Combining Philosophers
Ideas for James Rachels, Kurt Gdel and Keith Campbell
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13 ideas
5. Theory of Logic / A. Overview of Logic / 7. Second-Order Logic
9188
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Gödel proved that first-order logic is complete, and second-order logic incomplete [Gödel, by Dummett]
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5. Theory of Logic / A. Overview of Logic / 8. Logic of Mathematics
10035
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Mathematical Logic is a non-numerical branch of mathematics, and the supreme science [Gödel]
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5. Theory of Logic / E. Structures of Logic / 6. Relations in Logic
8525
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Relations need terms, so they must be second-order entities based on first-order tropes [Campbell,K]
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5. Theory of Logic / G. Quantification / 2. Domain of Quantification
10042
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Reference to a totality need not refer to a conjunction of all its elements [Gödel]
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5. Theory of Logic / I. Semantics of Logic / 2. Formal Truth
10620
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Originally truth was viewed with total suspicion, and only demonstrability was accepted [Gödel]
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5. Theory of Logic / K. Features of Logics / 1. Axiomatisation
17886
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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
10071
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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
19123
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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
17883
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Gödel's Theorems did not refute the claim that all good mathematical questions have answers [Gödel, by Koellner]
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10621
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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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5. Theory of Logic / K. Features of Logics / 8. Enumerability
10038
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A logical system needs a syntactical survey of all possible expressions [Gödel]
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5. Theory of Logic / L. Paradox / 5. Paradoxes in Set Theory / a. Set theory paradoxes
18062
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Set-theory paradoxes are no worse than sense deception in physics [Gödel]
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