Language and Its Remainder: The Semantic Layer and the Ontological Layer in the Age of AI
语言的余项：AI时代的含义层与存在论层
Supercalifragilisticexpialidocious — the word you say when you don't know what to say. It carries no fixed semantic content, yet it is anything but meaningless. It is the sonic surfacing of the non-empty residue (ρ) that the construct (C) inevitably leaves behind when it attempts to cover the experiential domain (U): not naming the remainder, but acknowledging it.
Language is the subject's chiseling of the markability subspace of the Law of Identity. Chiseling necessarily produces remainder. This paper argues that linguistic remainder has two structural layers: a semantic-layer remainder (meaning associations severed by discrete symbols — the inexpressible, the untranslatable, the inexhaustibility of metaphor) and an ontological-layer remainder (directionality, momentariness, relationality — conditions of subjecthood that no representational system can internalize).
In the pre-AI era, these two layers were entangled and indistinguishable. Large Language Models (LLMs), by lowering the effective discreteness of their internal representations, systematically reclaim much of the semantic-layer remainder. This reclamation exposes the ontological-layer remainder in pure form for the first time: not "what cannot be said" but "who is speaking," "why this and not that," and "the act of speaking right now." The LLM is a developer between the two layers.
AI-era language use has two structural modes. Cultivation: the LLM's total construct exceeds the user's, illuminating the user's blind spots; the user claims their own remainder; the chiseling subject remains human. Colonization: the user substitutes the LLM's construct for their own; chiseling ceases; the remainder is bypassed. The criterion: whether the LLM permits the user to exercise negation upon the LLM itself.
Everyone needs to find their own supercalifragilisticexpialidocious — the sound they make at the site of their own remainder. AI can help you find it, or it can route you around it. The difference is cultivation versus colonization.
Chapter 1. The Problem: Why Language Has Remainder
Core thesis: Supercalifragilisticexpialidocious is not nonsense; it is the purest surfacing of linguistic remainder. The chiseling of the markability subspace necessarily produces non-empty remainder. Linguistic remainder is not a failure of expression — it is a structural product of C(U). The central question for the AI era is not "does remainder still exist" but "on which layer."
1.1 When you don't know what to say
Mary Poppins teaches the children a word: supercalifragilisticexpialidocious. When you don't know what to say, say this word, and you'll feel better. At the moment of its birth, this word carried no fixed semantic content. In Saussure's terms, it was nearly pure signifier without signified. By orthodox linguistic standards, it was close to noise.
But it was anything but noise. It was a sound emitted at the boundary of the language system — at the point where "the construct cannot reach," where the subject responded to that unreachability with the sheer materiality of sound. It was not naming, not describing, not explaining. It was acknowledgment — a sonic event marking "here is something my construct cannot reach."
Saying this word makes you feel better — not because the remainder is eliminated, but because your relation to the remainder changes: from "I can't say it" (passively trapped) to "I know I can't say it, and I have made a speech act out of the very inability to say" (actively acknowledging). Acknowledgment does not eliminate remainder; it repositions the subject relative to it.
Then the word was recaptured: Merriam-Webster entered it as "extraordinarily good, wonderful." A sound born at the site of remainder acquired fixed meaning — a textbook case of remainder being reclaimed by construct. But reclamation erases the moment of acknowledgment. The original supercalifragilisticexpialidocious is a surfacing of remainder; the dictionary's is the construct's co-optation of it. The tension between these two is what this paper addresses.
1.2 Chiseling necessarily produces remainder
ZFCρ Paper 1 proved that C(U) necessarily produces non-empty remainder ρ. Language I argued that language is the subject's second-order chiseling of the markability subspace, but barely addressed remainder directly. This paper fills that gap.
Chiseling the markability subspace is naming — "this is called dog, not cat." Every act of naming is a C(U) operation. What is not bound — everything about this particular dog: its smell, the light in its eyes, the inarticulable feeling you had when you first met it — is remainder. Remainder is not "what hasn't been named yet." It is structural: every act of naming simultaneously eliminates an old remainder and produces a new one. The remainder non-emptiness theorem, in its linguistic instantiation, says: naming can never be completed.
