Relative, Not Deterministic — On the Universal Form of Intellectual Activity

We can only think in signs. Words, formulas, diagrams, code — the moment we grasp something as something, we are already inside a system of differences among signs. If that is so, then the universal form of intellectual activity is relative.

If there is another form, I would like to hear it.

This piece states that single point. Relative, not deterministic — this is neither resignation nor relativism, but the only form available to beings who think in signs. The rigorous formalization is done elsewhere¹; here I put it in shop-floor language.

§1 The recursion of signs has no bottom

The meaning of a sign does not reside in the sign itself. It arises from its difference from other signs, is passed on to yet another sign, and has its settlement endlessly deferred. Derrida called this différance. What matters is the implication: there is no final ground to the chain of signs. No absolute base point that secures meaning exists, in principle.

Picture it this way. Iterate the simple recurrence $z_{n+1} = z_n^2 + c$ over the complex plane and the Mandelbrot set is drawn. However far you magnify its boundary, forms closely resembling the whole appear again at another scale; the zoom never ends. There is no bottom image of which you can say “this is the smallest unit.” The recursion of signs is like this: one operation — take a difference, pass it on — keeps producing similar forms (meanings) at every magnification, and never hits a floor.

“Determinism” is the desire to halt this bottomless recursion at some absolute ground. Having lost its ground with the death of God, Western philosophy has kept hunting for a replacement — structuralism placed “structure” there, deconstruction let go even of that, and analytic philosophy now tries to seat “logic and rigor” as the new ground². In that itinerary of swapping one absolute for another, only the moment of deconstruction admitted that there is no ground. And that “groundlessness” is exactly where Eastern thought began — dependent origination, emptiness (śūnyatā), pure experience, the wasan mathematics of Seki Takakazu, none of which posits a substantial base, all reading the world from relation and difference. The place the West reached after two millennia is the place the East started from.

§2 So it cannot be axiomatized — in principle

Can Verification and Validation be reduced to a formal axiomatic system of necessary and sufficient conditions? Try, and it collapses.

Necessary and sufficient conditions require an observer-independent, objective axis of evaluation. But subjectivity cannot be eliminated, in principle. Specifications are written in natural language, and their interpretation depends on the judging subject. The very judgment “this is fit for purpose” rests on the stakeholders’ intent. And even if you reduce to parts and verify each, the behavior that emerges on integration cannot be derived from the parts (non-additivity). The consistency of a sufficiently complex system cannot be proved from inside that system — a structure isomorphic to Gödel sits here.

This is not “we have not axiomatized it yet.” It is “in principle, we do not.” To try to close a bottomless recursion in a formal system is itself the impossible request.

Having no bottom, and verification never ending, are the same fact.

§3 So, V&V — internalizing the subject

If it cannot be closed as a formal system, the judging subject must be internalized. Subjectivity is not a contaminant to be removed but a constitutive component. This is not a defeat but a more honest formulation: the harder you try to close the system formally, the more the subject — “who verifies?” — is pushed outside and made invisible. Internalize it, and that responsibility becomes visible.

$$ \text{V\&V}(S,\ \text{judging subject},\ \text{context}) \;\vdash\; \text{provisional confirmation of validity} $$

“Provisional” is différantial: when the context changes, the judgment is updated. V&V is not something completed once; it keeps running as the context shifts.

§4 Scale is the integration interval

What différance shows is that the object of intellectual activity may sit at any scale. The meaning of a word, a single design decision, the history of knowledge — the same operation, “take a difference and let meaning stand,” works in all of them. So the structure of intellectual activity is scalable: one form can be applied at any scale you choose.

What is observed is always an integral. We see not the individual micro-processes but their accumulated effect. To choose a scale is to choose the interval over which you sum.

Think of a camera’s exposure to feel it. A photograph is the light integrated over the time the shutter is open: keep it open long and you capture night scenes and light trails; cut it short and a water droplet freezes in mid-air. For the same subject, what is captured changes with the interval you integrate over — and scale selection is exactly this. If differentiation is shiki-soku-ze-kū (extracting a difference-structure from the series of phenomena), then choosing the integration interval is kū-soku-ze-shiki (accumulating the difference-structure to recover the phenomenon) — and that recovery always carries an arbitrary constant $C$, that is, a decision.

But the choice of scale is not unconstrained freedom. The principled impossibilities physics shows — the uncertainty principle (a floor below which observation fails), spontaneous symmetry breaking (the existence of a scale at which order stands up) — bound which scales are available, or meaningful. So “thinking from what is happening in front of you” means: start from the phenomenon, and choose, under constraints, the magnification appropriate to what interests you.

§5 Three faces of one operation

This single operation appears with a different face in each domain — three projections of the same thing:

• Philosophy (différance) — permission. Anything that can be placed, as a sign, into the system of differences becomes an object — fictions included. The reality and the scale of the referent are not asked.
• Physics — constraint. Under principled impossibilities, choose the scale appropriate to the object of interest.
• Engineering (V&V) — decision. Judge fitness for purpose, fix the granularity, run verification, and cut it off here and now without closure.

Différance permits, physics constrains, engineering forces the decision. Within that trio you select a scale while preserving the form — and that is what it means to think relatively. The formal treatment of all three is collected in the Preprints.

§6 The decision is yours to take on

The decision goes outside the system, I said. But “outside” is not some higher tribunal or stronger axiom system. Since there is no bottom, no external authority exists anywhere to ground the decision. The terminus of externalization is yourself, as the subject who takes it on.

Precisely because there is no ground to hide behind, whoever decides bears the responsibility. To cut V&V off with “this is fit for purpose” is to take on, whole, the residue that cannot be proved. The decision resolves into responsibility. This is the ethical core of relativity, and it is what pragmatism means when it says “think from what is in front of you, and own the consequences.”

Whoever decides, takes it on.

Coda

The universal form of intellectual activity is relative, and its structure is scalable. What we stand on is not the “results” obtained at some particular scale. It is the repetition — choosing a scale, operating while preserving the form, and taking the decision on ourselves.

Relative, not deterministic. This is not a confession of weakness but the only stance available to a being who thinks in signs, when it tries to remain robust while taking groundlessness on itself.