[bwoj]

I suspect that if formal systems were unequivocally “better” than formal systems our brains would be formal systems.

The desirable property of formal systems is that the results they produce are proven in a way that can be independently verified. Many informal systems can produce correct results to problems without a known, efficient algorithmic solution. Lots of scheduling and packing problems are NP-complete but that doesn’t stop us from delivering heuristic based solutions that work good enough.

Edit: I should probably add that I’m pretty rusty on this. Godels theorem tells ua that if a formal system is consistent, it will be incomplete. That is, there will be true statements that cannot be proven in the system. If the system is complete, that is, all true/false statements can be proven, then the system will be incomplete. That is you can prove contradictory things in the system.

AI we have now isn’t really either of these. It’s not working to derive truth and falsehood from axioms and a rule system. It’s just approximating the most likely answers that match its training data.

All of this has almost no relation to the questions we’re interested in like how intelligent can AI be or can it attain consciousness. I don’t even know that we have definitions for these concepts suitable for beginning a scientific inquiry.

[lanstin]

Asuuming said formal system incorporates Peano arithmetic.