Quotes about Gottfried Wilhelm Leibniz

21 Sourced Quotes

The minds of different generations are as impenetrable one by the other as are the monads of Leibniz.

Leibniz's theorem... sets forth fundamentally that of all the worlds that may be created, the actual world is that which contains, besides the unavoidable evil, the maximum good.

Each man, therefore, is the entire world, bearing within his genes a memory of all mankind. Or as Leibniz put it: 'Every living substance is a perpetual living mirror of the universe'

The analytical geometry of Descartes and the calculus of Newton and Leibniz have expanded into the marvelous mathematical method

Nicholas Murray Butler

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

Of Gottfried Wilhelm Leibniz:

When Sir A. Fountaine was at Berlin with Leibnitz in 1701, and at supper with the Queen of Prussia, she asked Leibnitz his opinion of Sir Isaac Newton. Leibnitz said that taking mathematicians from the beginning of the world to the time when Sir Isaac lived, what he had done was much the better half; and added that he had consulted all the learned in Europe upon some difficult points without having any satisfaction, and that when he applied to Sir Isaac, he wrote him in answer by the first post, to do so and so, and then he would find it.

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

The Encyclopedia presents a contemporary version of the ancient encyclopedic ideal of Aristotle, the Scholastics, Leibniz, the Encyclopedists, and Comte.

Charles W. Morris

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.

Leibniz's theory on the subject as substantia ideans in the sense of a causative agent of decision and acts stands much closer to a materialist interpretation of history than does a philosophy which reduces the thinking subject to the role of subsuming protocol sentences under general propositions and deducing other sentences from them.

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

The idea that reason requires an impartial treatment of individuals corresponds to well-known principles. To resolve the questions of distributive justice, Leibniz proposes the following maxim: Put your self in the place of everyone. In recent theories, this amounts to saying that the choice of a just organization of society must take place behind a veil of ignorance, an idea that can be interpreted in several ways. For utilitarianism, each individual must count as one, and none as more than one. For John Rawls, we have to choose the form of society that favors the least advantaged, whoever they might be. Another impartial idea is that of universal rights, embodied in the two declarations of 1776 and 1789.

Isaac Newton deserves to be included in a series of companions to major philosophers even though he was not a philosopher in the sense in which Descartes, Locke, and Kant were philosophers. That is, Newton made no direct contributions to epistemology or metaphysics that would warrant his inclusion in the standard list of major philosophers of the seventeenth and eighteenth centuries – Descartes, Spinoza, Locke, Leibniz, Berkeley, Hume, and Kant – or even in a list of other significant philosophers of the era – Bacon, Hobbes, Arnauld, Malebranche, Wolff, and Reid. The contributions to knowledge that made Newton a dominant figure of the last millennium were to science, not to philosophy.

I. Bernard Cohen

George Boole took up Leibniz's idea, and wrote a book he called The Laws of Thought. The laws he formulated are now called Boolean algebra... Boole seems to have had a grandiose vision about the applicability of his algebraic methods to practical problems—his book makes it clear that he hoped these laws would be used to settle practical questions. William Stanley Jevons heard of Boole's work, and undertook to build a machine to make calculations in Boolean algebra. He successfully designed and built... the Logical Piano... the first machine to do mechanical inference.

Michael J. Beeson

The stone that Dr. Johnson once kicked to demonstrate the reality of matter has become dissipated in a diffuse distribution of mathematical probabilities. The ladder that Descartes, Galileo, Newton, and Leibniz erected in order to scale the heavens rests upon a continually shifting, unstable foundation.

The German idealist philosophical tradition from which Hayek emerged is usually held to begin with Gottfried Leibniz.

Alan O. Ebenstein

This art is music. It stands quite apart from all the others. In it we do not recognize the copy, the repetition, of any Idea of the inner nature of the world. Yet it is such a great and exceedingly fine art, its effect on man's innermost nature is so powerful, and it is so completely and profoundly understood by him in his innermost being as an entirely universal language, whose distinctness surpasses even that of the world of perception itself, that in it we certainly have to look for more than that exercitium arithmeticae occultum nescientis se numerare animi [exercise in arithmetic in which the mind does not know it is counting] which Leibniz took it to be.

Arthur Schopenhauer

No matter where and how far we look, nowhere do we find a contradiction between religion and natural science. On the contrary, we find a complete concordance in the very points of decisive importance. Religion and natural science do not exclude each other, as many contemporaries of ours would believe or fear. They mutually supplement and condition each other. The most immediate proof of the compatibility of religion and natural science, even under the most thorough critical scrutiny, is the historical fact that the very greatest natural scientists of all times — men such as Kepler, Newton, Leibniz — were permeated by a most profound religious attitude.

When we consider a human work, we believe we know where the "intelligence" which fashioned it comes from; but when a living being is concerned, no one knows or ever knew, neither Darwin nor Epicurus, neither Leibniz nor Aristotle, neither Einstein nor Parmenides. An act of faith is necessary to make us adopt one hypothesis rather than another. Science, which does not accept any credo, or in any case should not, acknowledges its ignorance, its inability to solve this problem which, we are certain, exists and has reality.

Pierre-Paul Grassé

Gottlob Frege created modern logic including "for all," "there exists," and rules of proof. Leibniz and Boole had dealt only with what we now call "propositional logic" (that is, no "for all" or "there exists"). They also did not concern themselves with rules of proof, since their aim was to reach truth by pure calculation with symbols for the propositions. Frege took the opposite track: instead of trying to reduce logic to calculation, he tried to reduce mathematics to logic, including the concept of number.

Michael J. Beeson