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6. Mathematics / B. Foundations for Mathematics / 4. Axioms for Number / g. Incompleteness of Arithmetic
Gödel eventually hoped for a generalised completeness theorem leaving nothing undecidable [Gödel, by Koellner]
The real reason for Incompleteness in arithmetic is inability to define truth in a language [Gödel]
6. Mathematics / B. Foundations for Mathematics / 5. Definitions of Number / d. Hume's Principle
Two numbers are equal if all of their units correspond to one another [Hume]