Combining Texts
Ideas for
'fragments/reports', 'Must We Believe in Set Theory?' and 'The Republic'
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8 ideas
6. Mathematics / A. Nature of Mathematics / 2. Geometry
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8726
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Geometry can lead the mind upwards to truth and philosophy [Plato]
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6. Mathematics / A. Nature of Mathematics / 5. The Infinite / a. The Infinite
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10491
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Infinite natural numbers is as obvious as infinite sentences in English [Boolos]
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6. Mathematics / A. Nature of Mathematics / 5. The Infinite / f. Uncountable infinities
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10483
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Mathematics and science do not require very high orders of infinity [Boolos]
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6. Mathematics / C. Sources of Mathematics / 1. Mathematical Platonism / a. For mathematical platonism
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9863
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We aim for elevated discussion of pure numbers, not attaching them to physical objects [Plato]
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9864
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In pure numbers, all ones are equal, with no internal parts [Plato]
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8727
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Geometry is not an activity, but the study of unchanging knowledge [Plato]
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10490
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Mathematics isn't surprising, given that we experience many objects as abstract [Boolos]
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6. Mathematics / C. Sources of Mathematics / 4. Mathematical Empiricism / c. Against mathematical empiricism
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9861
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The same thing is both one and an unlimited number at the same time [Plato]
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