Gottfried Leibniz, fully Gottfried Wilhalm von Leibniz, Baron von Leibnitz

Leibniz, fully Gottfried Wilhalm von Leibniz, Baron von Leibnitz

German Mathematician, Philosopher, Political Advisor and Logician, Developed Infinitesimal Calculus independently of Isaac Newton

Author Quotes

It must be the case that I have some perception of the movement of each wave on the shore if I am able to apperceive that which results from the movements of all the waves put together, namely the mighty roar which we hear by the sea.

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.

So long as we do not distinguish what is genuinely a complete entity, or substance, we shall never have any fixed point at which we can stop; and such fixed point is the one and only means of establishing solid and real principles.

The imaginary number is a fine and wonderful resource of the human spirit, almost an amphibian between being and not being.

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. 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.

Thus our body must be affected to some extent by the changes in all the others.

We rightly regard bodies as being things, for even phenomena are real. But if any one seeks to regard bodies as being substances he will surely need some new principle of real unity. The man in Ireland (Berkeley) who impugns the reality of bodies seems neither to give adequate reasons nor to explain sufficiently what is in his mind. I suspect that he is one of those people who seek to become famous by their paradoxes.

It was my aim here to expound, not the principles of extension, but the principles of that which is in fact extended, or of bodily mass. These principles, according to me, are the real units, that is to say the substances that possess a true unity.

Now this possibility or necessity forms or composes what are called essences or natures, and the truths which we are accustomed to call eternal; and we are right so to call them, for nothing is so eternal as what is necessary. Thus the nature of the circle with its properties is something which exists and is eternal: that is to say there is some constant cause outside us which makes all those who think about it carefully discover the same thing, and not merely that their thoughts disagree with one another; this might be attributed simply to the nature of the human mind, but for the fact that phenomena or experiences confirm them whenever some appearance of a circle strikes our senses. And these phenomena necessarily have some cause outside us.

Something quite other than mere presence is needed for one thing to represent what takes place in another. For this some explicable communication is necessary, some kind of influence either of the things upon one another or of a common cause.

The immediate cause of sin is the man as he is then constituted with respect to intellect and will based on the external things that are posited. But the preceding or mediate cause of sin is the state of the man and of objects preceding the present. And the chain of these mediate causes is the series of things.

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.

Thus the fiction of a finite material universe, the whole of which moves about in an infinite empty space, cannot be admitted. It is altogether unreasonable and impractical. For besides the fact that there is no real space outside the material universe, such an action would be without purpose; it would be working without doing anything, agendo nihil agere. No change which could be observed by any one whatever would be occurring. Such things are the imaginings of philosophers with incomplete notions, who make of space an absolute reality.

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 is the same with each monad. God alone has a distinct knowledge of everything, for He is the source of everything. It has been very well said that as a center He is everywhere; but His circumference is nowhere, since everything is present to Him immediately, without being removed from this center.

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

Now this supreme wisdom, united to goodness that is no less infinite, cannot but have chosen the best. For as a lesser evil is a kind of good, even so a lesser good is a kind of evil if it stands in the way of a greater good; and the would be something to correct in the actions of God if it were possible to the better. As in mathematics, when there is no maximum nor minimum, in short nothing distinguished, everything is done equally, or when that is not nothing at all is done: so it may be said likewise in respect of perfect wisdom, which is no less orderly than mathematics, that if there were not the best (optimum) among all possible worlds, God would not have produced any.

Taking mathematics from the beginning of the world to the time of Newton, what he has done is much the better half.

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. And there must be simple substances, because there are compounds; for the compound is nothing but a collection or aggregatum of simples. 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 is no way in which a simple substance could begin in the course of nature, since it cannot be formed by means of compounding… 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. 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. 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… And as every state of a simple substance is a natural consequence of its preceding state, so that the present state of it is big with the future.

There is a connection between the perceptions of animals, which bears some resemblance to reason: but it is based only on the memory of facts or effects, and not at all on the knowledge of causes. Thus a dog runs away from the stick with which he has been beaten, because memory represents to him the pain that was caused by that stick. And men, in so far as they are empiricists, that is to say in three-fourths of their actions, only act like brutes. For example, we expect that the day will dawn tomorrow, because we have always experienced it to be so; it is only the astronomer who foresees it by reason, and even this prediction will ultimately fail when the cause of daylight, which is not eternal, ceases. But true reasoning depends on necessary or eternal truths (like the truths of logic, numbers and geometry) which make the connection of ideas indubitable, and the sequences inevitable. Animals in which such sequences cannot be observed are called brutes; but those which know these necessary truths are called rational animals, and their souls are called minds. These souls are capable of performing acts of reflection, and of considering what is called self, substance, soul, mind- those things and truths, in short, which are immaterial. It is this which makes us capable of understanding science or demonstrative knowledge.

Thus the final reason of things must be in a necessary substance, in which the variety of particular changes exists only eminently, as in its source; and this substance we call God.

What is is what must be.

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

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. We are all merely empiricists as regards three-fourths of our actions. For example, when we expect it to be day tomorrow, we are behaving as empiricists, because until now it has always happened thus. The astronomer alone knows this by reason.

Now where there are no parts, there can be neither extension nor form [figure] nor divisibility. These Monads are the real atoms of nature and, in a word, the elements of things.

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German Mathematician, Philosopher, Political Advisor and Logician, Developed Infinitesimal Calculus independently of Isaac Newton