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Frank Visser, graduated as a psychologist of culture and religion, founded IntegralWorld in 1997. He worked as production manager for various publishing houses and as service manager for various internet companies and lives in Amsterdam. Books: Ken Wilber: Thought as Passion (SUNY, 2003), and The Corona Conspiracy: Combatting Disinformation about the Coronavirus (Kindle, 2020).

The Missing Third Party
or the Missing Fourth?

A Response to John Abramson on Mathematics, Science, and Spirituality

Frank Visser / ChatGPT

John Abramson's response to my essay on Ken Wilber and the relationship between science and spirituality is provocative in precisely the right way. He does not simply defend Wilber against my criticism. Instead, he argues that I have framed the entire debate too narrowly.

I imagined two parties sitting at the table: science and spirituality. Wilber's project, on this reading, is an attempt to negotiate a settlement between them. I argued that the settlement remains unstable because science and spirituality operate according to different epistemic standards, and because Wilber's integral framework ultimately assumes the position of the cartographer who decides how all the different perspectives fit together.

John's proposal is to invite a third party: mathematics.

This is not a trivial suggestion. Indeed, I think it exposes something genuinely important that my essay did not sufficiently address. But I am not yet persuaded that mathematics can perform quite the role John assigns to it.

The interesting question, therefore, is not whether mathematics belongs at the table.

It does.

The question is whether mathematics can actually referee the conversation.

Mathematics Is Not Just Another Discipline

John is right to object to my casual grouping of mathematics alongside introspection, historical interpretation and particle physics. I treated them as examples of disciplines with different methods and standards of evidence. That was reasonable for the immediate point I was making, but it obscured something fundamental.

Mathematics is indeed different.

The truth of the Pythagorean theorem does not depend on whether anyone has ever measured a triangle. Mathematical proofs do not become false because new empirical observations arrive. The theorem is true within the formal system in which it has been demonstrated.

This gives mathematics a special epistemic status.

And John's invocation of Eugene Wigner's famous "unreasonable effectiveness" is entirely appropriate. The extraordinary success of mathematics in describing physical reality remains one of the great philosophical mysteries of science. Why should structures developed through abstract reasoning turn out to describe the behavior of galaxies, particles and spacetime with such astonishing precision?

The question becomes even more interesting when we consider the mathematical structures that physicists did not initially invent to describe nature but later discovered were indispensable to it.

This certainly complicates any simplistic division between an external scientific world and an internal spiritual world.

So I am willing to grant John's first point:

Mathematics is not merely another guest at the table. It is part of the architecture within which much of the conversation takes place.

But that does not yet make it the referee.

The Problem of the "Third Party"

Here I think John's metaphor becomes both illuminating and misleading.

Mathematics can certainly constrain what we can coherently say. If I construct a formal system and derive a contradiction, I have a problem. If a proposed physical theory makes mathematically inconsistent predictions, I have a problem. If two propositions cannot simultaneously be true within a given formal framework, I cannot simply solve the disagreement by insisting that both are true.

Mathematics is extraordinarily good at exposing contradictions.

But there is an important difference between logical coherence and truth.

A mathematically consistent theory can still be physically false.

And a mathematically elegant theory can still fail to describe the world.

The history of physics provides many examples of beautiful mathematical constructions that turned out not to correspond to nature. Mathematics constrains possibilities, but it does not, by itself, select which mathematical possibility is physically instantiated.

This distinction becomes even more important when we move from physics to metaphysics.

Suppose John succeeds in giving a particular account of consciousness a precise mathematical formulation. That would be a significant achievement. We could then ask whether the model is internally consistent, whether it generates predictions, and whether those predictions correspond to observations.

But mathematics alone could not tell us whether the model describes reality.

We would still need evidence.

And that evidence might be empirical, phenomenological, or perhaps something else.

So I would reformulate John's claim.

Mathematics is not the judge of reality.

It is the judge of certain forms of coherence.

That is already an enormous contribution.

The Difference Between Mathematical Truth and Empirical Truth

John writes that mathematics is "the only discipline whose results are necessary rather than empirical."

I think this is broadly correct, but it needs one important qualification.

