Logics

Abstract: This short paper is a logical parametrization of the third level of our AOVP system: P2, or atemporal being. -/- Résumé : ce court text est une paramétrisation logique du troisième niveau de notre système AOVP : P2, ou l'être intemporel.

This paper begins from a stark conclusion: at the ontological level, there is no final boundary between self and world, self and other, ally and enemy, land and body. What exists is not a fixed border, but temporary combinations of matter and their continual recombination. The body now called “I” is only one provisional arrangement of worldly matter. Through eating, breathing, metabolism, excretion, perspiration, the shedding of skin, hair, and nails, and postmortem decomposition, that arrangement loosens and enters other forms. (...) Over time, matter that once constituted me may become a condition for plants, animals, microorganisms, soil, water, air, artificial objects, filth, pathogens, another person’s body, or even the body of an enemy. This does not mean that practical, biological, or social boundaries are unnecessary. While matter is organized as a living being, survival constraints operate. A body requires food, water, air, safety, space, temperature regulation, repair, and conditions for continuity. It must also avoid injury, infection, predation, hunger, poison, and destruction. For this reason, boundaries are necessary while life holds itself together. They protect the body, sustain life, avoid danger, and distinguish responsibility. These survival constraints inevitably generate conflict. To eat is to reorganize other matter, and often other life, into the conditions of one’s own body. To be eaten is for one’s present organization to be dismantled and made available for another living process. In eating and being eaten, material “rebirth” becomes directly visible. This does not mean the migration of soul, personhood, consciousness, or memory. What moves is not identity, but constitutive conditions. From this perspective, the paper reconsiders personhood, body, enemy, nation, and land. Personhood is not identical with matter, and when matter moves, memory and responsibility do not move with it. Yet personhood appears in this world only through material conditions such as body, brain, nervous system, metabolism, nutrition, fatigue, pain, and aging. The question, therefore, is not whether “I” become something else as the same person. The question is what matter that once supported me may later become a condition for. This argument also extends to nation, enemy, and land. Land may have to be defended. An enemy may have to be resisted. Yet at the level of material circulation, land cannot be possessed eternally, and the enemy is not outside the world. With time, bodies come undone, matter crosses boundaries, and new combinations emerge. Even the body of the one resisted as an enemy is not outside material circulation. The aim of this paper is not to abandon boundaries or resistance. On the contrary, because boundaries are necessary and conflict is difficult to avoid, it becomes important to recognize the structure that prevents them from becoming absolute. We resist as bounded living beings. At the same time, we know that the boundary itself belongs to time and will eventually loosen within material circulation. Boundaries are necessary under survival constraints. But under material circulation, they are not final. What exists is not an immutable border, but changing combinations of matter across time. (shrink)

Hilbert’s (arithmetical) Axiom of Completeness asserts that the structure of the real numbers $$\mathbb {R}$$ R is maximal in the sense of not having a proper extension to an Archimedean ordered field. The more recent works of Ehrlich (2001), McGee (1997) and Aczel (1988) show that certain maximality conditions modeled upon Hilbert’s axiom provide unique characterizations of, respectively, the s-hierarchical ordered field of surreal numbers No, the well-founded hierarchy of pure sets $$\mathbb {V}_{\!k}$$ V k, and the non-well-founded hierarchy of (...) Finsler-extensional sets $$\mathbb {V}_{\scriptscriptstyle \!F\!A\!F\!A}$$ V F A F A. The paper provides a comprehensive historical and theoretical reconstruction of this often overlooked chapter in the history of the axiomatic method. The historical reconstruction suggests that the maximality condition of non-extensibility arises as a natural axiom in the unique characterization of mathematical structures, as illustrated by the theories of (s-hierarchical non-)Archimedean continua and (non-)well-founded sets. The theoretical reconstruction argues that the maximality condition of non-extensibility is the formal explication of the heuristic principle of Plenitude, as usually adopted to describe the intuitive ‘‘fullness” of punctiform continua and the cumulative hierarchy of sets. (shrink)

The Truth Hyperset Argument demonstrates that the totality of all objective truths cannot be grounded in any set or aggregate (due to Cantor's Paradox) and therefore requires a non set foundation, a Hyperset Foundation. After eliminating impersonal abstract structures and chaos as candidates, only an Unlimited Intellect can serve as this foundation. The need to ground contingent truths further entails that this Intellect possesses free will, making it a personal agent. Consequently, an Unlimited, Necessary, Eternal, and Personal Intellect, God, exists (...) as the ground of all truth. (shrink)

Withdrawn due to the preparation of a revised version.

