Combining Philosophers
Ideas for Edmund Husserl, Oswald Spengler and John P. Burgess
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10 ideas
6. Mathematics / A. Nature of Mathematics / 3. Nature of Numbers / l. Zero
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
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
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 / B. Foundations for Mathematics / 1. Foundations for Mathematics
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 / 6. Mathematics as Set Theory / a. Mathematics is set theory
10185
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Set theory is the standard background for modern mathematics [Burgess]
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6. Mathematics / B. Foundations for Mathematics / 7. Mathematical Structuralism / a. Structuralism
10184
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Structuralists take the name 'R' of the reals to be a variable ranging over structures, not a structure [Burgess]
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10189
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There is no one relation for the real number 2, as relations differ in different models [Burgess]
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6. Mathematics / B. Foundations for Mathematics / 7. Mathematical Structuralism / e. Structuralism critique
10186
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If set theory is used to define 'structure', we can't define set theory structurally [Burgess]
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10187
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Abstract algebra concerns relations between models, not common features of all the models [Burgess]
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10188
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How can mathematical relations be either internal, or external, or intrinsic? [Burgess]
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