Combining Texts
Ideas for
'In Defense of Essentialism', 'Individuals without Sortals' and 'What Numbers Could Not Be'
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11 ideas
6. Mathematics / A. Nature of Mathematics / 3. Nature of Numbers / a. Numbers
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9912
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There are no such things as numbers [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
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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
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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
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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 / d. Counting via concepts
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17518
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Counting 'coin in this box' may have coin as the unit, with 'in this box' merely as the scope [Ayers]
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17516
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If counting needs a sortal, what of things which fall under two sortals? [Ayers]
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6. Mathematics / A. Nature of Mathematics / 4. Using Numbers / g. Applying mathematics
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9897
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The application of a system of numbers is counting and measurement [Benacerraf]
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