# Does Gödel's second incompleteness theorem put a limitation on artificial intelligence systems?

According to Brian Cantwell Smith

no calculation without representation

Therefore, computers depend on models. So, we can say that AI is limited internally by the model and externally by the environment. This problem is discussed here in a previous question I have asked.

Now, consider Gödel's second incompleteness theorem

a coherent theory does not demonstrate its own coherence

Can we say that Gödel's second incompleteness theorem puts a limitation on artificial intelligence? How could AI bypass Gödel's second incompleteness theorem?

• This and this are two very related questions.
– nbro
May 13 '20 at 10:18
• Why should AI systems be consistent? Intelligent humans are not! Dec 11 '20 at 20:27

I think the colloquial understanding of Gödel's incompleteness theorems allows them to be too broadly applied. Gödel's second incompleteness regards the consistency of a formal system, which is a technical concept of formal systems that means the system cannot prove every formula. It is commonly framed as a system not being able to prove both a formula and its negation (e.g. $$2+2=4$$ and $$2+2 \neq 4$$), since many logical systems allow anything to be proven from a contradiction.