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Ideas for 'Function and Concept', 'Completeness of Axioms of Logic' and 'Investigations in the Foundations of Set Theory I'

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5 ideas

6. Mathematics / A. Nature of Mathematics / 3. Nature of Numbers / e. Ordinal numbers

13487

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

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]

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

8487	Arithmetic is a development of logic, so arithmetical symbolism must expand into logical symbolism [Frege]