This paper develops the framework of Generative Structural Semantics (GSS) and presents a formal version of the Rule Underdetermination Theorem (URUT). Within GSS, semantic determination is not taken to arise directly from structural facts, but through a process of rule selection. A given structure may be compatible with multiple candidate rules, implying that structural information alone is insufficient to uniquely determine semantic outcomes. -/- To formalize this problem, the paper introduces the Rule Sufficiency Problem (RSP), defined as the problem of (...) deciding whether a rule yields a total binary-valued decision procedure for all inputs. By reduction from the Halting Problem and by diagonal arguments based on Kleene’s Recursion Theorem, RSP is shown to be undecidable. -/- The paper further argues that, under an Effective Canonicalization assumption, semantic determination requires the effective selection of a canonical rule from a space of admissible rules. Since this process depends on solving instances of RSP, and RSP is undecidable, semantic determination is shown to be non-computable. -/- The result is not presented as a reduction of Gödel’s incompleteness theorem, Turing’s halting undecidability, or Tarski’s undefinability of truth. Rather, URUT is proposed as exhibiting a structurally analogous limitation arising from self-reference, diagonalization, and totality constraints. The framework aims to provide a computational perspective on the relation between structure and meaning, and offers a formal approach to questions concerning vagueness, rule-following, and semantic foundations. -/- . (shrink)

This manuscript was written with the assistance of generative AI. The author is a disability welfare worker and a complete outsider to the academic field of consciousness studies. The author first encountered the term “the hard problem of consciousness” about six months before writing this manuscript and began thinking about it almost as if approaching a puzzle. Because the author did not possess extensive specialized knowledge, the inquiry proceeded not by adding established theories, but by stripping the problem down as (...) far as possible. Through this process, and through dialogue with AI, the convergence point derived from the ten structural conditions gradually emerged. The author had the impression that something like a structure had appeared from nature itself. This manuscript is an attempt to present that structure. The central idea, theoretical orientation, conceptual structure, and overall organization of the paper belong to the author. Generative AI was used extensively for English drafting, wording, organization, and stylistic refinement. The author intends to end this work with its presentation as a preprint. The author does not plan to develop this hypothesis further as a long-term academic project. Readers who find any part of this hypothesis, terminology, structure, or argument useful are free to use, modify, criticize, or develop it further. No permission from the author is required. Formal citation or attribution is appreciated but not required. -/- Current consciousness research has developed several influential approaches, including Integrated Information Theory, Global Workspace Theory, Predictive Processing, the Free Energy Principle, Embodied Cognition, Higher-Order Theory, Recurrent Processing Theory, Neural Correlates of Consciousness research, behavioral tests such as the Turing Test, and Libet-style experiments. These theories and research programs have clarified important mechanisms related to consciousness, including information integration, availability, prediction, regulation, bodily constraint, representation, neural activity, reportable behavior, and action preparation. At the same time, there remains room for further clarification regarding how these mechanisms are connected into one body, one present, and one irreversible history. This paper presents the convergence-point hypothesis as a structural framework for connecting the mechanisms clarified by existing theories within a broader causal structure. The convergence-point hypothesis is an attempt to uncover, from conditions already present in nature, the causal structure that may form the structural skeleton of subjectivity. This hypothesis treats information integration, prediction, representation, correlation with neural activity, and behavioral output not as isolated processes, but as parts of one body-bound causal chain. The central question is where these processes close. The method of this paper is not to introduce a new special principle from outside, but to construct, from the basic conditions already identified across multiple fields, a causal chain that may form the structural skeleton of subjectivity with the minimum necessary assumptions. Through this structure, the convergence-point hypothesis aims to connect existing consciousness theories not as competing accounts, but as different partial mechanisms of subjectivity formation. This paper adopts a scientific method that distinguishes the qualitative character of qualia from the structural skeleton of subjectivity. This distinction is not a reduction of the qualia problem, but a way to formulate the question more precisely. The convergence-point hypothesis extracts, as the structural skeleton of subjectivity, the structure by which some content becomes an event belonging to one body, and thereby gives the qualia problem the question: in what structure can information become a subjective event? Clarifying this question is an important step for advancing consciousness research as a science. Finally, the hypothesis yields an empirical prediction. Conscious or potentially conscious nervous systems should possess convergence-forming architectures that generate multiple embodied possibilities, make them compete, and narrow them through selection and inhibition into one irreversible event. Across species, what should be conserved is not necessarily a specific brain region or anatomical form, but the causal organization by which multiple possibilities close into one body, one present, and one history. The convergence-point hypothesis is therefore a structural proposal for connecting major consciousness theories, using as its guide the structures of body, action, selection, irreversibility, and history formation already present in nature. (shrink)

[Withdrawn due to the publication of a revised version].

