Combining Philosophers
Ideas for B Hale / C Wright, Aristotle and J.H. Fetzer
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10 ideas
6. Mathematics / B. Foundations for Mathematics / 4. Axioms for Number / g. Incompleteness of Arithmetic
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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 / b. Greek arithmetic
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11041
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Some quantities are discrete, like number, and others continuous, like lines, time and space [Aristotle]
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17851
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Number is plurality measured by unity [Aristotle]
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17843
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The idea of 'one' is the foundation of number [Aristotle]
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17850
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Each many is just ones, and is measured by the one [Aristotle]
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6. Mathematics / B. Foundations for Mathematics / 5. Definitions of Number / d. Hume's Principle
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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
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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 / 7. Mathematical Structuralism / a. Structuralism
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9793
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Mathematics studies abstracted relations, commensurability and proportion [Aristotle]
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6. Mathematics / B. Foundations for Mathematics / 7. Mathematical Structuralism / e. Structuralism critique
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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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