Top 127 Quotes & Sayings by Gottfried Leibniz - Page 2

There are also two kinds of truths: truth of reasoning and truths of fact.

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.

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.

Nature does not make leaps.

There are also two kinds of truths, those of reasoning and those of fact. Truths of reasoning are necessary and their opposite is impossible, and those of fact are contingent and their opposite is possible. When a truth is necessary its reason can be found by analysis, resolving it into more simple ideas and truths until we reach those which are primitive.

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

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.

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.

We may say, that not only the soul (the mirror of an indestructible universe) is indestructible, but also the animal itself is, although its mechanism is frequently destroyed in parts.

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

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.

Justice is charity in accordance with wisdom.

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.

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.

The past is pregnant with the present.

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.

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

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.

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.

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

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.

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.

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.

Music is nothing but unconscious arithmetic.

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 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.

There is a world of created beings - living things, animals, entelechies, and souls - in the least part of matter.... Thus there is nothing waste, nothing sterile, nothing dead in the universe; no chaos, no confusions, save in appearance.

There is nothing without reason.

There are two famous labyrinths where our reason very often goes astray. One concerns the great question of the free and the necessary, above all in the production and the origin of Evil. The other consists in the discussion of continuity, and of the indivisibles which appear to be the elements thereof, and where the consideration of the infinite must enter in.

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.

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

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.

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.

The present is great with the future.

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.

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.

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.

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.

[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.

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

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.

All things in God are spontaneous.

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.

Either there are no corporeal substances, and bodies are merely phenomena which are true or consistent with each other, such as a rainbow or a perfectly coherent dream, or there is in all corporeal substances something analogous to the soul.

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

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

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.

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

...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 art of discovering the causes of phenomena, or true hypotheses, is like the art of deciphering, in which an ingenious conjecture often greatly shortens the road.

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.

I am so in favor of the actual infinite that instead of admitting that Nature abhors it, as is commonly said, I hold that Nature makes frequent use of it everywhere, in order to show more effectively the perfections of its Author.

..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.

For, above all, I hold a notion of possibility and necessity according to which there are some things that are possible, but yet not necessary, and which do not really exist. From this it follows that a reason that always forces a free mind to choose one thing over another (whether that reason derives from the perfection of a thing, as it does in God, or from our imperfection) does not eliminate our freedom.

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.

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.

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.

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.

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.