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Quote by Carl B. Boyer

“As the sensations of motion and discreteness led to the abstract notions of the calculus, so may sensory experience continue thus to suggest problem for the mathematician, and so may she in turn be free to reduce these to the basic formal logical relationships involved. Thus only may be fully appreciated the twofold aspect of mathematics: as the language of a descriptive interpretation of the relationships discovered in natural phenomena, and as a syllogistic elaboration of arbitrary premise.”

Quote by Carl B. Boyer

Book:The History of the Calculus and Its Conceptual Development
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The History of the Calculus and Its Conceptual Development

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Carl B. Boyer

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“We explain agreeable general feelings as produced by our trust in God, and by our consciousness of good deeds (the so-called "good conscience" — a physiological state which at times looks so much like good digestion that it is hard to tell them apart). They are produced by the successful termination of some enterprise (a naive fallacy: the successful termination of some enterprise does not by any means give a hypochondriac or a Pascal agreeable general feelings). They are produced by faith, charity, and hope — the Christian virtues. In fact, all these supposed causes are actually effects, and as it were, translate pleasant or unpleasant feelings into a misleading terminology. One is in a state of hope because the basic physiological feeling is once again strong and rich; one trusts in God because the feeling of fullness and strength gives a sense of rest. Morality and religion belong entirely to the psychology of error: in every single case, cause and effect are confused; or truth is confused with the effects of believing something to be true; or a state of consciousness is confused with its physiological origins.”

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“Don't dull the voice of your heart just to please your brain As it swells into overthought and the desire to be right Switch on the light of your inner lamp. Listen to your heart so you can feel from your soul Don’t discount your heart to make your logic fit.”

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Book:Rocks Into Roses: Life Lessons and Inspiration for Personal Growth
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“Review the multiplicity of language-games in the following examples, and in others: Giving orders, and obeying them— Describing the appearance of an object, or giving its measurements— Constructing an object from a description (a drawing)— Reporting an event— Speculating about an event— Forming or teasing a hypothesis— Presenting the results of an experiment in tables and diagrams— Making up a story; and reading it— Singing catches— Guessing riddles— Making riddles— Making a joke; telling it— Solving a problem in practical arithmetic— Translating from one language into another— Asking, thanking, cursing, greeting, praying. —It is interesting to compare the multiplicity of the tools in language and of the ways they are used, the multiplicity of kinds of word and sentence, with what logicians have said about the structure of language. (Including the author of the Tractatus Logico-Philosophicus.)”

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Book:Philosophical Investigations
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