Two Paths to One Insight

It's probably apparent by anyone who's come across my thinking that I've spent a lot of time digesting the work of Alain Badiou (not exclusively of course, as pertains to philosophers), and primarily because I find there's a certain clarification factor that happens when one applies mathematical thinking to problem sets. Another thinker that I've been highly drawn to is in the Buddhist tradition, Bhante Madawela Punnaji, and whose focus for many years was to unscramble several centuries of what one might call (after Eduardo Viveiros de Castro) uncontrolled equivocation --the false consensus or illusion of understanding that occurs when imagining that the Other is just a "version" of yourself who happens to have different opinions. 

So we have two thinkers, representing two movements, one ancient, one modern, approaching a mountain from opposite sides. Bhante Punnaji, interprets Pali Suttas such that the "illusion of existence" - our tendency to mistake fluid experience for fixed entities - becomes key to unraveling the 2nd Noble Truth (samudaya - the origin/cause of suffering). Alain Badiou, uses set and category theory to show how "existence" is merely appearance in a world, distinct from being itself.

To be clear, of course, they have very different objectives in their work and my bringing them together is mostly for curiosity's sake. Any conceptual alignments are thus taken in different directions and have different implications than they would have for their own projects. But I find that there is something helpful in exploring certain, perhaps deceptive, convergances between their defintions of "existence" for how they might inform our thinking about our own conceptions of it and its related concepts.

The Mathematical Structure of Appearance

In Badiou's "Logics of Worlds," existence isn't binary - things don't simply exist or not exist. Instead, existence comes in degrees, like a dimmer switch rather than an on/off button. But here the crucial technical detail is that these degrees don't directly measure existence itself. Rather, Badiou employs what he calls "transcendental indexing" - a function that measures degrees of identity between elements in a world.

Mathematically, this works through complete Heyting algebras (which Badiou calls "transcendentals"). Unlike classical set theory where an element either belongs to a set or doesn't (x ∈ S or x ∉ S), Badiou uses structures from topos theory - specifically the theory of Ω-sets - where relationships can have gradations. The transcendental T of a world is a complete Heyting algebra that provides the logical scaffolding for measuring identities and differences.

Here the key insight is that the existence of any element is defined as its self-identity: Ea = Id(a, a). Where : 

• $a$: An object or element in a specific "world."
• $Id(a,a)$: This is the "Identity" function. In an $\Omega$-set, this function doesn't return "True" or "False." Instead, it returns a value from the Heyting algebra (the "Transcendental").
• $Ea$: This stands for the Existence of $a$.

In sum, ones degree of existence in a world is precisely how identical you are to yourself in that worlds' logic of appearing.

Consider yourself reading this post. Your existence has varying intensities across different contexts:

• Maximum existence in your immediate phenomenological world (Id(you, you) = M in your experiential world)
• Moderate existence in your social networks (partial identity values in professional contexts)
• Minimal existence in distant contexts you've never encountered (Id(you, you) → μ in unreached worlds)

The Psychological Trap: From Process to Thing

Connecting this to Bhante Punnaji's insight becomes crucial. The "illusion of existence" isn't that nothing exists - it's that we mistake these degrees of appearing for non-fabricated permanent, substantial entities. We commit what we might call a "category error of consciousness."

Punnaji describes how we habitually transform experience (a process, a flow, a verb) into existence (a thing, an entity, a noun). Crucially, he shows that perception creates both subject and object. When we focus on perception, we believe in a perceiver (self) and something perceived (world). But when we focus on the process of perception itself, we realize both are constructions.

This is precisely what happens when we confuse Badiou's transcendental indexing with ontological permanence. We see strong appearance (high transcendental values) and think "natually existing, real, permanent self," when mathematically we're only observing temporarily high values in a transcendental algebra.

The Formalization of Suffering and Emptiness

Let's formalize this intersection of Buddhist psychology and mathematical ontology:

The Transcendental Indexing Function:

• Id: A × A → T (where T is the complete Heyting algebra)
• Measures degrees of identity between elements in a world

The Reification Error:

• Input: Fluid transcendental values (changing degrees of appearance)
• Cognitive Operation: Mistaking high Id values for essential properties
• Output: Presumed permanent non-fabricated entities
• Result: Suffering (mismatch between model and reality in lived experience)

When we're constantly trying to "solve" for permanent values in what is actually a dynamic system, we create suffering. It's like trying to find the fixed point of turbulent flow - mathematically possible in abstraction, psychologically exhausting in practice.

In my head I see the concept of suññatā (emptiness) - experience becoming empty of self and world - mapping onto Badiou's minimal degree μ in the transcendental. When Id(x, y) = μ, there is absolute difference, no identity between elements. This is the mathematical expression of non-self: not that nothing exists, but that nothing exists with the permanence we attribute to it.

