Combining Texts

Ideas for 'Mathematics without Numbers', 'The Question of Ontology' and 'Merely Possible Propositions'

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6 ideas

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

12215

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

6. Mathematics / B. Foundations for Mathematics / 7. Mathematical Structuralism / c. Nominalist structuralism

8698	Modal structuralism says mathematics studies possible structures, which may or may not be actualised [Hellman, by Friend]

9557	Statements of pure mathematics are elliptical for a sort of modal conditional [Hellman, by Chihara]

10263

Modal structuralism can only judge possibility by 'possible' models [Shapiro on Hellman]

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]