Music is a hidden arithmetic exercise of the soul, which does not know that it is counting.
GOTTFRIED LEIBNIZTaking mathematics from the beginning of the world to the time when Newton lived, what he had done was much the better half.
More Gottfried Leibniz Quotes
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Nature does not make leaps.
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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.
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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?
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Make me the the master of education, and I will undertake to change the world.
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There is a certain destiny of everything, regulated by the foreknowledge and providence of God in His works.
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The world is not a machine. Everything in it is force, life, thought.
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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.
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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.
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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.
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The past is pregnant with the present.
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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.
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Thus God alone is the primary Unity, or original simple substance, from which all monads, created and derived, are produced.
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The pleasure we obtain from music comes from counting, but counting unconsciously. Music is nothing but unconscious arithmetic.
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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.
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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.
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It’s easier to be original and foolish than original and wise.
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He who understands Archimedes and Apollonius will admire less the achievements of the foremost men of later times.
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Indeed in general I hold that there is nothing truer than happiness, and nothing happier and sweeter than truth.
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Natural religion itself, seems to decay very much. Many will have human souls to be material: others make God himself a corporeal being.
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To love is to be delighted by the happiness of someone, or to experience pleasure upon the happiness of another. I define this as true love.
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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
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Music is a secret and unconscious mathematical problem of the soul.
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But in simple substances the influence of one monad over another is ideal only.
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Music is the pleasure the human mind experiences from counting without being aware that it is counting.
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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.
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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.
GOTTFRIED LEIBNIZ