Why AGI Is Impossible

Artificial General Intelligence (AGI) is impossible because current computational models, including Turing machines and large language models, cannot spontaneously create new, non-deducible possibilities or perform multi-step 'jury-rigging' like biological systems and human minds.

• AGI is impossible because computers cannot perform open-ended evolution or non-deducible 'jury-rigging' like biological systems.

• Human minds and biological evolution create new possibilities that cannot be deduced from existing ones.

• Formal mathematical systems like set theory cannot fully describe the world's indefinite uses and complexities, proving 'the world is not a theorem'.

Achieving Artificial General Intelligence is deemed impossible because existing computational frameworks, such as universal Turing machines, cannot perform open-ended evolution or create novel solutions that are not deducible from prior possibilities. This limitation prevents them from 'jury-rigging' or finding new uses for things in a multi-step, non-deducible manner, a capacity fundamental to biological evolution and human creativity. The world itself is not a theorem, meaning its complexities cannot be fully captured or predicted by formal mathematical systems like set theory.

Limitations of AGI

• 00:00:05 Artificial General Intelligence is impossible because universal Turing machines cannot find affordances or create new possibilities that are not deducible from old ones, unlike Darwinian pre-adaptations and human minds. This capacity, known as 'jury-rigging,' involves finding non-deducible new uses for things, often in multi-step sequences where no intermediate step can be logically derived, which current computers and large language models cannot replicate.

• 00:02:35 Open-ended evolution has not been achieved in artificial life or general artificial intelligence on computers. In contrast, evolving organisms are embodied and embedded in the world, constructing themselves through dynamical systems without relying on representation. This self-construction allows cells to interact with and categorize the world in ways that are fundamentally different from how computational systems operate.

The World Is Not a Theorem

• 00:03:23 The concept that 'the world is not a theorem' arises from the inability of formal systems like set theory to fully model indefinite uses of things. Key axioms of set theory, such as extensionality and choice, break down because the indefinite number of uses for an object (e.g., a screwdriver) prevents listing or ordering them. This implies that many mathematical concepts, including numbers and equations, cannot be derived from these indefinite uses.

• 00:07:04 The inability to apply set theory's mathematics to compute or deduce the evolution of the biosphere indicates that the world cannot be described as a theorem. This means it's impossible to write a simple equation or define a phase space to deduce a trajectory for complex systems like biological evolution. Such phenomena are far too intricate and have evolved over billions of years, defying formal mathematical prediction or explanation.