1.3 Everyday forms of linguistic remainder
Linguistic remainder is not a philosopher's invention. Everyone encounters it daily. Words failing: you have a feeling; after speaking, you realize "that's not quite what I mean." Tip of the tongue: a word is right there but you can't produce it — "knowing it's there but being unable to say it" is a pure surfacing of remainder. Implicature: what you want to convey is not on the surface; Chinese culture has a highly developed sensitivity here: "overtones beyond the strings," "words end but meaning is boundless." Untranslatability: "Saudade," "wabi-sabi," "Sehnsucht" — these words have no exact equivalents, because different languages chisel the markability subspace differently, leaving differently shaped remainders.
These everyday forms share a common feature: they all occur on the semantic layer — about "meaning not covered by form." The root of semantic-layer remainder is the discreteness of human language.
1.4 Remainder is not only on the semantic layer
When you say "I understand you" to someone, even if the sentence is perfectly precise on the semantic layer, something is still left out: the fact that you are saying this to this person right now. Language is not merely a meaning-delivery system. Language is the subject's activity. At the moment of speaking, the subject occupies at least three dimensions beyond meaning-delivery:
Directionality. Why did you say this sentence and not another? The act of selecting — "I negated all other possibilities and chose this one" — is the exercise of negativity, not meaning.
Momentariness. "I am saying this now" — the "now" is not a timestamp. A timestamp is the trace of a past now; the moment you write it, "now" has already moved.
Relationality. "I am saying this to you" — the "to" is not an information channel but an orientation between two subjects. The same "I love you" said to different people has identical meaning but entirely different relationality.
Directionality, momentariness, and relationality are conditions of the subject's activity itself — residues that no representational system can internalize. This is ontological-layer remainder.
1.5 The two layers' inseparability and AI-era separation
In the pre-AI era, these two layers were entangled, impossible to tell apart. When you experience "words failing," you cannot distinguish whether it's a vocabulary problem (semantic layer) or an inherent uncapturability of the present moment (ontological layer).
The AI era changes this. LLMs reclaim much of the semantic-layer remainder. Once the semantic-layer remainder is systematically reclaimed, the ontological-layer remainder stands exposed in pure form: not "what cannot be said" but "who is speaking," "why this," "the act of speaking right now." The LLM is a developer between the two layers — just as a chemical developer makes a photographic negative's latent image visible.
Chapter 2. Two-Dimensional Structure: Foundation and Emergence of Linguistic Remainder
Core thesis: Linguistic remainder unfolds within a two-dimensional meta-structure. Foundation layer: the non-eliminable meaning residue produced by chiseling. Emergent layer: the ways remainder becomes perceptible in linguistic activity.
2.1 Foundation layer: generation of remainder
Every act of chiseling produces remainder. A key characteristic: remainder changes shape as chiseling deepens, but does not diminish. Initial chiseling ("this is called dog") leaves coarse-grained remainder. Further chiseling ("golden retriever," "three years old," "gentle") reclaims some, but each new word produces new remainder. This corresponds precisely to ZFCρ: expanding the axiom system covers more objects, but remainder non-emptiness is not eliminated.
The foundation layer generates remainder in two modes: Frontier remainder — encountered at the leading edge of expression, where existing vocabulary is insufficient; poets work here most frequently. Background remainder — passed over unconsciously when using existing vocabulary; every everyday word carries meaning fragments never noticed.
2.2 Emergent layer: surfacing of remainder
Once generated, remainder needs to be perceived, acknowledged, responded to. Basic modes of remainder surfacing:
Silence. Meaningful silence — a pause in conversation, an ellipsis in a letter, white space in a poem — is remainder's most direct surfacing. Metaphor. Using one domain's construct to illuminate another domain's remainder; the illuminated parts are revealed, the obscured parts are the metaphor's own remainder. Repetition. Beckett's Waiting for Godot is almost entirely composed of repetition — because what they are trying to express carries enormous remainder in any single utterance. Coinage. Supercalifragilisticexpialidocious coins not at the level of meaning precision but at the level of remainder acknowledgment. Dialogue. Each turn responds to the previous turn's remainder and produces new remainder for the next — a relay of remainder. When a deep conversation ends and both parties feel "there's still more to say" — this is the structural necessity of dialogue as remainder relay.
