Penrose on "Why" AI will never be Intelligent

..."Intelligence involves Consciousness

...there are also things that are incomputable, that mathematics cannot compute.

AI Summary of Gödel's incompleteness theorem:

Gödel's incompleteness theorem states that within any consistent formal system that can express basic arithmetic, there will always be true statements that cannot be proven within that system, meaning there are inherent limitations to what can be mathematically proven using a set of axioms; essentially, no matter how comprehensive a set of axioms is, there will always be true statements that fall outside its scope of provability.

Key points about the theorem:

Consistency is crucial:
The theorem only applies to consistent formal systems, meaning systems where no contradictions can be derived.

Self-referential proof:
Gödel's proof utilizes a self-referential argument, similar to the "This sentence is false" paradox, to demonstrate the existence of such unprovable statements.

Impact on mathematics:
This theorem significantly impacted the foundations of mathematics by showing that there can never be a complete, perfect axiomatic system for all of mathematics.

According to S.W.P Steen, Gödel's incompleteness theorem essentially demonstrates that within any consistent formal system robust enough to encompass basic arithmetic, there will always exist true statements that cannot be proven using the axioms and rules of that system; essentially, there will always be limitations to what can be formally proven within a given mathematical framework, highlighting the inherent incompleteness of such systems. "

"The Understanding Transcends Use"

The "Turing Test" is basically a demonstration of Godel's Incompleteness Theorum.  The "proof of Artificial Intelligence" must come from OUTSIDE the AI System (a human determination)... it's a "transcendental" determination.... answering/ knowing "why" (not just told "that") the computational rules are true, and to do that you must "understand" them from an external and "conscious" perspective.  AI alone can't know if its' own rules are true.

Consciousness Allows You to Transcend the Rules

Understanding is Different from Computing

Classical reality is ascertainable... Quantum reality (ie- spin) is merely confirmable, not ascertainable

Einstein, "If you can confirm with certainty, it's an element of (quantum) reality". [ie- EPR Experiments]

Roger Penrose, "The Emperor's New Mind" (1989)