gottfried Leibniz

Leibniz believed in freedom, both divine and human, and he thought that contingency was a necessary condition of freedom. That is, if an agent A acts freely when choosing X, then A's choosing X cannot be necessary. But there are some elements in his philosophy that seem to make contingency impossible. ~ Gonzalo Rodriguez-Pereyra

Consistent with the liberal views of the Enlightenment, Leibniz was an optimist with respect to human reasoning and scientific progress. Although he was a great reader and admirer of Spinoza, Leibniz, being a confirmed deist, rejected emphatically Spinoza's pantheism. ~ Shelby D. Hunt

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. ~ Neal Stephenson

... 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 ... ~ Gottfried Wilhelm Leibniz

Make me the the master of education, and I will undertake to change the world. ~ Gottfried Leibniz

Nature does not make leaps. ~ Gottfried Leibniz

Nothing is in the intellect that was not first in the senses, except the intellect itself. ~ Gottfried Wilhelm Leibniz

For since it is impossible for a created monad to have a physical influence on the inner nature of another, this is the only way in which one can be dependent on another. ~ Gottfried Leibniz

Leibniz endeavored to provide an account of inference and judgment involving the mechanical play of symbols and very little else. The checklists that result are the first of humanity's intellectual artifacts. They express, they explain, and so they ratify a power of the mind. And, of course, they are artifacts in the process of becoming algorithms. ~ David Berlinski

When a truth is necessary, the reason for it can be found by analysis, that is, by resolving it into simpler ideas and truths until the primary ones are reached. ~ Gottfried Leibniz

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 ~ Frank Kermode

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

When God works miracles, he does not do it in order to supply the wants of nature, but those of grace. Whoever thinks otherwise, must needs have a very mean notion of the wisdom and power of God. ~ Gottfried Leibniz

The past is pregnant with the present. ~ Gottfried Leibniz

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

Finally there are simple ideas of which no definition can be given; there are also axioms or postulates, or in a word primary principles, which cannot be proved and have no need of proof. ~ Gottfried Leibniz

It is worth noting that the notation facilitates discovery. This, in a most wonderful way, reduces the mind's labour. ~ Gottfried Leibniz

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 ... ~ Gottfried Wilhelm Leibniz