idea

Gödel, 1931

In 1931 Gödel showed that a system of rules can be sound and still leave true things unproven, and that it cannot vouch for itself from within.

Everything nearby grows from that: what proof and truth are, what systems can and cannot reach, and where people have carried the idea since.

Connects to

• what it says
• what true means
• what a system is
• the ladder
• Lucas, Penrose
• quantum bridge
• the asymmetry
• broken signature
• Franzén

Sources

1. Wikipedia: Gödel’s incompleteness theorems
2. Stanford Encyclopedia of Philosophy: Gödel’s Incompleteness Theorems
3. Gödel, K. (1931). Über formal unentscheidbare Sätze der Principia Mathematica und verwandter Systeme I. Monatshefte für Mathematik und Physik 38, 173–198.