Wei Wu

Before the core subject is addressed, several foundational concepts are clarified.

Throughout the development of philosophy, mathematics, physics, and other natural sciences, the construction of all human cognitive systems follows a shared underlying mechanism. Foundational concepts emerge within the constraints of human experience and cognitive capacities; conceptual systems built upon them are then tested and evaluated through empirical evidence and logical deduction. In essence, human knowledge progresses through iterative cycles of hypothesis formulation, empirical testing, and confirmation or falsification.

In its early stages, philosophy grounded its accounts of cosmic origins in cosmogonic or creation-narrative frameworks; mathematics constructs self-consistent logical systems from axioms; physics derives hypotheses from experience and validates, revises, and perfects theories through experimental observation. Human cognition advances within this iterative mechanism.

Yet beneath this seemingly comprehensive mechanism of knowledge production lies a profound and widely overlooked limitation. Human beings understand the world through established conceptual frameworks and repeatedly inquire into the nature of those concepts themselves, yet they remain trapped in this predicament: we define "time" but cannot articulate what time itself ultimately is; we model the evolution of the cosmos but continue to struggle with ultimate metaphysical questions such as "What, if anything, existed before the universe came into being?" These quandaries reveal the tensions and limits inherent in humanity's existing conceptual and cognitive systems. At these cognitive boundaries, there are neither settled conclusions nor well-established research paradigms. Thinkers of every epoch have confronted this intellectual predicament in the face of the unknown. Any theoretical research aiming to transcend traditional cognitive frameworks necessarily demands a fundamental paradigm leap.

Against this background, ALMA (Arche of Being: Logically Necessary Metatheoretical Architecture) formulates its central research question: Why can conceptual systems and cognitive models subjectively constructed by humans achieve structural correspondence with objective reality and remain empirically testable? It seeks to look beyond the surface phenomena of cognition, elucidate the underlying logic of the testability of conceptual systems, and derive conclusions that point beyond existing cognitive paradigms. ALMA is a philosophical paper and an Agda machine-checked formalization in dependent type theory and category theory, two facets of one work.

The paper advances propositions on Being. Self-Refutation: denying logical necessity uses language, logic, and argument, which already dwell within that very necessity, so the denial, in its very execution, presupposes and cancels itself; logical necessity is irreducible. Properties: Being has six mutually constituting properties—Self-Referentiality (taking itself as condition of its holding), Scale Invariance (fundamental properties and laws are applicable to all physical scales without exception), Infinity (unfolding with no termination or origin), Inhomogeneity (intrinsic differences at any scale), Conservation (invariant structure through change), Dynamic Interrelatedness (constituted by relations, not isolated). Not a flat list: Self-Referentiality needs infinite levels to avoid the self-devouring paradox; Infinity and Inhomogeneity together exclude any boundary-enclosed or absolutely homogeneous whole; Conservation and Dynamic Interrelatedness make change traceable under law; remove one and Being fails. On this basis, Beings condense from relational circuits into stable patterns, yielding causality and determinacy. A priori–empirical: these properties form an a priori framework, prior to and independent of empirical content, the condition for stating and understanding physical, mathematical, and logical content; thus causality and conservation are intrinsic to the a priori structure, not empirical inductions. Consciousness: emergence of bidirectional coupling between higher-order structures, irreducible to the superposition of lower-layer local relations. Being: from the foregoing, Being cannot be reduced to Nothingness—a necessary consequence of the a priori framework, not an added axiom. Overarching: these determinations constitute a logically necessary metatheoretical architecture.

The code realizes these one by one. Beings as containers (shapes = outward forms, positions = internal relation-nodes) realize Dynamic Interrelatedness; mappings and symmetries as functors and natural transformations make conservation a corollary of the functor laws, realizing conservation as a priori and intrinsic; the Grothendieck construction of the shape functor yields a category of shapes, capturing internal structure; a coalgebraic unfolding record—unfolding functor, next-layer seed assignment, position-to-shape condensation map, compatibility with the functorial action—formalizes parts condensing into wholes and the current layer generating the next, realizing Dynamic Interrelatedness and Infinity; homomorphisms between unfolding systems at two levels, object-level maps and higher-order coherence, the latter of which reserves a structural place for the higher-order bidirectional coupling posited in the consciousness proposition. Cosmos is the terminal coalgebra of the endofunctor induced by the unfolding structure Unfolding, coinductively Cosmos ≅ Unfolding(Cosmos), thereby making Self-Referentiality and Infinity (including its unbounded character) intrinsic, realizing Self-Referentiality and the Properties Proposition; UnitCosmos witnesses inhabitation—a constructive witness, at the formal level, that Being is indestructible; coalgebra homomorphisms give morphisms between cosmoses. Each fundamental property has a corresponding formal construction.

The central contribution of ALMA lies not in its transcendental-constitutive closure alone, but in the integration of that closure with a constructive, empirically substantive, and formally verifiable architecture. The closure rests on a deeper ontological commitment: logical necessity is not an arbitrary rule of thought but the structural expression of Being itself, and the Laws of Identity and Non-Contradiction are constitutive of any possible discourse. If isolated, however, this closure would risk being unfalsifiable; it is thus a necessary condition rather than a sufficient one. To address this, ALMA offers both positive theoretical construction and machine-checkable formalization, grounding the framework in empirical constraints without reducing it to a merely empirical model. At the same time, ALMA’s self-understanding remains subtly constructivist: its concepts are presented not as descriptions of an absolute ontology independent of cognition, but as cognitive coordinates reason constructs to grasp the unique, infinite, dynamic field it inhabits. This combination of ontological necessity and epistemic humility provides the basis for responding to nihilism, skepticism, and relativism while remaining open to empirical calibration and formal verification.

