Combining Texts
Ideas for
'Defending the Axioms', 'The Republic' and 'Review of Parsons (1983)'
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9 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 / g. Continuum Hypothesis
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17615
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Every infinite set of reals is either countable or of the same size as the full set of reals [Maddy]
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6. Mathematics / B. Foundations for Mathematics / 6. Mathematics as Set Theory / a. Mathematics is set theory
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17618
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Set-theory tracks the contours of mathematical depth and fruitfulness [Maddy]
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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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6. Mathematics / C. Sources of Mathematics / 4. Mathematical Empiricism / b. Indispensability of mathematics
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18198
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Mathematics is part of science; transfinite mathematics I take as mostly uninterpreted [Quine]
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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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17614
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The connection of arithmetic to perception has been idealised away in modern infinitary mathematics [Maddy]
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