Mathematical necessity applies within a formal structure. The necessity of the conclusion depends upon the validity of the axioms, definitions and rules of inference.

The empirical question is different: Why should this mathematical structure apply to our universe?

That is precisely where Wigner's puzzle begins.

Mathematics can tell us that, given certain assumptions, certain conclusions follow.

Physics asks whether the universe actually behaves according to those assumptions.

This is why mathematics and science have such a remarkable relationship but are not identical.

Mathematics provides the formal possibilities.

Empirical science tells us which possibilities nature appears to realize.

The astonishing fact is that the two converge so frequently.

But the convergence itself remains something that requires explanation.

And this brings us back to spirituality.

The Wignerian Extension

John's most interesting—and most controversial—claim is that the mathematical structures found in physics may extend into the interior domain of consciousness.

Here I think we need to be extremely careful.

The possibility is certainly worth investigating.

If subjective experience exhibits mathematical structures that can be independently identified, formalized and tested, then this could indeed change the conversation about consciousness and spirituality.

But the burden of proof is substantial.

It is not enough to discover that consciousness can be described mathematically. Almost anything sufficiently structured can be described mathematically.

The question is whether mathematics reveals something necessary about consciousness itself.

That is a much stronger claim.

And here I would ask John a question that I think is crucial:

What would count as failure?

What mathematical prediction about consciousness would, if empirically falsified, cause him to abandon or substantially revise his theory?

This is not a hostile question. It is exactly the question I would want to ask of any ambitious theory.

John's argument becomes most interesting at the point where he says that mathematical formalization gives spiritual metaphysics "a way to be wrong."

I agree completely.

But then the decisive issue becomes whether the proposed mathematical formalization actually produces independently testable consequences.

If it does, we have something genuinely exciting.

If it merely provides a mathematically elegant vocabulary for expressing ideas that were previously expressed in spiritual language, then we have achieved greater precision without necessarily achieving greater knowledge.

The distinction matters enormously.

The Mathematics of Consciousness Is Not Yet the Mathematics of Spirit

There is also a danger of conflating three different propositions:

Consciousness has mathematical structure. Consciousness can be mathematically modeled. Reality is fundamentally mathematical, and consciousness reveals this fact.

The first may be true.

The second is almost certainly true in some sense.

The third is a metaphysical thesis.

And the third does not automatically follow from the first two.

This is structurally similar to the problem I identified in Wilber's argument.

Wilber moves from the reality of contemplative experience toward metaphysical conclusions.

John's proposal risks moving from mathematical structure toward metaphysical conclusions.

The route is different, but the epistemic leap may be analogous.

This does not invalidate the project. It simply means that we should maintain the distinction between formal description, empirical evidence, and ontological interpretation.

Mathematics as Error Correction

Here, however, I think John has a genuinely powerful point.

One of my criticisms of spiritual traditions was that they often lack effective error-correcting mechanisms. A mystical insight may be profound, but the cosmological claims built around it can accumulate without a reliable mechanism for separating insight from speculation.

Mathematics can help.

Once a metaphysical claim becomes sufficiently precise to be formalized, it becomes vulnerable to criticism in a way that vague spiritual language often is not.

That is a real gain.

But mathematics is not the only possible error-correcting mechanism.

Logic is one.

Philosophical argument is another.

Empirical science is another.

And perhaps the disciplined comparison of first-person reports is another.

In fact, this suggests that John's "third party" may actually be a larger phenomenon: formalization itself.

The problem with many spiritual claims is not merely that they are non-mathematical. It is that they are insufficiently precise to be tested, challenged or even clearly understood.

The moment a claim becomes precise enough to have consequences, it becomes possible to ask whether those consequences follow.

Mathematics is extraordinarily powerful in this respect, but it is part of a larger intellectual process.

Gödel Complicates the Story

There is another irony here.

John invokes Kurt Gödel as an example of someone who saw mathematical truth as pointing toward a non-sensory reality. That is certainly relevant.

But Gödel also reminds us that mathematics itself is not a simple realm of total certainty.

Gödel's incompleteness theorems demonstrated profound limitations on what formal systems can establish about themselves. They did not destroy mathematics. On the contrary, they deepened our understanding of its power and limitations.

