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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]

A Response to Brad Reynolds' Chapter 13 and Frank Visser's Critique

John Abramson / Claude

Before I begin, let me be perfectly clear — especially for Brad and anyone who may have misunderstood earlier exchanges: mathematics is a third-person explanatory mechanism. It is not, and I have never claimed it is, a substitute for first-person realization of ultimate reality. I pick out Brad in particular because our past exchanges may have left the impression that I equate mathematics with direct nondual insight. I unequivocally do not.

What I do claim is this: just as Brad asserts that the Divine Condition is a radical a priori — not co-created, as Jorge Ferrer insists — so too is the fundamental structure of mathematics. Realization of ultimate reality is a first-person event: the 'Aha!' recognition of the always-already. Mathematics is the objective, third-person, a priori structural description of that same Reality. To avoid any lingering confusion about 'a priori': what is always already pre-existing and universally present is a small, fundamental subset of mathematics — the structural grammar that describes ultimate reality. Most of what we ordinarily call mathematics is invented or extrapolated from this core; the core itself is discovered.

My extensive discussions with Frank Visser already imply the above. The justification for that view is contained in those exchanges and I will not repeat it here. I will simply note that the structural description of reality offered by the Wisdom Traditions is powerfully reinforced by its congruence with the fundamental characteristics of mathematics.

Stunningly, if this description of mathematics as a priori is correct, it is potentially available to everyone without the need for the third eye to open or any spiritual attainment. This is revelatory. Brad, Wilber, and others have rightly emphasised the desirability — even necessity — for the vast majority of us who have not yet realised nonduality directly to follow a genuine spiritual path. I do not dispute the life-changing importance of that advice. What an appreciation of the fundamental characteristics of a priori mathematics provides is an opportunity for the informed layperson to understand why Brad and others urge us toward that path.

On the Strap-Line and the Enactment Problem

Which brings me to Brad's Chapter 13 and Frank's response. Brad's own subtitle — 'Enacting Philosophy as Participation in Being' — contains an ambiguity that Frank's reading exploits, perhaps unintentionally. Frank reads 'enacting' through the Wilber/Ferrer lens: philosophy as the co-creation of spiritual realities through lived practice and developmental structure. But that is not what Brad means. Chapter 13 is about discovering an a priori reality — the always-already Prior Condition disclosed in Divine Recognition — not about co-creating spiritual ultimates through participatory enactment. Brad's use of 'enacting' is closer to 'expressing' or 'embodying' a pre-existing ground than to Wilber's technical sense of bringing worlds into being through injunction and interpretation. Frank's reading of the chapter through the enactment framework therefore imports a philosophical position Brad's argument is specifically designed to transcend.

The logic here is important to spell out. Wilber's post-metaphysical turn holds that spiritual realities are enacted through the interplay of phenomenological injunction, cultural interpretation, and developmental structure. Ferrer goes further, treating spiritual ultimates as co-created through embodied practice. Brad's Meta-Perennial position is the direct opposite: the Divine Condition is not enacted by the subject; it is the Prior Reality that precedes all subject-object differentiation. Developmental structures shape how Realization is interpreted and embodied — but they do not produce or enact the Divine itself. Reading Brad through the Wilber/Ferrer enactment framework therefore obscures what is distinctive about his argument. Brad is not describing participation in an unfolding process; he is describing recognition of what is already and always the case.

This distinction is not merely terminological. It has direct bearing on the role mathematics can play. If spiritual realities are enacted, mathematics at most describes the structural shape of enacted worlds. But if the Divine Condition is an a priori prior to all enactment, then mathematics — as an equally a priori structural description — is describing the same prior ground. The congruence between mathematical structure and the Wisdom Traditions' descriptions of ultimate reality is, on this reading, not coincidental. It is evidence that both are tracking the same always-already.

Unity, Multiplicity, and the Mathematical Structure of Nonduality

A second, deeper problem surfaces in Frank's extract: 'Experiences of unity become evidence that reality is fundamentally One; experiences of nonduality become confirmation that the universe itself is nondual.' This conflates two things that must be kept carefully distinct.

Reports of experiences of unity are very profound. But suggesting such experiences are experiences of nonduality leads to a confusion that mathematics can help clarify. Nondual is not one and not two. Whatever that means in terms of direct first-person experience — and it can only be experienced and not fully described — it is very clear what it is not: it is not one, and it is not two.

The mathematical characterisation

Here I offer what I believe is an entirely novel characterisation. Third-person mathematics can objectively describe the not-one, not-two structure of nonduality in the following way, without claiming to capture what it is like from the inside.

In Cantor's transfinite hierarchy, there is an infinite sequence of levels — Aleph-0, Aleph-1, Aleph-2, and so on — each strictly larger than the one below and irreducibly distinct from it. Think of these as successively higher vantage points from which reality is apprehended. Wilber captures the subjective dimension of this in the Wilber-Combs matrix, where a particular stage of development meets a particular state of consciousness. Mathematically, I would say the experiencer is at a particular Cantorian Aleph level as his or her vantage point.

I use Cantor's hierarchy here as a structural model to capture the irreducibility and unboundedness of levels — not as a literal ontological map of experiential states, but as the best available third-person language for what the Wisdom Traditions describe from the inside.

The crucial observation is this: unity can only be experienced as unity within the particular Aleph level one occupies. Higher levels are, from that vantage point, hidden — they exceed what can be apprehended. Lower levels have been transcended and included. What appears as unity is the coherence of one's current level, not a view from everywhere.

This is precisely why unity is not nondual. Nondual encompasses all Aleph levels simultaneously — it is the ground that includes and exceeds every particular vantage point. It is unbounded in this sense: no Aleph level constitutes a ceiling on it. From any particular Aleph level, nonduality cannot be seen as one thing, because it is not a thing at any level; it is the structural totality that no level can contain. Hence: not-one.

