Combining Philosophers
Ideas for Wilhelm Dilthey, Edwin D. Mares and Tyler Burge
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6 ideas
6. Mathematics / A. Nature of Mathematics / 2. Geometry
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16901
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The equivalent algebra model of geometry loses some essential spatial meaning [Burge]
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9159
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You can't simply convert geometry into algebra, as some spatial content is lost [Burge]
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6. Mathematics / B. Foundations for Mathematics / 4. Axioms for Number / a. Axioms for numbers
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17715
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The truth of the axioms doesn't matter for pure mathematics, but it does for applied [Mares]
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6. Mathematics / B. Foundations for Mathematics / 4. Axioms for Number / d. Peano arithmetic
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16902
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Peano arithmetic requires grasping 0 as a primitive number [Burge]
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6. Mathematics / C. Sources of Mathematics / 4. Mathematical Empiricism / a. Mathematical empiricism
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17716
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Mathematics is relations between properties we abstract from experience [Mares]
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6. Mathematics / C. Sources of Mathematics / 10. Constructivism / b. Intuitionism
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18788
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For intuitionists there are not numbers and sets, but processes of counting and collecting [Mares]
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