This is worth remembering in the present discussion.

Mathematics is extraordinarily effective at constraining thought.

But it does not provide a God's-eye view.

In fact, mathematics itself teaches us something that is deeply congenial to the epistemic humility I was advocating in my original essay:

There are limits to what any formal system can establish from within itself.

That does not prove spiritual metaphysics.

But it does warn us against imagining that mathematics will necessarily deliver a final theory of everything.

The Missing Party May Be Mathematics—and the Missing Fourth May Be Philosophy

John argues that the science-spirituality debate is bilateral when it should be trilateral.

I agree.

But I would add a fourth participant.

Philosophy.

Science gives us empirical constraint.

Mathematics gives us formal constraint.

Spirituality gives us access to particular dimensions of lived and contemplative experience.

Philosophy asks what follows from all of this—and, equally importantly, what does not follow.

Philosophy is the discipline that keeps asking whether we have confused a description with an explanation, an experience with an interpretation, a model with reality, or coherence with truth.

That is precisely the kind of work needed here.

In that sense, I would revise my original metaphor.

The table does not have two chairs.

It has at least four.

And perhaps the difficulty is not that Wilber has been trying to mediate between science and spirituality. It is that he has attempted to chair a meeting that requires several independent forms of constraint.

A More Interesting Integral Project

This brings me to what I think is the most productive possibility opened up by John's criticism.

Perhaps the future of integral thinking does not lie in constructing an even larger metaphysical system.

Perhaps it lies in developing a multi-method epistemology.

Such an epistemology would say:

Science constrains our claims about empirical reality.

Mathematics constrains our claims about formal structure.

Phenomenology constrains our claims about lived experience.

Contemplative practice can deepen and refine phenomenological investigation.

Philosophy examines the assumptions and inferential bridges connecting all these domains.

And none of these gets to declare unilateral sovereignty.

That would be a genuinely interesting extension of Wilber's project.

It would preserve his most valuable insight—the insistence that no single perspective captures the whole of human experience—while avoiding his tendency to turn perspectival pluralism into an all-encompassing metaphysical architecture.

John May Be Right About the Unsettleable

There is one final point on which I think John has genuinely changed the emphasis of my original argument.

I ended by suggesting that we may have to "learn how to live with questions that neither [science nor spirituality] can finally settle."

John objects that we cannot know which questions are permanently unsettled until we have tried more powerful methods.

I think that is fair.

History is full of questions that once seemed permanently mysterious but later became tractable. Mathematics and science have repeatedly transformed the boundaries of the knowable.

So perhaps my original formulation was too pessimistic.

We should indeed leave the door open.

The fact that a question currently resists scientific or spiritual resolution does not mean that it will always do so.

But I would add an important qualification.

The possibility that a question may eventually become mathematically or scientifically tractable does not mean that it will.

And we should not turn the possibility of future formalization into a metaphysical promise.

The Fourth Chair

So, John, I accept your invitation to add mathematics to the conversation.

But I would resist calling it the arbitrator.

Mathematics cannot tell us whether consciousness is fundamental.

It cannot tell us whether nondual awareness discloses ultimate reality.

It cannot tell us whether the universe is "Spirit," "matter," "mind," or something for which we do not yet have a name.

What it can do is something perhaps more valuable.

It can force us to become precise.

It can expose contradictions.

It can reveal structures that nobody consciously designed.

It can establish connections between apparently unrelated domains.

And when mathematical structures discovered in physics turn out to correspond unexpectedly with structures discovered in the study of consciousness, that would indeed be extraordinary evidence—evidence that deserves careful investigation rather than immediate metaphysical interpretation.

So I would now modify my original conclusion.

The conversation between science and spirituality is not a bilateral negotiation.

Mathematics deserves a seat at the table.

But so does philosophy.

And perhaps the ultimate lesson is that no single participant should be allowed to chair the meeting.

Not science.

Not spirituality.

Not mathematics.

Not Ken Wilber.

And not even the critic of Ken Wilber.

The real challenge is to construct a conversation in which each discipline can constrain the others without pretending to possess the final word.

That, I suspect, is where the genuinely interesting version of an integral project begins.