在切入核心议题之前，先厘清若干基础概念。

纵观哲学、数学、物理学与其他自然科学的发展，人类所有认知体系的建构均遵循统一的底层机制：基础概念在人类经验与认知的约束下形成，依托这些概念搭建而成的概念体系，再经由实证证据与逻辑推演加以检验与评判。简言之，人类知识的演进，是提出假设、开展实证检验、予以证实或证伪的迭代循环。

早期哲学以各类创世论框架阐释宇宙本原；数学从公理出发构建自洽的逻辑系统；物理学从经验中提炼假说，借助实验观测完成理论的验证、修正与完善。人类认知就在这一迭代机制中不断推进。

然而，这套看似完备的知识生成机制，潜藏着一个深刻却普遍被忽视的局限。人类借助既有的概念框架理解世界，也一再试图追问概念自身的本质，却始终走不出这一困境 —— 我们定义 "时间"，却说不清时间本身究竟是什么；我们推演宇宙演化，却仍受困于 "宇宙诞生之前存在什么" 这类终极形而上学问题。这些困境暴露出人类现有概念与认知体系的内在张力与固有边界。 立于此类认知边界处，既没有确凿定论，也不存在成熟稳定的研究范式。面对未知，历代思想者都曾陷入过这一思想困境。任何旨在超越传统认知框架的理论研究，都必然需要一场根本性的范式跃迁。

在此背景下，ALMA（存在之本原：逻辑必然的元理论架构）提出核心研究问题：人类主观建构的概念体系与认知模型，何以能够与客观现实形成结构对应，并具备实证可检验性？力图跳出表层认知现象，阐明概念体系可检验性的底层逻辑，推导出超越常规认知框架的结论。ALMA由一篇哲学论文与一份在 Agda 中以依赖类型论和范畴论机器可检验的形式化代码构成，二者是同一工作的两面。

哲学论文提出一组关于存在的命题。自我反驳命题：否定逻辑必然性须借助语言、逻辑与论证，而这些工具本身已栖居于该必然性之内，故否定在执行之际即预设其所否定者，否定自相取消，由此逻辑必然性不可被消减。属性命题：存在由六项相互构成的属性刻画——自指性指存在以自身为成立条件，尺度不变性指根本属性与规律适用于所有物理尺度而无有例外，无限性指存在的展开无终止亦无起点，非均匀性指任意尺度上必然存在内在差异，守恒性指变化之中持守的不变结构，动态关联性指一切存在者皆由关系构成而非孤立自存。此六项并非并列清单：自指须依托无限层级方免于自噬的悖论，无限性与非均匀性共同排除任何被边界封闭或绝对均质的整体，守恒与关联共同使变化在规律下可追溯，缺一则存在不成立。在此基础上，存在者由关联回路凝聚为稳定模式，并由此导出因果律与确定性。先验—经验命题：上述属性构成先验框架，先于且不依赖于任何经验内容，是物理、数学、逻辑内容得以被表述与理解的条件，故因果律与守恒律是先验结构的内禀要求，而非对经验的归纳。意识命题：意识被刻画为高阶结构之间双向耦合的涌现，其耦合结构不可还原为低层局部关联的叠加。存在命题：由前述结构推出存在不可被消减为虚无，此为先验框架的必然结论，而非外加公理。其总论断是：这些规定共同构成一个逻辑必然的元理论架构。

形式化代码将上述命题逐条兑现。存在者以容器表示，形状与位置分别对应外在形态与内部关联节点，兑现动态关联性命题中“存在者由关系构成”的命题；映射与对称以函子与自然变换表示，使守恒作为函子定律的推论出现，兑现守恒为先验内禀而非外加的命题；形状函子的 Grothendieck 构造得到形状范畴，以刻画存在者的内部结构；余代数展开记录——含展开函子、下一层种子赋值、位置到形状的凝聚映射及其与函子作用的相容性——形式化“部分凝聚为整体、当前层生成下一层”，兑现动态关联性与无限性；展开系统间的同态分对象级映射与高阶相容两层，后者为意识命题中的高阶双向耦合预留结构位置。核心对象 Cosmos 是由展开结构 Unfolding 诱导出的自函子的终余代数，余归纳地满足 Cosmos ≅ Unfolding(Cosmos)，使自指性与无限性（含无界特性）成为结构的内禀性质，兑现自指性与属性命题；UnitCosmos 见证该类型的可居性，即存在不可消减在形式层面的构造性见证；余代数同态构成宇宙之间的态射。论文中的每一项根本属性，在此都有对应的形式构造。

ALMA 的核心贡献不在于其先验构成性封闭本身，而在于将这种封闭与一个建构性、经验上实质、并且可形式验证的架构相整合。这种封闭基于一个更深层的本体论承诺：逻辑必然性并非思维的任意规则，而是存在本身的结构性表达；同一律与不矛盾律是一切可能话语的构成性前提。然而，如果这一封闭被孤立，便有可能沦为不可证伪；因此，它只是必要条件，而非充分条件。为此，ALMA 同时提供正面的理论建构与机器可检验的形式化，使框架受到经验约束，而不将其降格为单纯的经验模型。与此同时，ALMA 的自我理解又带有一种微妙的建构主义色彩：其概念并非对独立于认知的绝对本体的描述，而是理性为把握自身所处的唯一、无限、动态场域而建构的认知坐标。这种本体论必然性与认识论谦逊的结合，为回应虚无主义、怀疑论与相对主义提供了基础，同时保持对经验校准与形式验证的开放。