Atoms of Appearing and Super-Perception

Badiou's theory includes a crucial concept: every object has an atomic decomposition. These "atoms of appearing" are the fundamental units through which a multiple's being manifests in a world. His "postulate of materialism" states that every atom is real - connected to actual elements of the underlying multiple. This provides the bridge between pure being (mathematics) and appearing (logic).

This atomic structure resonates with what Punnaji calls "super-perception" (abhiññā) or apperception. The ordinary person perceives objects and concludes they exist. The awakened person super-perceives - they're aware of the process of perception itself and therefore don't conclude that objects have independent existence.

In Punnaji's terms, this transforms normal perception (viññāna) into "anidassana viññāna" (non-manifest perception), where:

• No solid, liquid, heat, or motion is cognized as existing
• No long/short, large/small, pleasant/unpleasant appear as properties
• Not even names or images meet as entities
• When perception is stopped, all objects disappear (these are paraphrasings from the Kevatta Sutta DN11 if you're wondering.)

Put more clearly, non-manifest perception allows for a self-correction of the human propensity to fall into existence-being (subject) and existence-projecting (object) or put in Badiouan terms, a self-correction of the transcendental illusion, the mistaken belief that the way a multiple 'appears' in a world is identical to its absolute 'being'.

The Event of Awakening and Retroaction

Both thinkers point to moments of fundamental transformation. For Badiou, an event modifies the transcendental of a world, changing the very logic by which things appear. This creates what he calls a "retroactive effect" - appearing actually restructures being through the atomic decomposition.

For Punnaji's interpretation of the dhamma, awakening (from existential to experiential thinking) similarly transforms not just perception but the entire structure of experience. The Buddhist "paradigm shift" from existence to experience parallels Badiou's evental modification of transcendental structures. Both involve a fundamental restructuring of how appearing/experience functions.

Death as a Category of Appearing

Both thinkers converge on a profound point: death is not an ontological category but a logical/phenomenological one.

For Badiou, death is simply the passage from some degree of existence to minimal existence (μ) in a world. As he notes, following Spinoza: "No thing can be destroyed except through an external cause." Death is a consequence of changes in the transcendental indexing, not an internal property of being.

As Punnaji describes the teachings of the Buddha, death only exists within the illusion of existence. Once you awaken from the dream of existence, death loses its meaning because you realize you never existed as a fixed entity that could die. You were always a process appearing with varying intensity.

Experience vs. Existence: A Categorical Distinction

In category theory,  one distinguishes between:

• Objects (what we typically think "exists")
• Morphisms (transformations, relationships, processes)

The insight shared by both thinkers: consciousness is primarily morphism-like rather than object-like. Experience is the primary category, with "existence" being a derived concept - a snapshot we take of ongoing transformation.

In Punnaji's language experience is primary, existence is constructed. Badiou's mathematics gives us formal tools to understand how this construction happens through transcendental operations in specific worlds. Together, they point toward what we might call a phenomenological materialism - not crude materialism that reduces everything to matter, but a sophisticated understanding that recognizes both the reality of appearing/experience AND its constructed, processual nature.

Practical Implications: Debugging Consciousness

Think of meditation as debugging code. The bug isn't that you experience things - it's the reification function that converts experience into presumed permanent existence. Badiou's framework suggests this bug operates by:

1. Taking high transcendental values (strong appearance)
2. Interpreting them as essential properties
3. Creating fixed point assumptions where none exist
4. Generating attachment to these presumed fixed points

The fix? Recognize the categorical nature of experience. See the morphisms, not just the objects. Understand that your existence, mathematically speaking, is always indexed to a world, always partial, always in transformation.

Liberation in Mathematics

Understanding existence as graded appearance rather than binary being isn't just philosophically interesting - it's psychologically liberating. When you realize that your "self" is not a fixed set-theoretic object but a category-theoretic process with varying degrees of appearance, several things happen:

• Reduced Attachment: Why cling to what is mathematically shown to be processual?
• Increased Flexibility: You can work with degrees rather than fighting for absolutes
• Natural Compassion: Others are also processes appearing with varying intensity
• Freedom from Death-Anxiety: Death is just a modification in transcendental indexing, not annihilation of being

The Meeting Point

If one is not a fixed set but a site of appearance, not an existent but an experience undergoing constant transcendental indexing, then both mathematically and experientially - grasping relaxes. Not because nothing matters, but because you finally understand the actual structure of mattering itself. In Badiou's mathematical universe, you're a dynamic pattern of transcendental values. In Punnaji's phenomenology, you're the flowing process of experience itself.

Both paths lead to the same conceptual summit (but with different implications for the 'what to do about it' that we won't get into here): freedom from the illusion of fixed existence, and entry into the fluid reality of becoming. The mathematics of illusion reveals itself as the illusion of fixed mathematics - and in that revelation lies liberation.