Combining Texts

All the ideas for 'Leibniz', 'Rechnungsmethoden (dissertation)' and 'Mathematics without Numbers'

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6 ideas

6. Mathematics / A. Nature of Mathematics / 3. Nature of Numbers / c. Priority of numbers
Quantity is inconceivable without the idea of addition [Frege]
6. Mathematics / B. Foundations for Mathematics / 7. Mathematical Structuralism / c. Nominalist structuralism
Modal structuralism says mathematics studies possible structures, which may or may not be actualised [Hellman, by Friend]
Statements of pure mathematics are elliptical for a sort of modal conditional [Hellman, by Chihara]
Modal structuralism can only judge possibility by 'possible' models [Shapiro on Hellman]
6. Mathematics / C. Sources of Mathematics / 2. Intuition of Mathematics
Geometry appeals to intuition as the source of its axioms [Frege]
9. Objects / F. Identity among Objects / 7. Indiscernible Objects
The Identity of Indiscernibles is really the same as the verification principle [Jolley]