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Ideas for 'Logicism and Ontological Commits. of Arithmetic', 'The Folly of Trying to Define Truth' and 'Number Determiners, Numbers, Arithmetic'

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7 ideas

6. Mathematics / C. Sources of Mathematics / 1. Mathematical Platonism / a. For mathematical platonism

10021

It is claimed that numbers are objects which essentially represent cardinality quantifiers [Hodes]

10022

Numerical terms can't really stand for quantifiers, because that would make them first-level [Hodes]

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]