Smullyan, Raymond M. Formerly, Department of Philosophy, Indiana University, Bloomington, Indiana.
- Self-reference via Gödel numbering
- Gödel's second theorem
- Impossibility of mechanizing mathematics
- Additional Reading
The result, proved by K. Gödel in 1931, that any sufficiently advanced mathematical system must be incomplete in that there must always be a true sentence that is not provable in the system. Roughly speaking, Gödel showed how, for each such system, a sentence could be constructed that asserted its own nonprovability in the system.
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