Combining Philosophers

Ideas for Eubulides, Ruth Barcan Marcus 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 singular-terms, 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. Neo-logicism
21648 Neo-Fregeans are dazzled by a technical result, and ignore practicalities [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]