Combining Texts

All the ideas for 'Hobbes', 'Number Determiners, Numbers, Arithmetic' and 'On boundary numbers and domains of sets'

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14 ideas

4. Formal Logic / F. Set Theory ST / 4. Axioms for Sets / a. Axioms for sets
17832 Zermelo showed that the ZF axioms in 1930 were non-categorical [Zermelo, by Hallett,M]
4. Formal Logic / F. Set Theory ST / 4. Axioms for Sets / h. Axiom of Replacement VII
13028 Replacement was added when some advanced theorems seemed to need it [Zermelo, by Maddy]
5. Theory of Logic / F. Referring in Logic / 1. Naming / d. Singular terms
10001 An adjective contributes semantically to a noun phrase [Hofweber]
5. Theory of Logic / G. Quantification / 2. Domain of Quantification
10007 Quantifiers for domains and for inference come apart if there are no entities [Hofweber]
5. Theory of Logic / L. Paradox / 3. Antinomies
17626 The antinomy of endless advance and of completion is resolved in well-ordered transfinite numbers [Zermelo]
6. Mathematics / A. Nature of Mathematics / 3. Nature of Numbers / a. Numbers
10002 '2 + 2 = 4' can be read as either singular or plural [Hofweber]
9998 What is the relation of number words as singular-terms, adjectives/determiners, and symbols? [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 / d. Logicism critique
10006 First-order logic captures the inferential relations of numbers, but not the semantics [Hofweber]
13. Knowledge Criteria / D. Scepticism / 1. Scepticism
7413 Without confidence in our beliefs, how should we actually live? [Tuck]
15. Nature of Minds / C. Capacities of Minds / 4. Objectification
10004 Our minds are at their best when reasoning about objects [Hofweber]