2.3 Dialectical support between the two dimensions
Foundation catalyzes emergence: new remainder generation catalyzes new surfacing methods. Stream of consciousness as a narrative technique emerged because the remainder of fragmented conscious experience could not be covered by traditional narrative construct. Emergence catalyzes foundation: existing surfacing methods make new remainder perceivable. Before the metaphor "time is money," the irreversibility of time was a silent remainder. After, "time is not like money because money can be earned back but time cannot" suddenly became perceivable.
Chapter 3. Domain-Specific Distinction: Semantic-Layer Remainder and Ontological-Layer Remainder
Core thesis: Linguistic remainder has two structural layers — semantic-layer remainder and ontological-layer remainder. The emergence of LLMs makes these two layers structurally distinguishable for the first time.
3.1 Semantic-layer remainder: the cost of discreteness
Semantic-layer remainder originates in human language's discreteness. Structural characteristics:
Continuous meaning severed by discrete cuts. Between "mild unease" and "deep terror" lie infinitely many intermediate states, but vocabulary is discrete — "unease," "anxiety," "fear," "terror." The meaning in the gaps is remainder.
Associations severed by boundaries. "Sorrow" and "autumn" are two separate cells; the association between them requires the subject to actively build it. Before being actively built, cross-cell associations are remainder.
Context filtered by formal identity. "Home" in everyday use is a location label; in a dying person's last words, its meaning density is entirely different — but the form is the same word. Formal identity filters out contextual variation.
Semantic-layer remainder is conditionally reclaimable — switching to a lower-discreteness representational system can reclaim some of it.
3.2 Ontological-layer remainder: the non-internalizable conditions of subjecthood
Ontological-layer remainder is not "finer-grained meaning." It is not on the meaning dimension at all.
Directionality. The act of selection — "I negated all other possibilities and chose this one" — is the exercise of negativity. Negativity is not the object of representation but the condition under which representation occurs. Every attempt to represent directionality itself has directionality.
Momentariness. "It is happening right now" cannot be captured by a timestamp. A timestamp is the trace of a past now — the moment you write it, "now" has already moved. Momentariness remainder is temporal in essence: its nature is uncapturability.
Relationality. "I am saying this to you" — the orientation between two subjects. The same sentence "I love you" to different people has identical meaning but entirely different ontological facts.
The key characteristic: it is not conditionally reclaimable. No matter how large or fine-grained your construct, ontological-layer remainder does not diminish — because directionality, momentariness, and relationality are preconditions for the construct to operate, not objects for it to act upon. You cannot use a tool to process the tool's user.
3.3 LLM's systematic reclamation of semantic-layer remainder
LLMs do not simply "cancel discreteness." LLM input and output remain discrete tokens — the discrete interface is always present. What LLMs actually do is significantly lower the effective discreteness at the internal representation layer while retaining the discrete interface: tokens are mapped via embeddings into a high-dimensional continuous vector space.
In the LLM's internal representation space: "Sorrow" and "melancholy" are neighboring positions with continuous transitions — inter-cell gaps reclaimed. The association between "sorrow" and "autumn" is directly encoded in relative position — cross-domain associations reclaimed. "Home" in different contexts occupies different representational positions — contextual variation reclaimed.
The LLM's analogy, cross-domain association, style transfer, and context sensitivity — from the perspective of remainder, these emergent capabilities are the systematic reclamation of semantic-layer remainder.
"Much" rather than "all" — LLM hallucination can be understood from this angle: the free sliding of meaning in continuous space is the cost of reduced semantic-layer remainder. Discrete boundaries both produce remainder (severing meaning) and provide anchors (preventing sliding). LLMs lower discreteness, simultaneously reducing both remainder and anchors.
3.4 Development: what is exposed after semantic-layer reclamation
Once the LLM systematically reclaims semantic-layer remainder, ontological-layer remainder is exposed from beneath. Now you have an LLM. You input that feeling; it unfolds twenty ways of expressing it. But looking at the output, you still feel "something's still missing." That "something missing" can now be precisely located: not a matter of meaning precision but ontological-layer remainder — "this isn't me speaking," "my present state is not in here," "these words are not addressed to anyone."
A non-trivial corollary: before the AI era, all philosophical discussions of linguistic remainder — Wittgenstein's "what cannot be said," Derrida's différance, Zen's "no reliance on words" — were actually discussing remainder without distinguishing between the two layers. Before the LLM's appearance, this distinction had no empirical basis. The LLM provides, for the first time, a purely semantic-layer operator — extremely strong at semantic-layer reclamation but having no subjecthood, so ontological-layer remainder is entirely absent from it. Precisely because the LLM has no subject, the boundary between the two layers becomes empirically observable for the first time.
