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"Theoretically, I grant you, there is no possibility of error in necessary reasoning. But to speak thus "theoretically," is to uselanguage in a Pickwickian sense. In practice, and in fact, mathematics is not exempt from that liability to error that affects everything that man does."

— Charles Sanders Peirce
charles sanders peirce Quotes Grants,Certainty,Reasoning

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Charles Sanders Peirce
Grants
Certainty
Reasoning
Liability

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Out of the element of participation follows the certainty of faith; out of the element of separation follows the doubt in faith. And each is essential for the nature of faith. Sometimes certainty conquers doubt, but it cannot eliminate doubt. The conquered of today may become the conqueror of tomorrow. Sometimes doubt conquers faith, but it still contains faith. Otherwise it would be indifference.

— Paul Tillich

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I shall not mingle conjectures with certainties.

— Isaac Newton

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