If you ask five AI practitioners to define Artificial General Intelligence (AGI), you might get six answers. From “median human” to “generally capable” systems, there’s been a lot of hand-wavy vagueness. Some even reject the term entirely.

The definitions suggest the same North Star: AGI is a system that possesses human-level intelligence.

It is an intuitive idea. It is also, I believe, a logical impossibility.

I do not undermine the potential greatness of AI. But “human-level intelligence” is not a valid target. It’s important to bring in the lessons from Russell’s Paradox—and the crisis it caused in the mathematical community from 1901 to 1908—into our current AI discourse and research agenda. Specifically (no pun intended), we need to bring in the Axiom of Specification.

We need to discuss AI capabilities with precision instead of framing our technological goals around a paradox. Otherwise, we are creating confusion, fear, and hype, rather than clarity.

The Trap of Unrestricted Comprehension

In the early days of set theory, mathematicians operated under a principle called Unrestricted Comprehension. The idea was simple: If you can describe a property, you can create a set of all things that have that property.

For example, you can have a set of “all red things”, a set of “all even numbers”, or even a set of “all ideas.”

Bertrand Russell, however, found a fatal flaw in this freedom. He asked: What about the set of “all sets that do not contain themselves?”

If this set contains itself, it contradicts its own definition. If it does not contain itself, then it must be included, which again contradicts the definition. This was Russell’s Paradox. It proved that you cannot just define a collection loosely and expect it to exist logically.

It further revealed that the “set of all sets“ is an incoherent concept. It is a syntax error to define a set that contains all sets. Such an entity is not a well-defined set.

I propose that “human-level intelligence” is exactly this kind of syntax error and incoherent set. And we need to stop referring to it as our goal for AI.

“Human-Level Intelligence” is a “Set of all Sets”

We treat human intelligence as a fixed bar to be cleared. But strictly speaking, we have no definition for it.

Anecdotally, we know human intelligence operates like a "set of all sets." It is an unbounded, self-referential capacity that cannot...

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