Combining Texts
Ideas for
'The Evolution of Modern Metaphysics', 'On What There Is' and 'Review of Chihara 'Struct. Accnt of Maths''
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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 / 6. Logicism / d. Logicism critique
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1613
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Logicists cheerfully accept reference to bound variables and all sorts of abstract entities [Quine]
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6. Mathematics / C. Sources of Mathematics / 7. Formalism
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1616
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Formalism says maths is built of meaningless notations; these build into rules which have meaning [Quine]
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6. Mathematics / C. Sources of Mathematics / 10. Constructivism / b. Intuitionism
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1615
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Intuitionism says classes are invented, and abstract entities are constructed from specified ingredients [Quine]
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6. Mathematics / C. Sources of Mathematics / 10. Constructivism / c. Conceptualism
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1614
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Conceptualism holds that there are universals but they are mind-made [Quine]
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