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— Chinua Achebe"In the vocabulary of certain radical theorists contradictions are given the status of some deadly disease to which their opponents alone can succumb. But contradictions are the very stuff of life. If there had been a little dash of contradiction among the Gadarene swine some of them might have been saved from drowning."
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Suppose a student of mine writes in her exam that "morality is completely relative to culture, so nothing is absolutely right or wrong. Because of that, it is absolutely wrong to be culturally intolerant". This student, if she believes what she writes, believes a contradiction. She ought not to believe the contradiction - it's a basic epistemic norm. This is true even if she can't avoid believing it - no amount of studying will show her the light.
— Nomy Arpaly
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To exist (in mathematics), said Henri Poincaré, is to be free from contradiction. But mere existence does not guarantee survival. To survive in mathematics requires a kind of vitality that cannot be described in purely logical terms.
— Mark Kac
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