Combining Texts
Ideas for
'Physics', 'Constructibility and Mathematical Existence' and 'Every Thing Must Go'
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10 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 / g. Real numbers
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
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
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
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 / C. Sources of Mathematics / 4. Mathematical Empiricism / a. Mathematical empiricism
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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6. Mathematics / C. Sources of Mathematics / 6. Logicism / b. Type theory
10265
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Chihara's system is a variant of type theory, from which he can translate sentences [Chihara, by Shapiro]
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8759
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We can replace type theory with open sentences and a constructibility quantifier [Chihara, by Shapiro]
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6. Mathematics / C. Sources of Mathematics / 10. Constructivism / a. Constructivism
10264
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Introduce a constructibility quantifiers (Cx)Φ - 'it is possible to construct an x such that Φ' [Chihara, by Shapiro]
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