Combining Texts
Ideas for
'On What Grounds What', 'Review of Chihara 'Struct. Accnt of Maths'' and 'The Theory of Logical Types'
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10 ideas
6. Mathematics / B. Foundations for Mathematics / 6. Mathematics as Set Theory / a. Mathematics is set theory
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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
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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
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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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6. Mathematics / C. Sources of Mathematics / 1. Mathematical Platonism / a. For mathematical platonism
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13741
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If 'there are red roses' implies 'there are roses', then 'there are prime numbers' implies 'there are numbers' [Schaffer,J]
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6. Mathematics / C. Sources of Mathematics / 6. Logicism / b. Type theory
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23457
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Type theory cannot identify features across levels (because such predicates break the rules) [Morris,M on Russell]
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21556
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Classes are defined by propositional functions, and functions are typed, with an axiom of reducibility [Russell, by Lackey]
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6. Mathematics / C. Sources of Mathematics / 10. Constructivism / d. Predicativism
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21568
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A one-variable function is only 'predicative' if it is one order above its arguments [Russell]
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