Combining Texts
Ideas for
'Physics', 'Cours d'Analyse' and 'Toward a Philosophy of History'
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9 ideas
6. Mathematics / A. Nature of Mathematics / 2. Geometry
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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 / g. Real numbers
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22962
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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 / 5. The Infinite / a. The Infinite
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18090
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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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22929
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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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22930
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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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6. Mathematics / A. Nature of Mathematics / 5. The Infinite / k. Infinitesimals
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18085
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Values that approach zero, becoming less than any quantity, are 'infinitesimals' [Cauchy]
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6. Mathematics / A. Nature of Mathematics / 5. The Infinite / l. Limits
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18084
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When successive variable values approach a fixed value, that is its 'limit' [Cauchy]
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6. Mathematics / C. Sources of Mathematics / 4. Mathematical Empiricism / a. Mathematical empiricism
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9974
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Ten sheep and ten dogs are the same numerically, but it is not the same ten [Aristotle]
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