A Quote by Stendhal

Mathematics allows for no hypocrisy and no vagueness. — © Stendhal
Mathematics allows for no hypocrisy and no vagueness.
When people talk, they lay lines on each other, do a lot of role playing, sidestep, shilly-shally and engage in all manner of vagueness and innuendo. We do this and expect others to do it, yet at the same time we profess to long for the plain truth, for people to say what they mean, simple as that. Such hypocrisy is a human universal.
Outside of mathematics and logic, there are common sense truths, such as that it is snowing that normal observers, in a specified context can agree on, subject to vagueness considerations, and theoretical truths, such as that snow is crystallised water vapour, and maybe in-between truths.
Conservatives are often fond of La Rochefoucauld's famous aphorism that 'Hypocrisy is a tribute that vice pays to virtue,' and so tend to downplay hypocrisy as a sin. But in the marketplace of ideas they champion, hypocrisy may yet turn out to be the deadliest - or costliest - of sins.
Actually, we have misdefined "hypocrisy." Hypocrisy is not the failure to practice what you preach but the failure to believe it. Hypocrisy is propaganda.
Maybe vagueness has been good for me. The word means two different things in Tokyo and Osaka, you know. In Tokyo it means stupidity, but in Osaka they talk about vagueness in a painting and in a game of Go.
Mystery is an inescapable ingredient of mathematics. Mathematics is full of unanswered questions, which far outnumber known theorems and results. It's the nature of mathematics to pose more problems than it can solve. Indeed, mathematics itself may be built on small islands of truth comprising the pieces of mathematics that can be validated by relatively short proofs. All else is speculation.
Hypocrisy means deliberately pretending. None of us lives up to his ideals; none of us is all that he would like to be or all that he could be in Christ. But that is not hypocrisy. Falling short of our ideals is not hypocrisy. Pretending we have reached our ideals when we have not - that is hypocrisy.
To borrow from Mark Twain, I tend to think that reports of the death of supervaluationist approaches have been greatly exaggerated. The arguments that have been given against supervaluationism usually aim to show that it is just incoherent. But it's not. It may be false, as a general theory of vagueness, but it's a coherent and, I think, even correct way to think about some vagueness.
May not music be described as the mathematics of the sense, mathematics as music of the reason? The musician feels mathematics, the mathematician thinks music: music the dream, mathematics the working life.
I like science and mathematics. When I say mathematics, I don't mean algebra or math in that sense, but the mathematics of things.
But there is another reason for the high repute of mathematics: it is mathematics that offers the exact natural sciences a certain measure of security which, without mathematics, they could not attain.
If you ask ... the man in the street ... the human significance of mathematics, the answer of the world will be, that mathematics has given mankind a metrical and computatory art essential to the effective conduct of daily life, that mathematics admits of countless applications in engineering and the natural sciences, and finally that mathematics is a most excellent instrumentality for giving mental discipline... [A mathematician will add] that mathematics is the exact science, the science of exact thought or of rigorous thinking.
Mathematics has two faces: it is the rigorous science of Euclid, but it is also something else. Mathematics presented in the Euclidean way appears as a systematic, deductive science; but mathematics in the making appears as an experimental, inductive science. Both aspects are as old as the science of mathematics itself.
The only vice that cannot be forgiven is hypocrisy. The repentance of a hypocrite is itself hypocrisy.
Criticism is hypocrisy; society is hypocrisy. I'm a tourist. I'm a consumer. I do the things that I photograph and can be criticized of.
In fact, the answer to the question "What is mathematics?" has changed several times during the course of history... It was only in the last twenty years or so that a definition of mathematics emerged on which most mathematicians agree: mathematics is the science of patterns.
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