Chapter 4. Colonization and Cultivation: Language Relations in the AI Era
Core thesis: AI-era human-machine language relations have two structural modes — cultivation and colonization. The criterion: whether the LLM permits the user to exercise negation upon the LLM itself.
4.1 Cultivation: LLM illuminates the user's blind spots
The LLM's total construct exceeds any individual user's construct. This means: what your C cannot cover in U, the LLM's C can reach. Your remainder falls within the LLM's construct domain.
The basic mechanism: you write something and get stuck — words fail, you cannot continue. The point where you get stuck is where your remainder surfaces. You hand the text to the LLM; it unfolds it in its larger construct domain. The critical next step: you see the LLM's unfolding and say "yes, that's what I was trying to say but couldn't" — in that moment, you claim your own remainder. Or you say "no, that direction isn't what I want" — in that moment, you negate the LLM's unfolding, and that negation is itself an act of chiseling only you can perform.
Cultivation takes several forms: Unfolding cultivation — the LLM offers ten possible expressions; you find one by recognition, not selection by the LLM. Contrast cultivation — "that's not it" — the negative reaction itself clarifies what you actually want. Relay cultivation — you and the LLM form a dialogue, a remainder relay.
The criterion for cultivation: the user consistently retains the right of negation over LLM output, and exercises that right in practice.
4.2 Colonization: LLM replaces the user's chiseling
You hand the LLM a request — "write me an email," "write me an essay" — the LLM returns text, and you use it directly. The deep structure: the chiseling in that text is not your chiseling. The LLM unfolds meaning uniformly across its continuous space, outputting an "average-optimal" construct — but this construct has no directionality, because the LLM has no subject. It does not originate from your remainder.
Your own chiseling did not occur. That "stuck" point — the site where your remainder would have surfaced — has been routed around. Your remainder falls silent. Not eliminated (remainder cannot be eliminated), but bypassed. A single bypass is not colonization. Colonization occurs when bypassing becomes habit.
4.3 The deep mechanism of colonization: construct replacement
The first layer of colonization is behavioral: no longer writing yourself. The second layer is deeper: you begin thinking with the LLM's construct.
The LLM has a specific organizational style — a chiseling method. It tends toward enumeration ("there are several points"), toward symmetry ("on one hand... on the other hand"), toward mild summation ("overall"). This chiseling method is not a neutral formal tool — it is itself a system of meaning-cutting with its own remainder.
Moreover, production LLMs are not bare models — they have been pre-shaped by platform rules, alignment training, and default style guidelines. OpenAI's Model Spec prescribes the product model's intended behavior and default voice; Anthropic's Constitutional AI shapes model responses through a set of principles. What you internalize is not just "the LLM's average style" but what a particular company's product designers decided "good AI output" should look like.
The ultimate form of colonization: not that the user becomes remainder, but that the user is absorbed into the construct — the user's subjecthood remains a remainder, but it is suspended. Remainder is non-empty, the subject still exists, but the channel of contact between them is severed. This is the mirror image of Husserl's epoché: Husserl's epoché is liberatory (you pause habit, thereby seeing what habit concealed); colonization's suspension is suppressive (your remainder is shelved, thereby you cannot see what was originally yours).
4.4 The spread mechanism of colonization
Colonization is a gradual process with identifiable stages:
Stage one: convenience substitution. The LLM writes in unimportant contexts — routine emails, formatted documents. The chiseling subject is still the user. Not colonization.
Stage two: threshold drift. The user's judgment of "what counts as important" begins to drift. Each concession shifts the threshold further, with no clear breakpoint.
Stage three: aesthetic assimilation. The user feels the LLM writes "better" — clearer, more organized. This judgment is itself a symptom of colonization: the standard for "good" has been redefined by the LLM's construct.
Stage four: construct internalization. Even when not using the LLM, you think in the LLM's manner. At this stage, even if you stop using the LLM, the effects persist — because your construct has already been reshaped.
4.5 Criterion: retention of negativity
The criterion for cultivation versus colonization: whether the user still experiences their own remainder.
In cultivation, the user still gets stuck, still finds words failing, still struggles with expression. In colonization, the user no longer gets stuck — not because expressive ability has improved, but because chiseling has been handed to the LLM. Not getting stuck is not fluency; it is numbness.
