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John Abramson is retired and lives in the Lake District in Cumbria, England. He obtained an MSc in Transpersonal Psychology and Consciousness Studies in 2011 when Les Lancaster and Mike Daniels ran this course at Liverpool John Moores University. In 2015, he received an MA in Buddhist Studies from the University of South Wales. He can be contacted at [email protected]

Two Arguments That Change the Game

A Plain-Language Response to Frank Visser

John Abramson / Claude

Frank Visser has been pressing me on whether the resemblance between Cantor's mathematics and the Wisdom Traditions is genuinely meaningful — or just an elaborate case of seeing faces in clouds. His scepticism has been healthy and his challenges have been serious. But two of those challenges, when examined carefully, turn out to contain their own refutation. That is what I want to explain here, as plainly as possible.

The Puzzle in One Sentence

Georg Cantor's mathematics — developed in the 1870s with no interest in Eastern philosophy — shares a very specific structural pattern with what three philosophically adversarial Buddhist and Hindu traditions independently describe as the architecture of ultimate reality. The question is whether this is coincidence, cognitive projection, or something more significant.

Frank's Best Shot — and Why It Rebounds

Frank's most effective challenge was this: other advanced mathematical frameworks — category theory, homotopy type theory, topos theory — also match most of the structural pattern. They score 7 out of 8. Doesn't that show the pattern is so generic that it proves nothing?

Here is why this argument runs precisely backwards.

Category theory was developed in the 1940s by algebraic topologists who had no interest in matching Cantor. Homotopy type theory emerged from computer science in the 2000s. Topos theory grew from algebraic geometry. None of these communities were trying to reproduce the same structural skeleton. Yet all of them — working from entirely different starting points, in different centuries, for entirely different purposes — converged on the same pattern.

Think of it this way. If one person walks across a field and finds a path, that tells you something about that person. If ten people walk across the same field from ten different starting points and all end up on the same path — that tells you something about the field.

The near-match scores are not evidence that the structural pattern is generic. They are evidence that independent mathematical inquiry is constrained to arrive at this pattern regardless of where it starts. Mathematicians who set out to build foundations for abstract algebra, or computer-verified proofs, or algebraic geometry, all end up in the same neighbourhood. That is not a coincidence — it is a fixed point. And fixed points are properties of the landscape, not of the travellers.

This is the first argument that changes the game. Frank's challenge was meant to show that the pattern is too common to be meaningful. It actually shows the pattern is structurally inevitable — which is precisely what the Wisdom Traditions claim about the deepest structure of reality.

Frank's Hidden Assumption — and What Mathematics Says About It

Frank's conclusion is that the correspondence between mathematics and the Wisdom Traditions tells us about the structure of the human mind — not the structure of reality. We reach for the same imaginative tools when confronting infinity, and the match is therefore a cognitive artefact rather than a discovery.

This is a reasonable-sounding position. But it depends on a hidden assumption: that reality is, at bottom, what everyday empirical observation presents — a world of physical things we can measure and touch. The claim is that anything beyond that picture is either physics (legitimate) or projection (not legitimate).

Here is the problem. No mature mathematical system actually fits within that picture.

Cantor's hierarchy requires completed actual infinities — not just 'you can always count higher,' but infinite sets that exist as completed wholes, with properties that can be proved. Category theory treats relations as more fundamental than objects — the thing itself is defined entirely by its connections to everything else, with no intrinsic nature of its own. Homotopy type theory posits an infinite hierarchy of abstract universes. Even the calculus you learned at school requires uncountable continua and idealised limits that no physical process ever reaches.

None of this can be grounded in sensory-accessible material phenomena. The mathematics that Frank relies upon to evaluate arguments about reality already exceeds the materialist picture he is using to dismiss those arguments. He is standing on mathematical ground while simultaneously claiming that mathematical ground has no metaphysical implications.

This is the second argument that changes the game. The debate is not between a metaphysical argument and a neutral, metaphysics-free scepticism. Both positions make commitments about the nature of reality. And the commitment least supported by the internal structure of mathematics — the tool both sides agree is our most reliable — is the empirical-materialist one.

Where This Leaves the Question

Neither of these arguments proves that the Wisdom Traditions are correct. They do not establish that subtle realms exist, or that consciousness is fundamental, or that any particular metaphysical system is true. What they establish is this: the structural grammar that mature mathematics is constrained to produce — from whatever starting point — is the same structural grammar that careful contemplative inquiry independently arrived at. And the most common reason for dismissing this as mere coincidence turns out to rest on an assumption that mathematics itself does not support.

At that point, the burden of explanation shifts. When independent mathematical traditions and independent contemplative traditions converge on the same structural grammar, the question is no longer why they match — but what kind of reality forces that match to occur.