Gottfried Leibniz Quotations

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. It is this way that in mathematics speculative theorems and practical canons are reduced by analysis to definitions, axioms and postulates.

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.

Music is the pleasure the human mind experiences from counting without being aware that it is counting.

Men act like brutes in so far as the sequences of their perceptions arise through the principle of memory only, like those empirical physicians who have mere practice without theory.

The ultimate reason of things must lie in a necessary substance, in which the differentiation of the changes only exists eminently as in their source; and this is what we call God.

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.

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.

It follows from what we have just said, that the natural changes of monads come from an internal principle, since an external cause would be unable to influence their inner being.

I maintain also that substances, whether material or immaterial, cannot be conceived in their bare essence without any activity, activity being of the essence of substance in general.

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.

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

Whence it follows that God is absolutely perfect, since perfection is nothing but magnitude of positive reality, in the strict sense, setting aside the limits or bounds in things which are limited.

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.

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.

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.

Indeed every monad must be different from every other. For there are never in nature two beings, which are precisely alike, and in which it is not possible to find some difference which is internal, or based on some intrinsic quality.

This is why the ultimate reason of things must lie in a necessary substance, in which the differentiation of the changes only exists eminently as in their source; and this is what we call God.

But in simple substances the influence of one monad over another is ideal only.

It is this way that in mathematics speculative theorems and practical canons are reduced by analysis to definitions, axioms and postulates.

Indeed in general I hold that there is nothing truer than happiness, and nothing happier and sweeter than truth.

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.

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

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.

There is nothing without reason.

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.

All the different classes of beings which taken together make up the universe are, in the ideas of God who knows distinctly their essential gradations, only so many ordinates of a single curve so closely united that it would be impossible to place others between any two of them, since that would imply disorder and imperfection. Thus men are linked with the animals, these with the plants and these with the fossils which in turn merge with those bodies which our senses and our imagination represent to us as absolutely inanimate.

It is God who is the ultimate reason things, and the Knowledge of God is no less the beginning of science than his essence and will are the beginning of things.

I am convinced that the unwritten knowledge scattered among men of different callings surpasses in quantity and in importance anything we find in books, and that the greater part of our wealth has yet to be recorded.

According to their [Newton and his followers] doctrine, God Almighty wants to wind up his watch from time to time: otherwise it would cease to move. He had not, it seems, sufficient foresight to make it a perpetual motion. Nay, the machine of God's making, so imperfect, according to these gentlemen; that he is obliged to clean it now and then by an extraordinary concourse, and even to mend it, as clockmaker mends his work.

Virtue is the habit of acting according to wisdom.

All things in God are spontaneous.

There is nothing waste, nothing sterile, nothing dead in the universe; no chaos, no confusions, save in appearance.

There is no way in which a simple substance could begin in the course of nature, since it cannot be formed by means of compounding.

The pleasure we obtain from music comes from counting, but counting unconsciously. Music is nothing but unconscious arithmetic.

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.

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

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.

Our reasonings are grounded upon two great principles, that of contradiction, in virtue of which we judge false that which involves a contradiction, and true that which is opposed or contradictory to the false.

Therefore, I have attacted [the problem of the catenary] which I had hitherto not attempted, and with my key [the differential calculus] happily opened its secret. Acta eruditorum

Nature does not make leaps.

I don't say that bodies like flint, which are commonly called inanimate, have perceptions and appetition; rather they have something of that sort in them, as worms are in cheese.

Let there be two possible things, A and B, one of which is such that it is necessary that it exists, and let us assume that there is more perfection in A than in B. Then, at least, we can explain why A should exist rather than B and can foresee which of them will exist; indeed, this can be demonstrated, that is, rendered certain from the nature of the thing.

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

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.

Why is there anything at all rather than nothing whatsoever?

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

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

The greatness of a life can only be estimated by the multitude of its actions. We should not count the years, it is our actions which constitute our life.

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

If you have a clear idea of a soul, you will have a clear idea of a form; for it is of the same genus, though a different species.

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.

The larger the mass of collected things, the less will be their usefulness. Therefore, one should not only strive to assemble new goods from everywhere, but one must endeavor to put in the right order those that one already possesses.

These principles have given me a way of explaining naturally the union or rather the mutual agreement [conformité] of the soul and the organic body. The soul follows its own laws, and the body likewise follows its own laws; and they agree with each other in virtue of the pre-established harmony between all substances, since they are all representations of one and the same universe.

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.

Music is nothing but unconscious arithmetic.

A great doctor kills more people than a great general.

