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Ideas for 'Plural Quantification', 'Philosophy of Mathematics' and 'Number Determiners, Numbers, Arithmetic'

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11 ideas

6. Mathematics / A. Nature of Mathematics / 3. Nature of Numbers / a. Numbers
9998 What is the relation of number words as singular-terms, adjectives/determiners, and symbols? [Hofweber]
10002 '2 + 2 = 4' can be read as either singular or plural [Hofweber]
6. Mathematics / B. Foundations for Mathematics / 4. Axioms for Number / g. Incompleteness of Arithmetic
23446 You can't prove consistency using a weaker theory, but you can use a consistent theory [Linnebo]
6. Mathematics / B. Foundations for Mathematics / 7. Mathematical Structuralism / a. Structuralism
23448 Mathematics is the study of all possible patterns, and is thus bound to describe the world [Linnebo]
6. Mathematics / C. Sources of Mathematics / 1. Mathematical Platonism / a. For mathematical platonism
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]
6. Mathematics / C. Sources of Mathematics / 5. Numbers as Adjectival
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]
23441 Logical truth is true in all models, so mathematical objects can't be purely logical [Linnebo]
6. Mathematics / C. Sources of Mathematics / 7. Formalism
23442 Game Formalism has no semantics, and Term Formalism reduces the semantics [Linnebo]