Ideas from 'works' by Kurt Gödel [1930], by Theme Structure
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2. Reason / A. Nature of Reason / 1. On Reason
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For clear questions posed by reason, reason can also find clear answers
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5. Theory of Logic / A. Overview of Logic / 7. Second-Order Logic
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Gödel proved that first-order logic is complete, and second-order logic incomplete [Dummett]
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5. Theory of Logic / I. Semantics of Logic / 2. Formal Truth
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Originally truth was viewed with total suspicion, and only demonstrability was accepted
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5. Theory of Logic / K. Features of Logics / 5. Incompleteness
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Gödel's Theorems did not refute the claim that all good mathematical questions have answers [Koellner]
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6. Mathematics / B. Foundations for Mathematics / 4. Axioms for Number / g. Incompleteness of Arithmetic
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Gödel eventually hoped for a generalised completeness theorem leaving nothing undecidable [Koellner]
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The real reason for Incompleteness in arithmetic is inability to define truth in a language
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