Combining Texts

All the ideas for 'The Architecture of Mathematics', 'Modal Realism at Work: Properties' and 'Letters to Russell'

expand these ideas     |    start again     |     specify just one area for these texts

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5 ideas

6. Mathematics / A. Nature of Mathematics / 3. Nature of Numbers / g. Real numbers

18253

I wish to go straight from cardinals to reals (as ratios), leaving out the rationals [Frege]

6. Mathematics / B. Foundations for Mathematics / 7. Mathematical Structuralism / a. Structuralism

10190

From the axiomatic point of view, mathematics is a storehouse of abstract structures [Bourbaki]

6. Mathematics / C. Sources of Mathematics / 6. Logicism / a. Early logicism

18166

The loss of my Rule V seems to make foundations for arithmetic impossible [Frege]

8. Modes of Existence / B. Properties / 11. Properties as Sets

4038	Properties are sets of their possible instances (which separates 'renate' from 'cordate') [Lewis, by Mellor/Oliver]

9. Objects / A. Existence of Objects / 2. Abstract Objects / c. Modern abstracta

18269

Logical objects are extensions of concepts, or ranges of values of functions [Frege]