A Quote by George Polya

Geometry is the science of correct reasoning on incorrect figures. — © George Polya
Geometry is the science of correct reasoning on incorrect figures.
Geometry is the art of correct reasoning from incorrectly drawn figures.
The best road to correct reasoning is by physical science; the way to trace effects to causes is through physical science; the only corrective, therefore, of superstition is physical science.
Geometry enlightens the intellect and sets one's mind right. All of its proofs are very clear and orderly. It is hardly possible for errors to enter into geometrical reasoning, because it is well arranged and orderly. Thus, the mind that constantly applies itself to geometry is not likely to fall into error. In this convenient way, the person who knows geometry acquires intelligence.
To govern is to correct. If you set an example by being correct, who would dare to remain incorrect?
Unfortunately, The End of Nature turns out to be correct, although I wish it were not so. The only places that I was incorrect was, as with environmental science at the time, the estimation of the speed at which we see the effects of global warming.
You will be right, over the course of many transactions, if your hypotheses are correct, your facts are correct, and your reasoning is correct. True conservatism is only possible through knowledge and reason.
Geometry is beautifully logical, and it teaches you how to think and prove that things are so, step by step by step. Proofs are excellent lessons in reasoning. Without logic and reasoning, you are dependent on jumping to conclusions or - worse - having empty opinions.
Inferences of Science and Common Sense differ from those of deductive logic and mathematics in a very important respect, namely, when the premises are true and the reasoning correct, the conclusion is only probable.
Reasoning will never make a man correct an ill opinion, which by reasoning he never acquired
But that the reasoning from these facts, the drawing from them correct conclusions, is a matter of great difficulty, may be inferred from the imperfect state in which the Science is now found after it has been so long and so intensely studied.
I don't want to make a film that offends people, but the whole world is so politically correct - I'm not going to not do something because it may be politically incorrect. At some point, the metaphors and allegories break down. They disappear, and you just have science fiction.
Obviously I don't want to make a film that offends people, but the whole world is so politically correct - I'm not going to not do something because it may be politically incorrect. At some point, the metaphors and allegories break down. They disappear, and you just have science fiction.
All possible knowledge, then, depends on the validity of reasoning...Unless human reasoning is valid no science can be true.
Considerable obstacles generally present themselves to the beginner, in studying the elements of Solid Geometry, from the practice which has hitherto uniformly prevailed in this country, of never submitting to the eye of the student, the figures on whose properties he is reasoning, but of drawing perspective representations of them upon a plane. ...I hope that I shall never be obliged to have recourse to a perspective drawing of any figure whose parts are not in the same plane.
What we take ourselves to be doing when we think about what is the case or how we should act is something that cannot be reconciled with a reductive naturalism, for reasons distinct from those that entail the irreducibility of consciousness. It is not merely the subjectivity of thought but its capacity to transcend subjectivity and to discover what is objectively the case that presents a problem....Thought and reasoning are correct or incorrect in virtue of something independent of the thinker's beliefs, and even independent of the community of thinkers to which he belongs. (p. 71)
It is easier to write an incorrect program than understand a correct one.
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