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'Classical Cosmology (frags)', 'On Formally Undecidable Propositions' and 'Whitehead and the Rise of Modern Logic'
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6 ideas
5. Theory of Logic / A. Overview of Logic / 7. Second-Order Logic
13639
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Quine says higher-order items are intensional, and lack a clearly defined identity relation [Quine, by Shapiro]
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5. Theory of Logic / K. Features of Logics / 1. Axiomatisation
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The limitations of axiomatisation were revealed by the incompleteness theorems [Gödel, by Koellner]
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5. Theory of Logic / K. Features of Logics / 2. Consistency
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Second Incompleteness: nice theories can't prove their own consistency [Gödel, by Smith,P]
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5. Theory of Logic / K. Features of Logics / 3. Soundness
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If soundness can't be proved internally, 'reflection principles' can be added to assert soundness [Gödel, by Halbach/Leigh]
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5. Theory of Logic / K. Features of Logics / 5. Incompleteness
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Gödel's First Theorem sabotages logicism, and the Second sabotages Hilbert's Programme [Smith,P on Gödel]
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17888
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The undecidable sentence can be decided at a 'higher' level in the system [Gödel]
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