Ideas from 'works' by Kurt Gödel [1930], by Theme Structure

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2. Reason / A. Nature of Reason / 1. On Reason
For clear questions posed by reason, reason can also find clear answers
5. Theory of Logic / A. Overview of Logic / 7. Second-Order Logic
Gödel proved that first-order logic is complete, and second-order logic incomplete
5. Theory of Logic / I. Semantics of Logic / 2. Formal Truth
Originally truth was viewed with total suspicion, and only demonstrability was accepted
5. Theory of Logic / K. Features of Logics / 5. Incompleteness
Gödel's Theorems did not refute the claim that all good mathematical questions have answers
6. Mathematics / B. Foundations for Mathematics / 3. Axioms for Number / g. Incompleteness of Arithmetic
Gödel eventually hoped for a generalised completeness theorem leaving nothing undecidable
The real reason for Incompleteness in arithmetic is inability to define truth in a language