Combining Philosophers
Ideas for Michael Burke, Rayo,A/Uzquiasno,G and Thomas Hofweber
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13 ideas
6. Mathematics / A. Nature of Mathematics / 3. Nature of Numbers / a. Numbers
9998

What is the relation of number words as singularterms, adjectives/determiners, and symbols? [Hofweber]

10002

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

21644

Numbers are used as singular terms, as adjectives, and as symbols [Hofweber]

21646

The Amazonian Piraha language is said to have no number words [Hofweber]

6. Mathematics / A. Nature of Mathematics / 4. Using Numbers / f. Arithmetic
21665

The fundamental theorem of arithmetic is that all numbers are composed uniquely of primes [Hofweber]

6. Mathematics / A. Nature of Mathematics / 4. Using Numbers / g. Applying mathematics
21649

How can words be used for counting if they are objects? [Hofweber]

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 / a. Early logicism
21647

Logicism makes sense of our ability to know arithmetic just by thought [Hofweber]

6. Mathematics / C. Sources of Mathematics / 6. Logicism / c. Neologicism
21648

NeoFregeans are dazzled by a technical result, and ignore practicalities [Hofweber]

6. Mathematics / C. Sources of Mathematics / 6. Logicism / d. Logicism critique
10006

Firstorder logic captures the inferential relations of numbers, but not the semantics [Hofweber]
