Combining Texts
Ideas for
'Defending the Axioms', 'Thinking About Logic' and 'Brainstorms:Essays on Mind and Psychology'
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7 ideas
6. Mathematics / A. Nature of Mathematics / 5. The Infinite / d. Actual infinite
11025
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Infinite cuts and successors seems to suggest an actual infinity there waiting for us [Read]
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6. Mathematics / A. Nature of Mathematics / 5. The Infinite / g. Continuum Hypothesis
17615
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Every infinite set of reals is either countable or of the same size as the full set of reals [Maddy]
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6. Mathematics / B. Foundations for Mathematics / 4. Axioms for Number / e. Peano arithmetic 2nd-order
10979
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Although second-order arithmetic is incomplete, it can fully model normal arithmetic [Read]
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10980
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Second-order arithmetic covers all properties, ensuring categoricity [Read]
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6. Mathematics / B. Foundations for Mathematics / 5. Definitions of Number / g. Von Neumann numbers
10997
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Von Neumann numbers are helpful, but don't correctly describe numbers [Read]
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6. Mathematics / B. Foundations for Mathematics / 6. Mathematics as Set Theory / a. Mathematics is set theory
17618
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Set-theory tracks the contours of mathematical depth and fruitfulness [Maddy]
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6. Mathematics / C. Sources of Mathematics / 4. Mathematical Empiricism / c. Against mathematical empiricism
17614
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The connection of arithmetic to perception has been idealised away in modern infinitary mathematics [Maddy]
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