To love is to take delight in happiness of another, or, what amounts to the same thing, it is to account another's happiness as one's own.

The art of discovering the causes of phenomena, or true hypothesis, is like the art of decyphering, in which an ingenious conjecture greatly shortens the road.

Each portion of matter may be conceived of as a garden full of plants, and as a pond full of fishes. But each branch of the plant, each member of the animal, each drop of its humors, is also such a garden or such a pond.

I do not believe that a world without evil, preferable in order to ours, is possible; otherwise it would have been preferred. It is necessary to believe that the mixture of evil has produced the greatest possible good: otherwise the evil would not have been permitted. The combination of all the tendencies to the good has produced the best; but as there are goods that are incompatible together, this combination and this result can introduce the destruction of some good, and as a result some evil.

And there must be simple substances, because there are compounds; for the compound is nothing but a collection or aggregatum of simples.

I agree with you that it is important to examine our presuppositions, throughly and once for all, in order to establish something solid. For I hold that it is only when we can prove all that we bring forward that we perfectly understand the thing under consideration. I know that the common herd takes little pleasure in these researches, but I know also that the common herd take little pains thoroughly to understand things.

..This is why the ultimate reason of things must lie in a necessary substance, in which the differentiation of the changes only exists eminently as in their source; and this is what we call God.

Thus God alone is the primary Unity, or original simple substance, from which all monads, created and derived, are produced.

The monad, of which we shall speak here, is nothing but a simple substance which enters into compounds; simple, that is to say, without parts.

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.

The present is great with the future.

We never have a full demonstration, although there is always an underlying reason for the truth, even if it is only perfectly understood by God, who alone penetrated the infinite series in one stroke of the mind.

Of what use would it be to you, sir, to become King of China on condition that you forgot what you have been? Would it not be the same as if God, at the same time he destroyed you, created a King in China?

The past is pregnant with the present.

What is is what must be.

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...

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

There is no argument so cogent not only in demonstrating, the indestructibility of the soul, but also in showing that it always preserves in its nature traces of all its preceding states with a practical remembrance which can always be aroused. Since it has the consciousness of or knows in itself what each one calls his me. This renders it open to moral qualities, to chastisement and to recompense even after this life, for immortality without remembrance would be of no value.

It is unworthy of excellent men to lose hours like slaves in the labor of calculation which could be relegated to anyone else if machines were used.

I have seen something of the project of M. de St. Pierre, for maintaining a perpetual peace in Europe. I am reminded of a device in a cemetery, with the words: Pax perpetua ; for the dead do not fight any longer: but the living are of another humor; and the most powerful do not respect tribunals at all.

In symbols one observes an advantage in discovery which is greatest when they express the exact nature of a thing briefly and, as it were, picture it; then indeed the labor of thought is wonderfully diminished.

One cannot explain words without making incursions into the sciences themselves, as is evident from dictionaries; and, conversely, one cannot present a science without at the same time defining its terms.

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

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.

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

Nothing is more important than to see the sources of invention which are, in my opinion more interesting than the inventions themselves.

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

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

...a distinction must be made between true and false ideas, and that too much rein must not be given to a man's imagination under pretext of its being a clear and distinct intellection.

The most perfect society is that whose purpose is the universal and supreme happiness.

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

Philosophy consists mostly of kicking up a lot of dust and then complaining that you can't see anything.

Although the whole of this life were said to be nothing but a dream and the physical world nothing but a phantasm, I should call this dream or phantasm real enough, if, using reason well, we were never deceived by it.

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.

We should like Nature to go no further; we should like it to be finite, like our mind; but this is to ignore the greatness and majesty of the Author of things.

It has long seemed ridiculous to me to suppose that the nature of things has been so poor and stingy that it provided souls only to such a trifling mass of bodies on our globe, like human bodies, when it could have given them to all, without interfering with its other ends.

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.

Natural religion itself, seems to decay very much. Many will have human souls to be material: others make God himself a corporeal being.

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

[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.

In my judgment an organic machine new to nature never arises, since it always contains an infinity of organs so that it can express, in its own way, the whole universe; indeed, it always contains all past and present times.

Now this connection or adaption of all created things with each, and of each with all the rest, means that each simple substance has relations which express all the others, and that consequently it is a perpetual living mirror of the universe.

But it is the knowledge of necessary and eternal truths which distinguishes us from mere animals, and gives us reason and the sciences, raising us to knowledge of ourselves and God. It is this in us which we call the rational soul or mind.

We live in the best of all possible worlds