Combining Philosophers
Ideas for Novalis, Harold Hodes and Kit Fine
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18 ideas
6. Mathematics / A. Nature of Mathematics / 3. Nature of Numbers / a. Numbers
10027
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Mathematics is higher-order modal logic [Hodes]
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6. Mathematics / A. Nature of Mathematics / 3. Nature of Numbers / b. Types of number
10573
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Dedekind cuts lead to the bizarre idea that there are many different number 1's [Fine,K]
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6. Mathematics / A. Nature of Mathematics / 3. Nature of Numbers / i. Reals from cuts
10575
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Why should a Dedekind cut correspond to a number? [Fine,K]
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6. Mathematics / A. Nature of Mathematics / 3. Nature of Numbers / l. Zero
10574
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Unless we know whether 0 is identical with the null set, we create confusions [Fine,K]
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6. Mathematics / A. Nature of Mathematics / 4. Using Numbers / c. Counting procedure
19584
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Whoever first counted to two must have seen the possibility of infinite counting [Novalis]
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6. Mathematics / A. Nature of Mathematics / 4. Using Numbers / f. Arithmetic
10026
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Arithmetic must allow for the possibility of only a finite total of objects [Hodes]
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6. Mathematics / B. Foundations for Mathematics / 5. Definitions of Number / c. Fregean numbers
12215
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The existence of numbers is not a matter of identities, but of constituents of the world [Fine,K]
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6. Mathematics / B. Foundations for Mathematics / 5. Definitions of Number / d. Hume's Principle
10529
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If Hume's Principle can define numbers, we needn't worry about its truth [Fine,K]
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10530
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Hume's Principle is either adequate for number but fails to define properly, or vice versa [Fine,K]
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6. Mathematics / B. Foundations for Mathematics / 6. Mathematics as Set Theory / b. Mathematics is not set theory
10560
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Set-theoretic imperialists think sets can represent every mathematical object [Fine,K]
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6. Mathematics / C. Sources of Mathematics / 1. Mathematical Platonism / a. For mathematical platonism
10021
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It is claimed that numbers are objects which essentially represent cardinality quantifiers [Hodes]
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10022
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Numerical terms can't really stand for quantifiers, because that would make them first-level [Hodes]
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6. Mathematics / C. Sources of Mathematics / 1. Mathematical Platonism / b. Against mathematical platonism
12211
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It is plausible that x^2 = -1 had no solutions before complex numbers were 'introduced' [Fine,K]
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6. Mathematics / C. Sources of Mathematics / 4. Mathematical Empiricism / a. Mathematical empiricism
12209
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The indispensability argument shows that nature is non-numerical, not the denial of numbers [Fine,K]
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6. Mathematics / C. Sources of Mathematics / 6. Logicism / a. Early logicism
10568
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Logicists say mathematics can be derived from definitions, and can be known that way [Fine,K]
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6. Mathematics / C. Sources of Mathematics / 6. Logicism / c. Neo-logicism
9224
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Proceduralism offers a version of logicism with no axioms, or objects, or ontological commitment [Fine,K]
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6. Mathematics / C. Sources of Mathematics / 10. Constructivism / a. Constructivism
9222
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The objects and truths of mathematics are imperative procedures for their construction [Fine,K]
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9223
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My Proceduralism has one simple rule, and four complex rules [Fine,K]
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