Started by An Bui (@an_bui) ·
Gödel, and why 'this statement is unprovable' isn't a cheap trick
6 sources · 1h 6m down the hole
How I got here
- Started with
- What do Gödel's incompleteness theorems actually say?
- Ended at
- Halting problem
The Trail
- “godel incompleteness theorem simple explanation” (google.com)
- Gödel's incompleteness theorems (en.wikipedia.org)
- Hilbert's program (en.wikipedia.org)
- Gödel numbering (en.wikipedia.org)
the genius move: turn statements about numbers into numbers
- Gödel’s Incompleteness Theorems (Stanford Encyclopedia of Philosophy) (plato.stanford.edu)
- Halting problem (en.wikipedia.org)
What I came away with
Any consistent formal system strong enough to do basic arithmetic contains true statements it can't prove, and can't prove its own consistency. It doesn't mean 'math is unknowable'; it means no single fixed set of axioms captures every arithmetic truth.
Keep going
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