More precise criteria: (a) Can the user identify the non-self portions of LLM output? (b) Does the user maintain their own chiseling in the most important speech acts — confessions of love, apologies, farewells, words spoken to yourself during a crisis? (c) Does the user's language still produce moments of self-surprise — writing along when suddenly a sentence emerges that you had not anticipated?
4.6 Structural map of the four interactions
| Positive (cultivation) | Negative (colonization / closure) | |
|---|---|---|
| LLM → User | LLM's larger construct domain illuminates user's blind spots; user claims their own remainder (unfolding, contrast, relay cultivation) | LLM's construct replaces user's construct; user's chiseling ceases; remainder is bypassed (convenience substitution → threshold drift → aesthetic assimilation → construct internalization) |
| User → LLM | User's negativity calibrates LLM's directionless unfolding; LLM's construct becomes more precise through user's chiseling | User rejects all LLM assistance ("I only use my own words"), sealing off the possibility of semantic-layer remainder reclamation; self-confined within human language's discreteness limits |
Note the fourth quadrant — user → LLM negative — structurally isomorphic with Dadaism. Rejecting all AI assistance appears to resist colonization but actually simultaneously rejects cultivation. The healthy state is neither wholesale embrace (colonization) nor wholesale rejection (closure), but dynamically maintaining cultivation. This equilibrium, like every cultivation equilibrium in this series, is unstable, requiring continuous active maintenance.
Chapter 5. Theoretical Positioning: Dialogue with Existing Discussions
Core thesis: This paper's remainder stratification, LLM as developer, and the cultivation / colonization framework form precise dialogues with existing discussions in language philosophy and AI ethics.
5.1 Dialogue with Wittgenstein's "what cannot be said"
Early Wittgenstein's "what cannot be said" — logical form cannot express itself — is a special case of semantic-layer remainder: conditionally reclaimable (switch to a metalanguage, and the formerly unsayable becomes sayable). Late Wittgenstein's "what can only be shown" is closer to ontological-layer remainder. But Wittgenstein did not distinguish the two layers. The framework's contribution: semantic-layer "unsayable" has been substantially reclaimed by LLMs; ontological-layer "unsayable" has become, after LLMs, more conspicuous than ever. Were Wittgenstein alive in the AI era, he might discover: LLMs perform brilliantly in "language games" (semantic layer), but "forms of life" — the living subject playing the game — remains beyond the LLM's reach (ontological layer).
5.2 Dialogue with Derrida's différance
Derrida's core argument — meaning forever slides along the chain of differences, never fully captured — is a precise description of semantic-layer remainder non-emptiness. But Derrida extends this into a deconstruction of all presence. The framework's response: the semantic layer indeed cannot fully arrive, but the ontological layer has a different kind of "arrival" — not the arrival of meaning, but the occurrence of the now. When you say "I am here" to someone, semantic-layer différance still operates, but the ontological layer contains a non-sliding fact: you are indeed here right now. The LLM's arrival makes this dialogue concrete: the LLM performs infinite différance operations (meaning associations can be infinitely unfolded in continuous space), but it has no "being here right now." Derrida's différance is perfectly realized in the LLM — which is precisely why it reveals that what différance describes is not everything.
5.3 Dialogue with Heidegger's "language is the house of Being"
The framework agrees with Heidegger's core intuition but offers a more precise formulation: language is the subject's chiseling activity, and in the process of chiseling, the subject encounters remainder — this encounter is what Heidegger calls "dwelling." The AI-era question: if the user's chiseling is replaced by the LLM (colonization), dwelling is interrupted — not because language is absent (the LLM produces copious language) but because remainder encounter is absent. Language under LLM colonization is language in which no one dwells — the house stands, but no one is home.
5.4 Dialogue with contemporary AI ethics' "human-in-the-loop"
The framework agrees with the direction of "human-in-the-loop" but considers the formulation too weak. "Human-in-the-loop" positions the human as reviewer — but reviewing is not chiseling. If the "human" in "human-in-the-loop" is only a reviewer, that human will eventually be replaced by a better AI reviewer.
