Interval Semantics

At the mini-conference held on May 2, 2026, the presenter—a researcher specializing in linguistics rather than computer science—delivered a talk centered on the intersection of their primary fields: linguistics, philosophy, and ethics. The presentation was structured into three sections, but due to time constraints only Sections 1 and 2 were covered. Active Q&A with the audience accompanied the talk, and an interdisciplinary discussion unfolded that drew together mathematics, computer science, and both Eastern and Western philosophy.

Section 1: An Inquiry into Interval Semantics

The Concept of the Interval and Its Mathematical Origins

An interval is a range defined by two edges, and it appears most frequently in mathematics and in everyday language (especially in temporal expressions). The presenter proposed ancient Greek geometry as its archetype. Rather than employing symbolic arithmetic, the ancient Greeks would designate an arbitrary length as "1" and represent numbers by repeatedly combining that unit—the oldest case in which the interval functions as the minimal unit of meaning.

In the context of number theory, the presenter distinguished three categories of number:

Ordinal numbers: Numbers that indicate order (1st, 2nd, 3rd…); the most familiar category.

Cardinal numbers: Notated with the Hebrew letter Aleph; bounded as the set of all ordinals; used to distinguish infinities of different magnitudes (e.g., the infinity of decimals between 1 and 2 vs. the infinity of all natural numbers).

Binary / computation: 0 and 1 are defined with respect to one another as edges, likewise forming an interval structure.

Electron Energy Levels and the Problem of the Reference Point

The presenter offered Paul Dirac's discovery as a key case study. Electron energy levels had been understood as a structure in which the ground state serves as a single reference point (zero) from which energy is absorbed and emitted. Dirac, however, discovered that the positron (anti-electron) could descend infinitely into negative energy levels below the ground state—the so-called Dirac sea. This demonstrates that a single reference point cannot encompass all possibilities of a system, and the presenter linked this to the problem of reference points in ethics.

The Philosophical Genealogy of Subjectivism and Moralism

The presenter summarized the debate over reference points in ethics as follows:

Kant: Posits the subject as the sole reference point of ethics; argues that only what arises from within—rather than from external pressure—can serve as a trustworthy ethical ground. Kant nevertheless acknowledged the existence of an objective external world and built his ethical system on the premise that the subject is an imperfect perceiver.

Descartes / Hobbes: Endorse a subjectivism that fixes the subject as experiencer.

Hume / Locke: Argue that the subject's ethics must remain fluid in response to environment, society, and pressure.

Moralism: Rather than a single subject-based criterion, it adopts multiple reference points—social values, historical context, interpersonal cues—but its excessive rigor tends to foreclose actual possibilities.

Language and Interval: The Definitional Problem of "human" and "good"

Using the definition of the English word "human" as an example, the presenter argued that the meaning of natural language is determined not by a single reference point but by an interval. Within a subjectivist frame, the ground states of two persons cannot be synchronized, and so the reference point for any given signal is always in flux.

In addressing the definitional problem of "good," the presenter applied formal logic to point out that the opposite of "all" within a set is not "zero" but "some"—that is, the set of all possibilities. To bound "good" solely by contrast with "bad," then, commits a logical error that excludes the countless possibilities of neutrality, slightly good, slightly bad, and so on.

Eastern and Western Philosophy and the Interval: Taikyoku and the Ring

A point raised in discussion with the audience was that Eastern philosophy accommodates the concept of the interval more naturally.

Taikyoku (太極): A closed-ring structure in which good and bad are defined with reference to one another; each concept takes the other as its edge, operating like a finite state machine (FSM).

Western philosophy: Tends to introduce an externally encompassing infinity, corresponding to an open-group structure.

Mathematically, Eastern philosophy denies the existence of infinity; paradoxically, however, that strong negation generates a self-reference adjacent to the very concept of infinity.

The Limits of a Single Reference Point and Its Statistical Resolution

The presenter took the rating system of a film review site (e.g., out of 10) as an example to show that a single reference point is manipulable as users shift their personal baselines and that the result converges on a normal distribution. An audience member suggested that statistical methodology is the practical means by which reference points are established in real life; the presenter agreed and added dialectics—the acquisition of standards through one's relations with others—as a complementary approach. Citing the case of an AI detector classifying the U.S. Declaration of Independence as AI-generated text, the presenter noted that a system cannot establish its reference point from within itself alone and must rely on external systems (e.g., OpenAI's usage records).

Section 2: An Epistemology of Translation in the Context of Machine Assembly and Program Code

LLMs and the Transactionality of Language

Introducing LLM research that draws on text mining and regression analysis, the presenter reported that millions of regression analyses over billions of variables have shown human language to be replicable. This empirically supports the transactionality of language—its transactional structure of input and output—and reinforces an analytic interpretation that treats language as a formal system.

The Noumena / Phenomena Distinction in Translation

Borrowing concepts from Kant's philosophy, the presenter distinguished two layers of translation:

Noumenal translation: Reproducible expression that exists independently of perception—for example, the fact that "Let's go" and its Japanese equivalent both elicit the same action (following along).

Phenomenal translation: The subject's conscious experience of the same meaning upon hearing the two expressions in the two languages.

Layers of Code Abstraction and Language Acquisition

The presenter argued that the abstraction hierarchy of program → assembly → machine code is defined by the way humans experience code. Applied to language acquisition, this parallels the hierarchical structure of proto-language, intermediate language, and fully-fledged natural language.

The two main axes of language acquisition theory contrast as follows:

Usage-based theory: Language is acquired through the accumulation of input; evidence includes the fact that an infant can compose sentences after only two years of input. The object-orientation of programming languages partially supports this view, but the existence of features shared across languages (word order, phonology, etc.) suggests an innate capacity, generating an internal contradiction.

Generative grammar: Humans are born with an innate capacity for linguistic performance (universal grammar); the hypothesis being that a German infant and an Indian infant, were their environments swapped, would exhibit identical patterns of language acquisition. The presenter noted that this theory leans on non-linguistic domains such as psychology and spirituality, and judged that any attempt to equate code with language along this axis leads to a dead end.

Conclusion

The presenter proposed that interval semantics is the first abstraction layer underlying both subjectivism and modern moralism. Single-reference-point systems reveal their limits across diverse domains—electron energy levels, the definition of natural language, ethical systems, rating systems—and an interval structure consisting of two edges is required if the full range of real possibilities is to be encompassed. Drawing a connection to the way developments in communication technology have tended to reduce the frequency of genocide, the presenter also offered the optimistic prospect that ethical outcomes improve as the edges of the interval narrow. Section 2, through its analysis of LLMs, translation, and language acquisition, argued that language has a transactional and modular structure, and concluded that the innateness hypothesis of generative grammar runs into limits in the context of any analogy with code. Section 3 was not delivered owing to time constraints.