Combining Texts
Ideas for
'On the Question of Absolute Undecidability', 'Mathematical Thought from Ancient to Modern Times' and 'A Subject with No Object'
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6 ideas
6. Mathematics / A. Nature of Mathematics / 3. Nature of Numbers / a. Numbers
9923
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We should talk about possible existence, rather than actual existence, of numbers [Burgess/Rosen]
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6. Mathematics / A. Nature of Mathematics / 5. The Infinite / i. Cardinal infinity
17890
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There are at least eleven types of large cardinal, of increasing logical strength [Koellner]
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6. Mathematics / B. Foundations for Mathematics / 4. Axioms for Number / d. Peano arithmetic
17887
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PA is consistent as far as we can accept, and we expand axioms to overcome limitations [Koellner]
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6. Mathematics / B. Foundations for Mathematics / 4. Axioms for Number / g. Incompleteness of Arithmetic
17891
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Arithmetical undecidability is always settled at the next stage up [Koellner]
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6. Mathematics / B. Foundations for Mathematics / 7. Mathematical Structuralism / c. Nominalist structuralism
9925
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Structuralism and nominalism are normally rivals, but might work together [Burgess/Rosen]
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6. Mathematics / C. Sources of Mathematics / 1. Mathematical Platonism / b. Against mathematical platonism
9934
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Number words became nouns around the time of Plato [Burgess/Rosen]
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