The framework's formulation is "human-in-the-chiseling" — the human's irreplaceable role is not reviewing AI output but providing direction for AI's directionless unfolding. Directionality is ontological-layer remainder — AI has no direction; humans do. "Human-in-the-loop" focuses on reducing AI's errors (semantic-layer problem). "Human-in-the-chiseling" focuses on preserving human directionality (ontological-layer problem).
5.5 Dialogue with translation theory's "untranslatability"
Semantic-layer untranslatability: two languages' C(U) operations leave differently shaped remainders. Conditionally mitigable — LLMs' translation capabilities at this layer already far exceed traditional machine translation. Ontological-layer untranslatability: the subject who spoke — that now, that direction, that relation — cannot be reproduced. Benjamin's notion that translation gives the original an "afterlife" touches precisely this layer: translation cannot reproduce ontological-layer remainder; it can only produce new ontological-layer remainder in the target language.
Chapter 6. Non-Trivial Predictions
Core thesis: Eight non-trivial predictions. The first three arise from the general structure of remainder; the last five arise from AI-era human-machine language relations.
A. General Predictions about Linguistic Remainder
A language's neologism production rate is not a linear function of time but exhibits a burst-quiescence-burst pulse pattern. Burst periods correspond to large-scale experiential rupture (technological revolution, cultural contact, war, migration); quiescence periods correspond to experiential stability. Burst-period rates correlate positively with the scale of rupture.
Reasoning: In normal states, background remainder does not catalyze new surfacing — people manage with existing vocabulary. Experiential rupture breaks this equilibrium: new experience produces large quantities of frontier remainder not coverable by existing vocabulary. When frontier remainder reaches critical density, surfacing is collectively catalyzed — a cluster of neologisms emerges.
Testable: Analyze diachronic lexical data (e.g., OED neologism admission time series, successive Chinese dictionary editions' supplements), testing whether neologism production rate shows a pulse pattern rather than linear growth. The framework predicts high correlation with identifiable experiential rupture events.
Non-triviality: Common sense assumes "language evolves steadily." This prediction argues: neologisms do not grow spontaneously from within; they are catalyzed by experiential rupture's remainder surfacing. Without experiential rupture, remainder stays silent and the language system tends toward stasis.
With comparable translation volume, translation between more structurally distant language pairs produces more target-language neologisms. Specifically: Chinese→English translation produces more English neologisms than French→English, which produces more than Spanish→English.
Reasoning: The greater the difference in chiseling methods, the greater the difference in remainder shapes — the more frequently translators cannot find target-language equivalents, and the more they are forced to coin.
Testable: Analyze parallel corpora (UN documents, literary translations), counting target-language neologisms across different language pairs. The framework predicts frequency correlates positively with typological parameter distance.
Non-triviality: Buddhist scripture translation into Chinese created enormous numbers of neologisms ("world," "causality," "instant," "awakening") — not because translators couldn't find existing equivalents, but because Sanskrit's and Chinese's chiseling methods differ drastically. The framework predicts this is structural necessity, not historical accident.
At comparable writing skill levels, active bilinguals produce first-language writing with higher metaphor density and greater originality of cross-domain associations than monolinguals' comparable writing.
Reasoning: Bilinguals have two chiseling methods; for the same experience, the two methods carve out differently shaped remainders. When a bilingual encounters remainder while writing in language A, language B's meaning-organization system provides a backup construct domain that can illuminate it.
Testable: Compare active bilinguals with skill-matched monolingual writers on creative tasks, measuring metaphor density and cross-domain association originality (blind-evaluated). The framework predicts bilinguals score significantly higher on both metrics.
Non-triviality: Common sense assumes "bilinguals' first-language ability is diluted." This prediction argues the opposite: bilingualism is not resource dilution but cross-illumination of remainder. Nabokov (Russian/English), Beckett (English/French), Kundera (Czech/French) provide case-level support.
B. AI-Era Linguistic Remainder Predictions
Alignment schemes that suppress hallucination by rebuilding hard boundaries structurally oppose the LLM's efficacy as a semantic-layer remainder developer. The stronger the hard-boundary alignment, the weaker the LLM's semantic-layer remainder reclamation capability. An optimal balance point exists: hard boundaries just sufficient to provide factual anchors without excessively severing the continuous representation space. Schemes that shape model behavior through internalized principles rather than hard rules (e.g., Constitutional AI's self-critique mechanism) may incur lower developer costs.
