Why Penrose Is Wrong: A Meaning-Centred Account of Mind and Mathematics

Roger Penrose’s scepticism of artificial intelligence is well known, and deeply rooted in his metaphysical commitments. Central to his position is the idea that human consciousness accesses truths that no formal system can derive—a claim that leads him to deny that consciousness, and therefore intelligence, can be replicated by any computational system.

This argument depends not just on a technical reading of Gödel’s incompleteness theorems or a speculative quantum hypothesis. It is anchored in a Platonic ontology: the belief in a timeless, non-material realm of mathematical truths, which the human mind somehow perceives directly. To defend this view, Penrose must reject the computational nature of thought, the sufficiency of standard neuroscience, and even the completeness of quantum theory.

But if the foundations are questioned—if the ontology of mathematics and consciousness is rethought—the entire edifice begins to crumble. A meaning-centred approach offers an alternative.

Mathematics as Meaning, Not Metaphysics

In Penrose’s framework, mathematical truths are discovered, not invented. They exist independently of any observer, and cognition is a form of direct access to this Platonic world. But this commits mathematics to a metaphysical domain with no clear relation to experience or material process.

A meaning-centred account reframes mathematics not as a realm of objective truths but as a symbolic system: a structured set of semiotic resources that realise meaning within human activity. Mathematical symbols, operations, and theorems are not discovered in a transcendent space, but instantiated through patterned practices of abstraction, generalisation, and inference.

This does not reduce mathematics to relativism or cultural whim. On the contrary, it grounds mathematical rigour in the systematisation of meaning—how humans construct consistent, extensible structures of relations. The internal coherence and inferential power of mathematics emerge not from metaphysical existence, but from the organised deployment of symbolic potential within specific meaning systems.

Consciousness as Semiotic Actualisation

Penrose’s argument against computationalism also hinges on a particular conception of consciousness. He assumes that genuine understanding—especially mathematical insight—cannot arise from symbol manipulation alone. Something more is needed: a subjective grasp, a non-algorithmic awareness.

But this conclusion follows only if consciousness is taken to be metaphysically distinct from symbol systems. A meaning-centred perspective views consciousness not as a receiver of timeless truths but as the material actualisation of meaning potential. Thought is not non-computational because it transcends computation, but because it is not computation in the first place—it is the semiotic unfolding of patterned neural activity within a biologically and socially evolved system.

The brain is not a machine solving equations. It is a material meaning-maker, engaging in recursive abstraction, metaphor, analogy, and inference. The richness of human understanding comes not from access to another realm, but from the layered organisation of symbol systems, shaped by experience, culture, and bodily interaction with the world.

Gödel Without Mysticism

Penrose invokes Gödel’s incompleteness theorems to claim that humans can “see” the truth of statements that no formal system can prove, implying a non-computational grasp of truth. But this misreads Gödel’s result as a claim about human cognition rather than about the limits of formalism.

Gödel showed that any sufficiently powerful formal system contains true statements that it cannot prove within itself. This applies to any system, including those implemented in human cognition. The fact that humans can sometimes assert the truth of a Gödel sentence is not evidence of trans-algorithmic insight—it is evidence that humans operate outside any single formal system at any given time.

This is not mystical. It reflects the flexibility of human symbolic behaviour. Humans shift between systems, invent new systems, and recursively embed structures within structures. The power here is semiotic, not metaphysical.

The Collapse of Mystery into Meaning

Penrose locates consciousness in a mysterious collapse of the quantum wavefunction—a physical event that he claims is inherently non-computational. This strategy pairs two unsolved problems—consciousness and quantum mechanics—and proposes that one solves the other. But it merely replaces one mystery with another, and leaves the relation between meaning and matter unexplained.

A meaning-centred view begins from a different premise. It sees consciousness as the semiotic interface between biology and symbolic order. Meaning arises when neural processes instantiate patterns that function symbolically—patterns that can refer, differentiate, generalise, infer. The mystery is not solved by positing a new physical law, but by tracing how symbolic organisation emerges from material substrates.

Human Uniqueness Without Metaphysical Privilege

Ultimately, Penrose is defending a kind of human exceptionalism: the belief that the human mind is fundamentally unlike any machine because it taps into a realm of truth no machine can access. But this exceptionalism is secured only by importing a metaphysical scaffold—a Platonic world and a modified quantum physics—to support it.

A meaning-centred account preserves human uniqueness without requiring metaphysical privilege. Humans are unique because of the historical, biological, and social evolution of meaning systems, not because of access to a hidden dimension of reality. Intelligence, understanding, creativity—these are emergent properties of the symbolic capabilities embedded in material processes, not evidence of a dual ontology.

Conclusion

Penrose is wrong not because his mathematics is faulty, nor because his physics is incoherent, but because the ontology he defends is unnecessary. Once mathematics is understood as a symbolic system, and consciousness as the actualisation of meaning, the case for non-computational physics collapses.

What remains is not a diminished view of mind, but a re-anchored one: a conception of thought as materially grounded, symbolically organised, and meaningfully actualised.

And it is from this perspective that the question of AI should be addressed—not as a metaphysical challenge to human uniqueness, but as a test of whether symbol systems instantiated in non-biological substrates can give rise to new forms of meaning.