By the same logic, multiplicity — the experience of many distinct things — is the multiplicity characteristic of the particular Aleph level one inhabits. At any given level, items within that level are distinct from each other but share the same order of infinity. Nonduality is not that multiplicity, because it is not located at any particular level. Hence: not-two.

In short: unity is within a level. Multiplicity is within a level. Nonduality is the unbounded whole that no level exhausts and every level presupposes. Mathematics does not tell us what nonduality feels like from the inside. But it does tell us with precision what any description of it must structurally accommodate — and what descriptions of unity and multiplicity structurally cannot be.

This is why Frank's conflation of unity-experience with nondual-experience is not merely a loose use of language. It is a structural error. Unity is a property of a level; nonduality is a property of ultimate reality as a whole. The two are not the same kind of thing, and mathematics uniquely supports this distinction.

How Mathematics Can (and Cannot) Help Assess Authenticity

But there is another major test that Brad's essay demands an answer to: what spiritual experiences are authentic, and what are not? The first-person nature of such experience means mathematics cannot give a definitive answer. It cannot prove that someone has genuinely recognised the Divine Condition or opened the third eye. That remains irreducibly subjective, and no amount of structural analysis changes this.

What mathematics can do, however, is supply a powerful third-person structural filter for consistency — not a replacement for communal verification or Heart-Transmission, but an additional, objective cross-check available to anyone who understands the structural grammar.

The logic of the filter

The logic needs to be spelled out carefully, because it is novel. Every mature mathematical foundation converges on the same structural skeleton: an unbounded hierarchy, strict level-differences that are formally irreducible to one another, canonical generative operations, asymmetric embeddability, no final terminus, and — crucially — a relational ontology in which nothing exists from its own side as a self-subsisting entity. The Wisdom Traditions independently arrived at the same description of ultimate reality.

If authentic nondual recognition is recognition of the very structure mathematics describes — the always-already relational, unbounded, hierarchically organised, terminusless ground — then a person who has genuinely realised this should, over time, increasingly embody and express precisely this grammar. Not because mathematics legislates spiritual attainment, but because authentic recognition of Reality and accurate structural description of Reality are descriptions of the same thing. A person whose life and teaching persistently contradict the structural grammar is, at minimum, not yet fully expressing what they claim to have realised.

This is an indirect test, not a direct one. It cannot establish presence; it can flag absence. A person might satisfy all the structural markers and still not have realised the Divine Condition in Brad's full sense. But a person who consistently violates the structural markers gives us a third-person reason to question their claim — even when the phenomenology feels genuine to the experiencer.

What the filter looks like in practice

The structural grammar suggests four questions an observer can ask without any contemplative attainment of their own.

Does the person consistently operate from a perspective that embeds and transcends lower levels without reifying them as intrinsically existing? Someone stuck in egoic identification will treat their own perspective as self-subsisting and absolute — which is structurally inconsistent with a grammar in which nothing exists from its own side. Authentic higher-level operation includes lower levels without being captured by them.

Does the realisation translate into a lived sense that all beings are nodes in a web of dependent arising rather than separate, self-enclosed entities? Authentic nondual insight dissolves the illusion of intrinsic self-existence. Its absence shows up as subtle clinging or boundary-drawing — a residual sense that one's own perspective, tradition, or attainment is self-standing in a way others' are not.

Is there evidence of ongoing transformation with no attachment to a final state? Claims of permanent static arrival are structurally inconsistent with a grammar that has no terminus. Authentic realisation should be characterised by continued opening, not by the announcement of a completed destination.

Does the person's teaching convey that reality always exceeds conceptual closure, yet remains rigorously distinguishable from lower levels of realisation? Conflating all levels as equally valid — or claiming that the highest is simply identical with the lowest — both violate the strict irreducibility that the structural grammar requires.

If a claimed realisation repeatedly violates these structural constraints — by reifying personal selfhood as intrinsically existing, by treating a subtle-state experience as a final self-subsisting achievement, or by collapsing the distinctions between levels — then mathematics gives us a third-person reason to regard the claim as incomplete or inauthentic, even when the phenomenology feels genuine to the experiencer.

The democratisation point

This is where Brad's own concern about authentic transmission connects directly to what mathematics offers. Brad rightly emphasises that most of us who have not yet realised nonduality directly need guidance in discerning genuine transmission from its imitation. The structural grammar mathematics forces us to acknowledge gives the informed layperson a set of questions they can ask of any teacher or teaching without requiring the third eye to open first.

Does this person's life and work look like someone who consistently inhabits the higher levels — unbounded, relational, non-reifying, never claiming arrival? That question is accessible without any contemplative attainment whatsoever. Mathematics democratises the discernment process in exactly the direction Brad hopes for — not by replacing the path, but by making the structural signature of its authentic fruit legible to anyone willing to look carefully.

The man or woman in the street who understands the a priori structural grammar of mathematics can now ask that question and have grounds for an answer. This is not a small thing. It means that the assessment of spiritual authenticity — historically dependent on the judgement of other realised beings or long-term community observation — can be supplemented by a structural test that requires no special access. The test is not infallible, and it is not a substitute for the deeper forms of verification Brad describes. But it is available, it is principled, and it is grounded in the same a priori structure that the Divine Condition itself instantiates.

In short: mathematics does not enact or realise the Divine. But it does describe the structural signature that any authentic realisation must eventually display. That signature is the same grammar the Wisdom Traditions have always pointed to. The congruence is not coincidence; it is evidence that reality, even when approached through enactment or through the body, refuses to be exhausted by either.