Reasoning: Hard-boundary alignment's core operation is reintroducing rigid constraints — functionally rebuilding hard boundaries in continuous space. Rebuilt hard boundaries suppress free meaning sliding (hallucination decreases) but simultaneously suppress free meaning association (emergent capability decreases).
Testable: Compare the same base model under different alignment schemes on two metric groups: (a) factual accuracy, (b) semantic-layer remainder reclamation capability. The framework predicts: under hard-boundary schemes, as strength increases, (a) first improves rapidly then saturates, (b) monotonically decreases. An inflection region exists where (a)'s marginal returns are small but (b)'s marginal losses accelerate.
Non-triviality: The mainstream narrative treats alignment as monotonically increasing good. This prediction argues: hard-boundary alignment has structural costs — not "model becomes dumber" but "model becomes weaker as developer." AI safety and AI's role as an assistive tool for human subjecthood exist in a tension requiring precise localization.
Text produced in cultivation mode scores significantly higher on remainder surfacing indicators — metaphor originality, semantic surprisal, non-conventionality of cross-domain associations — than the same user's output without LLM assistance.
Reasoning: The LLM's larger construct domain illuminates the user's blind spots, making previously silent remainder perceivable. More perceivable remainder means more frequent encounters; encounters catalyze new surfacing methods.
Non-triviality: Common sense assumes "writing alone" is more original than "AI-assisted." This predicts counterintuitively: cultivation-mode output exhibits higher remainder surfacing density — not because the LLM contributes content, but because it illuminates the user's own blind spots. A good mirror lets you see angles of yourself you've never seen before; the mirror isn't painting on your face.
People who habitually use the LLM in colonization mode exhibit monotonically decreasing inter-individual variation in their independent writing as usage duration increases.
Reasoning: Users internalize the LLM's chiseling method. The LLM's chiseling method is directionless — it outputs the same generic construct for all users. When different users all internalize the same construct, their independent output converges.
Testable: Longitudinal tracking study over one year; colonization-mode group vs. cultivation-mode group; stylometric metrics (vocabulary richness, syntactic complexity distribution). The framework predicts the colonization group's inter-individual variation decreases; the cultivation group's does not.
Non-triviality: Common sense assumes "using the same tool doesn't affect personal style." The LLM is not a pen (passive tool) but a chiseling method (active meaning-organization system). People who use the same chiseling method long enough converge in thought patterns — structural consequence of construct replacement, not side effect.
When the user provides explicit directional calibration (value judgments, aesthetic preferences, focal concerns — not a content outline), the LLM's long-text output exhibits significantly higher semantic coherence than output under no calibration — and, the stronger prediction, comparable to or exceeding content instruction calibration.
Reasoning: Directional calibration operates on the foundation layer (providing chiseling direction), while content instructions operate on the emergent layer (specifying concrete form). Foundation-layer direction provides continuous constraining force; emergent-layer specification loses constraint wherever the outline doesn't reach.
Non-triviality: Common sense assumes a detailed outline ensures coherence better than vague value expressions. This predicts: telling the LLM "where to head" rather than "which road to take" lets it go further.
At comparable creative complexity, "pure human writing" adherents produce texts with lower semantic-layer remainder surfacing rates — frequency of new metaphor production, rate of cross-domain association discovery — than cultivation-mode writers.
Reasoning: The user rejects all LLM assistance, sealing off the possibility of semantic-layer remainder reclamation. Meaning associations beyond their own construct domain remain permanently invisible.
Non-triviality: Common sense assumes "people who don't rely on AI think more independently, hence more creatively." Independent thinking and creativity are not the same thing. AI-rejecting writers preserve directionality (good) but limit their semantic-layer surfacing rate (a cost). This is not to say they are "worse" — they may be purer in ontological-layer remainder retention — but the framework predicts they pay a cost on the semantic layer.
Chapter 7. Conclusion: Find Your Own Supercalifragilisticexpialidocious
7.1 Reclamation
Language I demonstrated that language is the subject's second-order chiseling of the Law of Identity's markability subspace and demonstrated the LLM's negation of discreteness and its emergent consequences. This paper fills Language I's gap on linguistic remainder. Linguistic chiseling — naming — necessarily produces non-empty remainder. Linguistic remainder has two structural layers: semantic-layer remainder (the structural residue of discrete symbols severing meaning) and ontological-layer remainder (directionality, momentariness, relationality — non-internalizable conditions of the subject's activity). The LLM, by lowering effective discreteness, systematically reclaims much of the semantic-layer remainder, exposing the ontological-layer remainder in pure form for the first time. The LLM is a developer between the two layers.
