Combining Philosophers
Ideas for Edmund Husserl, Friedrich Engels and Ernst Zermelo
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9 ideas
6. Mathematics / A. Nature of Mathematics / 3. Nature of Numbers / e. Ordinal numbers
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13487
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In ZF, the Burali-Forti Paradox proves that there is no set of all ordinals [Zermelo, by Hart,WD]
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6. Mathematics / A. Nature of Mathematics / 3. Nature of Numbers / l. Zero
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9837
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0 is not a number, as it answers 'how many?' negatively [Husserl, by Dummett]
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6. Mathematics / A. Nature of Mathematics / 4. Using Numbers / a. Units
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9576
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Multiplicity in general is just one and one and one, etc. [Husserl]
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6. Mathematics / A. Nature of Mathematics / 4. Using Numbers / e. Counting by correlation
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17444
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Husserl said counting is more basic than Frege's one-one correspondence [Husserl, by Heck]
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6. Mathematics / A. Nature of Mathematics / 5. The Infinite / e. Countable infinity
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15897
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Zermelo realised that Choice would facilitate the sort of 'counting' Cantor needed [Zermelo, by Lavine]
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6. Mathematics / B. Foundations for Mathematics / 1. Foundations for Mathematics
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21224
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Pure mathematics is the relations between all possible objects, and is thus formal ontology [Husserl, by Velarde-Mayol]
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6. Mathematics / B. Foundations for Mathematics / 5. Definitions of Number / f. Zermelo numbers
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18178
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For Zermelo the successor of n is {n} (rather than n U {n}) [Zermelo, by Maddy]
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6. Mathematics / B. Foundations for Mathematics / 6. Mathematics as Set Theory / a. Mathematics is set theory
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13027
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Zermelo believed, and Von Neumann seemed to confirm, that numbers are sets [Zermelo, by Maddy]
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6. Mathematics / B. Foundations for Mathematics / 7. Mathematical Structuralism / e. Structuralism critique
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9627
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Different versions of set theory result in different underlying structures for numbers [Zermelo, by Brown,JR]
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