Ideas from 'Number Determiners, Numbers, Arithmetic' by Thomas Hofweber [2005], by Theme Structure

[found in 'Philosophical Review 114' (ed/tr -) [Phil Review 2005,]].

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5. Theory of Logic / F. Referring in Logic / 1. Naming / d. Singular terms
An adjective contributes semantically to a noun phrase
5. Theory of Logic / G. Quantification / 2. Domain of Quantification
Quantifiers for domains and for inference come apart if there are no entities
6. Mathematics / A. Nature of Mathematics / 3. Numbers / a. Numbers
'2 + 2 = 4' can be read as either singular or plural
What is the relation of number words as singular-terms, adjectives/determiners, and symbols?
6. Mathematics / C. Sources of Mathematics / 1. Mathematical Platonism / a. For mathematical platonism
Why is arithmetic hard to learn, but then becomes easy?
6. Mathematics / C. Sources of Mathematics / 1. Mathematical Platonism / b. Against mathematical platonism
Arithmetic is not about a domain of entities, as the quantifiers are purely inferential
6. Mathematics / C. Sources of Mathematics / 4. Mathematical Empiricism / c. Against mathematical empiricism
Arithmetic doesn’t simply depend on objects, since it is true of fictional objects
6. Mathematics / C. Sources of Mathematics / 5. Numbers as Adjectival
We might eliminate adjectival numbers by analysing them into blocks of quantifiers
6. Mathematics / C. Sources of Mathematics / 6. Logicism / d. Logicism critique
First-order logic captures the inferential relations of numbers, but not the semantics
15. Nature of Minds / C. Capacities of Minds / 4. Objectification
Our minds are at their best when reasoning about objects