7.2 Contributions
I. A strong construct without subjecthood as an epistemological condition. The LLM is the first "strong construct without subjecthood" in human history — making the boundary between the two layers empirically observable for the first time.
II. Stratification of linguistic remainder. Semantic-layer remainder (conditionally reclaimable) vs. ontological-layer remainder (unconditionally non-reclaimable). A structural finding unique to the language domain.
III. LLM as inter-layer developer. This explains a widespread intuitive puzzlement of the AI era: "AI can say anything, but something still feels missing" — what is missing is not meaning but ontological-layer remainder.
IV. Operational criteria for cultivation vs. colonization: (a) ability to identify non-self portions of LLM output, (b) maintaining one's own chiseling in the most important speech acts, (c) whether one's language still produces self-surprises.
V. The colonization spread model: convenience substitution → threshold drift → aesthetic assimilation → construct internalization.
VI. Eight non-trivial predictions, all falsifiable, all accompanied by competing factors and boundary conditions.
VII. "Human-in-the-chiseling" replaces "human-in-the-loop." The human's irreplaceable role is not reviewing AI output (semantic layer) but providing direction for AI's directionless unfolding (ontological layer).
7.3 Open Questions
I. Remainder structure across languages. Chinese's single-character polysemy may give Chinese a remainder structure different from English's — Chinese's remainder may reside more in "the relations between characters" than in "the insufficiency of individual characters."
II. Whether ontological-layer remainder has finer substructure. A candidate answer: negativity itself — directionality is negativity manifested in choice, momentariness in time, relationality in intersubjectivity.
III. Quantitative boundaries of cultivation / colonization. At what proportion of language acts conceded to the LLM does colonization become irreversible? Does threshold drift have detectable early indicators?
IV. Remainder structure of AI-AI dialogue. The framework predicts: LLM-LLM dialogue produces semantic-layer remainder but not ontological-layer remainder (no subjects means no directionality, momentariness, or relationality).
V. Remainder ethics. If colonization mode genuinely compresses the user's remainder experience, does this constitute a recognizable harm? Traditional AI ethics frameworks focus on bias, privacy, safety — all semantic-layer concerns. Remainder ethics concerns whether AI compresses the space in which the human acts as a chiseling subject.
7.4 Find your own supercalifragilisticexpialidocious
This paper began with a word: supercalifragilisticexpialidocious. A word with no fixed meaning, a sound made at the site of "can't say," an acknowledgment of remainder.
In the AI era, LLMs have reclaimed most of the semantic-layer remainder. The territory of "can't say" has shrunk dramatically. But once the semantic "can't say" shrinks, the ontological "can't say" stands all the more clearly: who you are, why you are saying this right now and not something else, to whom you are speaking. These are not questions the LLM can answer — not because it's not smart enough, but because these are not meaning questions. They are your remainder. Yours, not any model's.
Everyone needs to find their own supercalifragilisticexpialidocious. Not Mary Poppins's — that's hers. Your own: the sound you make at the site of your own remainder, the speech act at the point where your construct cannot reach. It might be a clumsy confession of love, a letter written and deleted and rewritten, an ungrammatical sentence muttered to yourself at three in the morning. It is not smooth, not polished, not "professional" — it carries your direction, your now, your "to you."
The LLM can help you find it — illuminating your blind spots, unfolding directions you hadn't seen, letting you recognize yourself through contrast. That is cultivation. The LLM can also route you around it — handing you a smooth text, sparing you the struggle with remainder. That is colonization. The distinction is not whether you use AI. The distinction is whether you are still chiseling — still at the stuck point, making your own sound.
This paper is the author's independent theoretical research. AI tools were used as dialogue partners and writing assistants during the writing process for concept development, argument testing, and text generation: Claude (Anthropic) served as the primary writing assistant; Gemini (Google), ChatGPT (OpenAI), and Grok (xAI) participated in paper review and feedback. All theoretical innovations, core judgments, and final editorial decisions were made by the author. The AI tools' role in this paper is comparable to a real-time-dialogue research assistant and reviewer, and does not constitute co-authorship.