Combining Texts
Ideas for
'On the Question of Absolute Undecidability', 'Guidebook to Wittgenstein's Tractatus' and 'Varieties of Meaning'
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6 ideas
6. Mathematics / A. Nature of Mathematics / 4. Using Numbers / c. Counting procedure
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23451
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Counting needs to distinguish things, and also needs the concept of a successor in a series [Morris,M]
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23460
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To count, we must distinguish things, and have a series with successors in it [Morris,M]
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23452
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Discriminating things for counting implies concepts of identity and distinctness [Morris,M]
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6. Mathematics / A. Nature of Mathematics / 5. The Infinite / i. Cardinal infinity
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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
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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
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17891
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Arithmetical undecidability is always settled at the next stage up [Koellner]
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