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Ideas for 'Logical Pluralism', 'Number Determiners, Numbers, Arithmetic' and 'Philosophy of Mathematics'

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14 ideas

6. Mathematics / C. Sources of Mathematics / 1. Mathematical Platonism / a. For mathematical platonism
9606 The irrationality of root-2 was achieved by intellect, not experience [Brown,JR]
10003 Why is arithmetic hard to learn, but then becomes easy? [Hofweber]
6. Mathematics / C. Sources of Mathematics / 1. Mathematical Platonism / b. Against mathematical platonism
10008 Arithmetic is not about a domain of entities, as the quantifiers are purely inferential [Hofweber]
6. Mathematics / C. Sources of Mathematics / 4. Mathematical Empiricism / c. Against mathematical empiricism
10005 Arithmetic doesn’t simply depend on objects, since it is true of fictional objects [Hofweber]
9612 There is an infinity of mathematical objects, so they can't be physical [Brown,JR]
9610 Numbers are not abstracted from particulars, because each number is a particular [Brown,JR]
6. Mathematics / C. Sources of Mathematics / 5. Numbers as Adjectival
9620 Empiricists base numbers on objects, Platonists base them on properties [Brown,JR]
10000 We might eliminate adjectival numbers by analysing them into blocks of quantifiers [Hofweber]
6. Mathematics / C. Sources of Mathematics / 6. Logicism / d. Logicism critique
10006 First-order logic captures the inferential relations of numbers, but not the semantics [Hofweber]
6. Mathematics / C. Sources of Mathematics / 7. Formalism
9630 The most brilliant formalist was Hilbert [Brown,JR]
9629 For nomalists there are no numbers, only numerals [Brown,JR]
9639 Does some mathematics depend entirely on notation? [Brown,JR]
6. Mathematics / C. Sources of Mathematics / 10. Constructivism / a. Constructivism
9608 There are no constructions for many highly desirable results in mathematics [Brown,JR]
9645 Constructivists say p has no value, if the value depends on Goldbach's Conjecture [Brown,JR]