Combining Philosophers
Ideas for B Hale / C Wright, Nicholas P. White and Michle Friend
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13 ideas
6. Mathematics / B. Foundations for Mathematics / 1. Foundations for Mathematics
8676
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Is mathematics based on sets, types, categories, models or topology? [Friend]
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6. Mathematics / B. Foundations for Mathematics / 4. Axioms for Number / g. Incompleteness of Arithmetic
10624
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The incompletability of formal arithmetic reveals that logic also cannot be completely characterized [Hale/Wright]
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6. Mathematics / B. Foundations for Mathematics / 5. Definitions of Number / d. Hume's Principle
8784
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Neo-logicism founds arithmetic on Hume's Principle along with second-order logic [Hale/Wright]
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6. Mathematics / B. Foundations for Mathematics / 5. Definitions of Number / e. Caesar problem
8787
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The Julius Caesar problem asks for a criterion for the concept of a 'number' [Hale/Wright]
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6. Mathematics / B. Foundations for Mathematics / 6. Mathematics as Set Theory / a. Mathematics is set theory
8678
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Most mathematical theories can be translated into the language of set theory [Friend]
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6. Mathematics / B. Foundations for Mathematics / 7. Mathematical Structuralism / a. Structuralism
8701
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The number 8 in isolation from the other numbers is of no interest [Friend]
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8702
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In structuralism the number 8 is not quite the same in different structures, only equivalent [Friend]
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6. Mathematics / B. Foundations for Mathematics / 7. Mathematical Structuralism / b. Varieties of structuralism
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Are structures 'ante rem' (before reality), or are they 'in re' (grounded in physics)? [Friend]
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6. Mathematics / B. Foundations for Mathematics / 7. Mathematical Structuralism / c. Nominalist structuralism
8696
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Structuralist says maths concerns concepts about base objects, not base objects themselves [Friend]
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8695
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Structuralism focuses on relations, predicates and functions, with objects being inessential [Friend]
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6. Mathematics / B. Foundations for Mathematics / 7. Mathematical Structuralism / d. Platonist structuralism
8700
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'In re' structuralism says that the process of abstraction is pattern-spotting [Friend]
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6. Mathematics / B. Foundations for Mathematics / 7. Mathematical Structuralism / e. Structuralism critique
10629
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If structures are relative, this undermines truth-value and objectivity [Hale/Wright]
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10628
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The structural view of numbers doesn't fit their usage outside arithmetical contexts [Hale/Wright]
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