Combining Texts
Ideas for
'Thinking About Mathematics', 'New Essays on Human Understanding' and 'Logicism, Some Considerations (PhD)'
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7 ideas
6. Mathematics / A. Nature of Mathematics / 2. Geometry
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13008
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Geometry, unlike sensation, lets us glimpse eternal truths and their necessity [Leibniz]
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6. Mathematics / A. Nature of Mathematics / 3. Nature of Numbers / a. Numbers
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13412
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Obtaining numbers by abstraction is impossible - there are too many; only a rule could give them, in order [Benacerraf]
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13413
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We must explain how we know so many numbers, and recognise ones we haven't met before [Benacerraf]
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6. Mathematics / A. Nature of Mathematics / 3. Nature of Numbers / b. Types of number
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8763
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The number 3 is presumably identical as a natural, an integer, a rational, a real, and complex [Shapiro]
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6. Mathematics / A. Nature of Mathematics / 3. Nature of Numbers / c. Priority of numbers
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13411
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If numbers are basically the cardinals (Frege-Russell view) you could know some numbers in isolation [Benacerraf]
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6. Mathematics / A. Nature of Mathematics / 3. Nature of Numbers / h. Reals from Cauchy
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18249
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Cauchy gave a formal definition of a converging sequence. [Shapiro]
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6. Mathematics / A. Nature of Mathematics / 4. Using Numbers / a. Units
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12956
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Only whole numbers are multitudes of units [Leibniz]
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