Combining Philosophers
Ideas for David Fair, Paul Benacerraf and Douglas Edwards
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13 ideas
6. Mathematics / A. Nature of Mathematics / 1. Mathematics
9935
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Mathematical truth is always compromising between ordinary language and sensible epistemology [Benacerraf]
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6. Mathematics / A. Nature of Mathematics / 3. Nature of Numbers / a. Numbers
9912
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There are no such things as numbers [Benacerraf]
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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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9901
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Numbers can't be sets if there is no agreement on which sets they are [Benacerraf]
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6. Mathematics / A. Nature of Mathematics / 3. Nature of Numbers / c. Priority of numbers
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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9151
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Benacerraf says numbers are defined by their natural ordering [Benacerraf, by Fine,K]
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6. Mathematics / A. Nature of Mathematics / 3. Nature of Numbers / f. Cardinal numbers
13891
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To understand finite cardinals, it is necessary and sufficient to understand progressions [Benacerraf, by Wright,C]
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17904
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A set has k members if it one-one corresponds with the numbers less than or equal to k [Benacerraf]
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17906
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To explain numbers you must also explain cardinality, the counting of things [Benacerraf]
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6. Mathematics / A. Nature of Mathematics / 4. Using Numbers / c. Counting procedure
9898
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We can count intransitively (reciting numbers) without understanding transitive counting of items [Benacerraf]
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17903
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Someone can recite numbers but not know how to count things; but not vice versa [Benacerraf]
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6. Mathematics / A. Nature of Mathematics / 4. Using Numbers / g. Applying mathematics
9897
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The application of a system of numbers is counting and measurement [Benacerraf]
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