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All mathematics is tautology.

Ludwig Wittgenstein

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Ludwig Wittgenstein
Age: 62 †
Born: 1889
Born: April 26
Died: 1951
Died: April 29
Aphorist
Architectural Theoretician
Epistemologist
Logician
Mathematician
Philosopher
Philosopher Of Language
Professor
Teacher
Vienna
Austria
Tautology
Mathematics

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The face is the soul of the body.
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We must plow through the whole of language.
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Suppose someone were to say: 'Imagine this butterfly exactly as it is, but ugly instead of beautiful'?!
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Imagine someone pointing to a place in the iris of a Rembrandt eye and saying, 'The walls of my room should be painted this color.
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Black seems to make a colour cloudy, but darkness doesn't. A ruby could thus keep getting darker without ever becoming cloudy but if it became blackish red, it would become cloudy.
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Logic is not a body of doctrine, but a mirror-image of the world. Logic is transcendental.
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My day passes between logic, whistling, going for walks, and being depressed. I wish to God that I were more intelligent and everything would finally become clear to me - or else that I needn't live much longer.
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What signs fail to express, their application shows. What signs slur over, their application says clearly.
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I sit astride life like a bad rider on a horse. I only owe it to the horse's good nature that I am not thrown off at this very moment.
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Philosophy unravels the knots in our thinking hence its results must be simple, but its activity is as complicated as the knots that it unravels.
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There can never be surprises in logic.
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One of the most misleading representational techniques in our language is the use of the word 'I.'
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Nothing is more important than the formation of fictional concepts, which teach us at last to understand our own.
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Transparency painted in a picture produces its effect in a different way than opaqueness.
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It is possible--indeed possible even according to the old conception of logic--to give in advance a description of all 'true' logical propositions. Hence there can never be surprises in logic.
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The form is the possibility of the structure.
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The world of those who are happy is different from the world of those who are not.
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The world divides into facts.
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We are asleep. Our Life is a dream. But we wake up sometimes, just enough to know that we are dreaming.
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Concerning that which cannot be talked about, we should not say anything.
Ludwig Wittgenstein