Combining Texts
Ideas for
'Frege's Concept of Numbers as Objects', 'Ideas: intro to pure phenomenology' and 'Physics'
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9 ideas
6. Mathematics / A. Nature of Mathematics / 2. Geometry
9790
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Geometry studies naturally occurring lines, but not as they occur in nature [Aristotle]
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6. Mathematics / A. Nature of Mathematics / 3. Nature of Numbers / a. Numbers
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Number theory aims at the essence of natural numbers, giving their nature, and the epistemology [Wright,C]
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6. Mathematics / A. Nature of Mathematics / 3. Nature of Numbers / c. Priority of numbers
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One could grasp numbers, and name sizes with them, without grasping ordering [Wright,C]
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6. Mathematics / A. Nature of Mathematics / 3. Nature of Numbers / g. Real numbers
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Two is the least number, but there is no least magnitude, because it is always divisible [Aristotle]
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6. Mathematics / A. Nature of Mathematics / 4. Using Numbers / d. Counting via concepts
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Instances of a non-sortal concept can only be counted relative to a sortal concept [Wright,C]
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6. Mathematics / A. Nature of Mathematics / 5. The Infinite / a. The Infinite
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Without infinity time has limits, magnitudes are indivisible, and numbers come to an end [Aristotle]
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6. Mathematics / A. Nature of Mathematics / 5. The Infinite / c. Potential infinite
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Aristotle's infinity is a property of the counting process, that it has no natural limit [Aristotle, by Le Poidevin]
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6. Mathematics / A. Nature of Mathematics / 5. The Infinite / j. Infinite divisibility
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Lengths do not contain infinite parts; parts are created by acts of division [Aristotle, by Le Poidevin]
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18833
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A continuous line cannot be composed of indivisible points [Aristotle]
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