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

10001

An adjective contributes semantically to a noun phrase

5. Theory of Logic / G. Quantification / 2. Domain of Quantification

10007

Quantifiers for domains and for inference come apart if there are no entities

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?

10002

'2 + 2 = 4' can be read as either singular or plural

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

10003

Why is arithmetic hard to learn, but then becomes easy?

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

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

6. Mathematics / C. Sources of Mathematics / 5. Numbers as Adjectival

10000

We might eliminate adjectival numbers by analysing them into blocks of quantifiers

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

15. Nature of Minds / C. Capacities of Minds / 4. Objectification

10004

Our minds are at their best when reasoning about objects