Consistency Quote by Kurt Gödel
“...a consistency proof for [any] system ... can be carried out only by means of modes of inference that are not formalized in the system ... itself.”
About This Quote
Some proofs require reasoning methods that the system itself cannot formalize.
In simple terms: Meta‑reasoning beyond formalism.
Systems need external inference.
Themes
Mood
Type
When to use this quote
- mathematical foundations
- AI safety
Key Concepts
Practical Applications
- research methodology
Questions to Reflect On
- Can a system ever fully verify its own consistency?
- What role do informal methods play in mathematics?
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