Combining Philosophers
Ideas for B Hale / C Wright, Peter Lipton and Thomas Hofweber
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23 ideas
6. Mathematics / A. Nature of Mathematics / 3. Nature of Numbers / a. Numbers
21644
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Numbers are used as singular terms, as adjectives, and as symbols [Hofweber]
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9998
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What is the relation of number words as singular-terms, adjectives/determiners, and symbols? [Hofweber]
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10002
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'2 + 2 = 4' can be read as either singular or plural [Hofweber]
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21646
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The Amazonian Piraha language is said to have no number words [Hofweber]
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6. Mathematics / A. Nature of Mathematics / 4. Using Numbers / f. Arithmetic
21665
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The fundamental theorem of arithmetic is that all numbers are composed uniquely of primes [Hofweber]
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6. Mathematics / A. Nature of Mathematics / 4. Using Numbers / g. Applying mathematics
21649
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How can words be used for counting if they are objects? [Hofweber]
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6. Mathematics / B. Foundations for Mathematics / 4. Axioms for Number / g. Incompleteness of Arithmetic
10624
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The incompletability of formal arithmetic reveals that logic also cannot be completely characterized [Hale/Wright]
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6. Mathematics / B. Foundations for Mathematics / 5. Definitions of Number / d. Hume's Principle
8784
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Neo-logicism founds arithmetic on Hume's Principle along with second-order logic [Hale/Wright]
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6. Mathematics / B. Foundations for Mathematics / 5. Definitions of Number / e. Caesar problem
8787
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The Julius Caesar problem asks for a criterion for the concept of a 'number' [Hale/Wright]
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6. Mathematics / B. Foundations for Mathematics / 7. Mathematical Structuralism / e. Structuralism critique
10629
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If structures are relative, this undermines truth-value and objectivity [Hale/Wright]
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10628
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The structural view of numbers doesn't fit their usage outside arithmetical contexts [Hale/Wright]
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6. Mathematics / C. Sources of Mathematics / 1. Mathematical Platonism / a. For mathematical platonism
10003
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Why is arithmetic hard to learn, but then becomes easy? [Hofweber]
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6. Mathematics / C. Sources of Mathematics / 1. Mathematical Platonism / b. Against mathematical platonism
10008
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Arithmetic is not about a domain of entities, as the quantifiers are purely inferential [Hofweber]
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6. Mathematics / C. Sources of Mathematics / 4. Mathematical Empiricism / c. Against mathematical empiricism
10005
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Arithmetic doesn’t simply depend on objects, since it is true of fictional objects [Hofweber]
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6. Mathematics / C. Sources of Mathematics / 5. Numbers as Adjectival
10000
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We might eliminate adjectival numbers by analysing them into blocks of quantifiers [Hofweber]
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6. Mathematics / C. Sources of Mathematics / 6. Logicism / a. Early logicism
8788
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Logicism is only noteworthy if logic has a privileged position in our ontology and epistemology [Hale/Wright]
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21647
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Logicism makes sense of our ability to know arithmetic just by thought [Hofweber]
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6. Mathematics / C. Sources of Mathematics / 6. Logicism / c. Neo-logicism
10622
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The neo-Fregean is more optimistic than Frege about contextual definitions of numbers [Hale/Wright]
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8783
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Logicism might also be revived with a quantificational approach, or an abstraction-free approach [Hale/Wright]
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12225
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Neo-Fregeanism might be better with truth-makers, rather than quantifier commitment [Hale/Wright]
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21648
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Neo-Fregeans are dazzled by a technical result, and ignore practicalities [Hofweber]
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6. Mathematics / C. Sources of Mathematics / 6. Logicism / d. Logicism critique
12224
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Are neo-Fregeans 'maximalists' - that everything which can exist does exist? [Hale/Wright]
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10006
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First-order logic captures the inferential relations of numbers, but not the semantics [Hofweber]
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