Combining Philosophers
Ideas for Friedrich Schlegel, Benedetto Croce and Ernst Zermelo
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5 ideas
6. Mathematics / A. Nature of Mathematics / 3. Nature of Numbers / e. Ordinal numbers
13487

In ZF, the BuraliForti Paradox proves that there is no set of all ordinals [Zermelo, by Hart,WD]

6. Mathematics / A. Nature of Mathematics / 5. The Infinite / e. Countable infinity
15897

Zermelo realised that Choice would facilitate the sort of 'counting' Cantor needed [Zermelo, by Lavine]

6. Mathematics / B. Foundations for Mathematics / 5. Definitions of Number / f. Zermelo numbers
18178

For Zermelo the successor of n is {n} (rather than n U {n}) [Zermelo, by Maddy]

6. Mathematics / B. Foundations for Mathematics / 6. Mathematics as Set Theory / a. Mathematics is set theory
13027

Zermelo believed, and Von Neumann seemed to confirm, that numbers are sets [Zermelo, by Maddy]

6. Mathematics / B. Foundations for Mathematics / 7. Mathematical Structuralism / e. Structuralism critique
9627

Different versions of set theory result in different underlying structures for numbers [Zermelo, by Brown,JR]
