Leibniz Quotes

Can you really believe that a drop of urine is an infinity of monads, and that each of these has ideas, however obscure, of the universe as a whole?

Voltaire

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.

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

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. No observations or experiments could ever reveal whether we lived in universe One or Two.

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.

Nihil est sine ratione.[There is nothing without a reason.]

Gottfried Wilhelm 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

[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.

Morality consists in this for each individual: to attempt each time to extend its region of clear expression, to try to augment its amplitude, so as to produce a free act that expresses the most possible in one given condition or another. -- Gilles Deleuze, The Fold: Leibniz and the Baroque, 73

Because children have abounding vitality, because they are in spirit fierce and free, therefore they want things repeated and unchanged. They always say, "Do it again"; and the grown-up person does it again until he is nearly dead. For grown-up people are not strong enough to exult in monotony. But perhaps God is strong enough to exult in monotony. It is possible that God says every morning, "Do it again" to the sun; and every evening, "Do it again" to the moon. It may not be automatic necessity that makes all daisies alike; it may be that God makes every daisy separately, but has never got tired of making them. It may be that He has the eternal appetite of infancy; for we have sinned and grown old, and our Father is younger than we.

G.K. Chesterton