Mathematics is a body of knowledge, but it contains no truths.
What humans do with the language of mathematics is to describe patterns.
Logic doesn't apply to the real world.
Arithmetic is where the content lies, and not logic; but logic prompts certainty, and not arithmetic.
Logic has made me hated in the world.
Most likely, logic is capable of justifying mathematics to no greater extent than biology is capable of justifying life.
The theoretician believes in logic and believes that he despises dreams, intuition, and poetry. He does not recognize that these three fairies have only disguised themselves in order to dazzle him.... He does not know that he owes his greatest discoveries to them.
Formality Thus the absence of all mention of particular things or properties in logic or pure mathematics is a necessary result of the fact that this study is, as we say, "purely formal".
Mathematical science is in my opinion an indivisible whole, an organism whose vitality is conditioned upon the connection of its parts.
The circumstances of human society are too complicated to be submitted to the rigor of mathematical calculation.
Mathematics consists in proving the most obvious thing in the least obvious way.
The whole world knows that American TV companies have monopolized Olympic broadcasts and in order to please the fans in their country they do everything they can to keep American viewers interested in what is going on at the hockey rink in Sochi. According to their logic, Americans should always win, no matter what. It was absolutely obvious that [Fyodor] Tyutin's goal yesterday should have been allowed. This was clear to the whole world except the American referee, American TV and those officials with American passports who rule international hockey, grossly neglecting all Olympic principles.
The minute you take away somebody the public's voting for, you're screwing with the program. There's no logic to it.
Scientists actively approach the door to knowledge—the boundary of the domain of what we know. We question and explore and we change our views when facts and logic force us to do so. We are confident only in what we can verify through experiments or in what we can deduce from experimentally confirmed hypotheses.
There is perhaps no field aspiring to be scientific where flagrant personal bias, logic martyred in the cause of supporting a prejudice, unfounded assertions, and even sentimental rot and drivel, have run riot to such an extent as here.
But, in fact, materialism is among the most problematic of philosophical standpoints, the most impoverished in its explanatory range, and among the most willful and (for want of a better word) magical in its logic, even if it has been in fashion for a couple of centuries or more.
Logic might be unanswerable because it was so absolutely wrong.
When money, instead of man, is at the center of the system, when money becomes an idol, men and women are reduced to simple instruments of a social and economic system, which is characterized, better yet dominated, by profound inequalities. So we discard whatever is not useful to this logic; it is this attitude that discards children and older people, and is now affecting the young.
I am delighted to know that Principia Mathematica can now be done by machinery. . . I am quite willing to believe that anything in deductive logic can be done by machinery.
No living creature, not even man, has achieved, in the centre of his sphere, what the bee has achieved in her own: and were some one from another world to descend and ask of the earth the most perfect creation of the logic of life, we should needs have to offer the humble comb of honey.
Statistics have shown that mortality increases perceptibly in the military during wartime.
Aristotelian logic is massive and marmoreal, but every monument accumulates graffiti.
You can be totally rational with a machine. But if you work with people, sometimes logic often has to take a backseat to understanding.
The Greeks invented logic but were not fooled by it.
Pop is everything art hasn't been for the last two decades...It springs newborn out of a boredom with the finality and over-saturation of Abstract-Expressionism, which, by its own esthetic logic, is the END of art, the glorious pinnacle of the long pyramidal creative process. Stifled by this rarefied atmosphere, some young painters turn back to some less exalted things like Coca-Cola, ice-cream sodas, big hamburgers, super-markets and 'EAT' signs. They are eye-hungry; they pop.
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