On the evening of 8 September 1930, David Hilbert spoke to Germany by radio from Königsberg. He finished with six words, later carved on his gravestone: “Wir müssen wissen. Wir werden wissen.” We must know. We shall know.
He was a day late. At a small meeting in the same city the day before, a 24-year-old Kurt Gödel had quietly shown that any consistent set of rules strong enough for arithmetic leaves some true statements it can never prove. Fix your axioms however you like. Something true will always sit outside them.
It is tempting to read that as “we can’t know”. That is not quite what Gödel showed. We can often see that the unprovable statement is true. We just can’t prove it from inside the system that produced it. The view has to come from outside.
I spent a career inside systems like that. I can’t count the number of times a system was handed over as complete, only to find that an important feature had been overlooked, or a supposedly complete suite of tests went green, and the system still failed in the real world. Every specification I ever signed off had the same quiet assumption buried in it: that the rules described everything that mattered. They never did. Not because anyone was careless, but because no set of rules can vouch for itself.
That is the useful kind of humility. Not “we can’t know”, but “the system can’t tell us everything about itself”. Somebody has to stand outside it and look.
Which is exactly the question we should be asking of the AI systems now being sold to us as complete. Who is standing outside?
Prompted by “The century-long search for the limits to knowledge” in Aeon: https://aeon.co/essays/the-century-long-search-for-the-limits-to-knowledge
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