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Ideas for 'Metaphysics: the logical approach', 'Review of Frege's 'Grundlagen'' and 'The Question of Ontology'

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7 ideas

6. Mathematics / A. Nature of Mathematics / 2. Geometry

3332	Greeks saw the science of proportion as the link between geometry and arithmetic [Benardete,JA]

6. Mathematics / A. Nature of Mathematics / 3. Nature of Numbers / b. Types of number

3330	Negatives, rationals, irrationals and imaginaries are all postulated to solve baffling equations [Benardete,JA]

3337	Natural numbers are seen in terms of either their ordinality (Peano), or cardinality (set theory) [Benardete,JA]

6. Mathematics / B. Foundations for Mathematics / 5. Definitions of Number / c. Fregean numbers

9992	The 'extension of a concept' in general may be quantitatively completely indeterminate [Cantor]

12215

The existence of numbers is not a matter of identities, but of constituents of the world [Fine,K]

6. Mathematics / C. Sources of Mathematics / 1. Mathematical Platonism / b. Against mathematical platonism

12211

It is plausible that x^2 = -1 had no solutions before complex numbers were 'introduced' [Fine,K]

6. Mathematics / C. Sources of Mathematics / 4. Mathematical Empiricism / a. Mathematical empiricism

12209

The indispensability argument shows that nature is non-numerical, not the denial of numbers [Fine,K]