The Unsigned Universe and the Staircase of Axioms: Language and Intelligence through the Circulation of Difference and Sameness (서명 없는 우주와 공리의 계단: 다름과 같음의 순환으로 본 언어와 지능의 원리)

As an epistemological counterpoint to purely experiential, post-linguistic superintelligence ("Era of Experience" · "Ineffable Intelligence"), this paper establishes why human language, dialogue, and shared axioms are structural prerequisites for the sustained growth of intelligence through three foundational principles: 1. The Unsigned Universe and the 4-Cell Epistemic Lattice: Unlike a simulation where a designer explicitly defines ("signs") the rules and reward function, the universe we inhabit never officially declares or signs any hypothesis as eternal, final truth; it merely returns working outcomes when we act upon it. Scientific inquiry classifies phenomena within this unsigned universe into a four-cell lattice: (1) Decidable Observation (True/False), (2) Undecidable Observation (structural indeterminacy such as 0/0), (3) Known Unknown, and (4) Unknown Unknown (etc.). Because the fourth cell (etc.) encompasses everything not yet conceived, the structure of the four cells is logically complete (MECE), yet inside an unsigned universe their interior can never be 100% filled. 2. The Law of the Asymptote and the Axiomatic Leap (0.999... ≡ 1): Within the unsigned universe, neither humans nor superintelligence can ever reach absolute truth (1) through observation alone; both can only approach the asymptote (0.999...). Nevertheless, to initiate the next level of inquiry rather than halting in infinite regress, intelligence must lay down a stepping stone—an Axiom (shared agreement) that declares 0.999... ≡ 1 once cross-validated across diverse perspectives. 3. The Circulation of Difference and Sameness, and the Essence of Language: Examined down to microscopic limits and spacetime coordinates (x, y, z, t), no two entities in the physical world are identical; the essence of the physical world is pervasive Difference. Complete, non-asymptotic Sameness (1 = 1) holds strictly as truth only within the axioms and language established between distinct observers through dialogue. Even the digital world of 0s and 1s rests upon the two deepest foundations of all information: There is Difference (0 ≠ 1) and There is Sameness (1 = 1). Genuine growth is the unending circulation: Difference → Agreed Sameness (Axiom & Word) → Discovery of New Difference → Wider Sameness. --- 본 논문은 순수 경험 기반의 탈언어적(Post-linguistic) 초지능론(Era of Experience · Ineffable Intelligence)에 대한 인식론적 반론으로서, ① 서명 없는 우주(Unsigned Universe)와 관측의 4분류 격자(결정 가능, 결정 불가능, 모름, 모름의 모름 etc.), ② 점근선(0.999...)에서 공리(=1)로의 도약, ③ 물리 세계의 ‘다름’과 공리 세계의 ‘같음(1=1)’의 순환이라는 세 가지 원리를 통해 왜 지능의 지속적 성장에 인간의 언어와 대화가 필수불가결한지 규명한다.