Combining Texts
Ideas for
'On the Question of Absolute Undecidability', 'Tractatus Logico-Philosophicus' and 'In Defense of Essentialism'
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8 ideas
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 / 5. Definitions of Number / a. Defining numbers
18153
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A number is a repeated operation [Wittgenstein]
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18160
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The concept of number is just what all numbers have in common [Wittgenstein]
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6. Mathematics / B. Foundations for Mathematics / 6. Mathematics as Set Theory / b. Mathematics is not set theory
18161
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The theory of classes is superfluous in mathematics [Wittgenstein]
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6. Mathematics / C. Sources of Mathematics / 6. Logicism / d. Logicism critique
6849
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Wittgenstein hated logicism, and described it as a cancerous growth [Wittgenstein, by Monk]
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23509
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The logic of the world is shown by tautologies in logic, and by equations in mathematics [Wittgenstein]
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