Combining Texts
Ideas for
'Actions', 'The Republic' and 'Elements of Intuitionism'
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7 ideas
6. Mathematics / A. Nature of Mathematics / 2. Geometry
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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 / c. Potential infinite
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Platonists ruin infinity, which is precisely a growing structure which is never completed [Dummett]
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6. Mathematics / C. Sources of Mathematics / 1. Mathematical Platonism / a. For mathematical platonism
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We aim for elevated discussion of pure numbers, not attaching them to physical objects [Plato]
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In pure numbers, all ones are equal, with no internal parts [Plato]
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Geometry is not an activity, but the study of unchanging knowledge [Plato]
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6. Mathematics / C. Sources of Mathematics / 4. Mathematical Empiricism / c. Against mathematical empiricism
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The same thing is both one and an unlimited number at the same time [Plato]
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6. Mathematics / C. Sources of Mathematics / 10. Constructivism / a. Constructivism
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For intuitionists it is constructed proofs (which take time) which make statements true [Dummett]
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