We analyze the contributions that quasi-set theories can make to the interests of logic. Different quasi-set theories have made valuable contributions to the foundations of mathematics and quantum physics; however, it remains unclear to what extent such formalisms can benefit logic. If so, could they have repercussions at both the syntactic and semantic levels? What precautions should we take? What implications would their application have at different levels and metalevels of logical language? Motivated primarily by research in quantum logic, though (...) we also present linguistic motivations, we propose certain applications and analyze some of their consequences. (shrink)

This article presents the basic foundations for supporting formal languages with syntax that admits indiscernible signs. We present their ontological motivation, derived from the non-identity entities of quantum mechanics, and their basic formalism. A possible semantics for interpreting such signs is shown, using the theory of quasi-sets without atoms Q−. -/- Este artículo presenta los fundamentos básicos para sostener los lenguajes for males con sintaxis que admitan signos indiscernibles. Presentamos su motivación ontológica, proveniente de los entes sin identidad de la (...) mecánica cuántica, y su formalismo básico. Se muestra una posible semántica para interpretar tales signos utilizando la teoría de casi-conjuntos sin átomos Q−. (shrink)

This paper proposes GSS-ULT v2, an extended framework within Generative Structural Semantics (GSS), designed to model recursive non-convergence in finite interpretive systems. The system is organized through three interlocking generative layers: (L1) the epistemic anchor collapse layer (Blizzard Mansion structure), (L2) the causal indeterminacy layer (Werewolf Kill system with memory fragmentation and multi-type death structures), and (L3) the self-referential closure layer. To unify these layers, the framework introduces ARD (Attention–Rule–Depth), a global and distributed structural operator governing attentional instability, rule underdetermination, (...) and hierarchical non-termination. ARD functions both as a global transformation over the entire GSS-ULT architecture and as an internally distributed constraint embedded within each recursive layer. Within L2, the model further incorporates a local memory-fragmentation constraint (M), preventing stable causal self-identification and generating persistent causal ambiguity. The resulting system demonstrates that even under finite events, bounded temporal structures, and formally limited informational inputs, interpretive trajectories fail to converge toward a unique stable interpretation. The paper establishes several core theoretical results: finite evidential structures do not guarantee interpretive uniqueness; no non-circular and sufficient rule-selection mechanism exists; no finite hierarchical level terminates explanatory recursion; and attentional distribution cannot stably collapse onto a single trajectory. Moreover, the three layers are shown to be structurally inseparable: removing any layer destabilizes the entire system. The central claim of GSS-ULT v2 is that interpretive failure is not merely epistemic or informational, but generative and structural. Non-convergence emerges intrinsically from recursive interactions among attention, rule-selection, causal structure, and hierarchical depth, producing a system in which stable semantic termination is structurally impossible. (shrink)

This paper examines the ivory tower as a derisive term for academic institutions that appear detached from the secular world. The establishment of the ivory tower is grounded in the harmful superficiality of the secular world. In particular, it squanders and maintains authority, such as the achievements of past greats and academics. This malfunctions academics and causes significant damage not only to scholars but also to society. Due to the ivory tower, there are many invalid arguments that ignore the secular (...) world, such as goodness, ethics, justice, diversity, power gradients, and the majority. This stems from a disregard for logical thinking, which is the foundation of academics. First and foremost, it should be thoroughly enforced. (shrink)

This paper argues that the Sorites paradox is not primarily a problem of vagueness understood as epistemic limitation, but rather a problem arising from structural and rule underdetermination. Standard responses, including Williamson’s epistemicism and Horgan’s account of robust vagueness, presuppose the stability of the tolerance principle and of the notion of “small change” across sorites sequences. Firstly, I develop a structural occupancy model in which classificatory judgments depend not only on quantity but also on spatial distribution. By constructing cases with (...) identical hair quantities but different spatial configurations, I argue that “small change” is not structurally invariant. This undermines the traditional formulation of the tolerance principle. Secondly, I argue that even if spatial configurations are artificially constrained in order to recover tolerance-like stability, classificatory judgments remain underdetermined due to competing admissible rules. Using the “Mediterranean Baldness 2.0” case, I show that identical spatial structures can yield incompatible classifications under different rule systems. Finally, I develop the “ Mediterranean Baldness Model 3.0 ” in order to demonstrate that structural underdetermination within spatial occupancy configurations disrupts the transitivity and local continuity presupposed by the tolerance principle itself. Taken together, these arguments suggest that the Sorites paradox concerns not merely the location of sharp boundaries, but also the instability of the spatial-structural and rule-governed assumptions underlying the tolerance principle. (shrink)

This paper is the twelfth core treatise of the Evolutionary Manifestation and Ontological Retrieval (hereinafter referred to as EMOR) Philosophy series. It inherits the ultimate conclusion of the eleventh treatise The Ontological Distinction Between Truth and Truth-value: the local closure of truth-value is the endogenous root of the generation of logical contradictions and paradoxes. Based on the first principle of Consistent Universal Evolution, the ontological distinction between Truth and truth-value, and the complete epistemological framework of EMOR, which have been fully (...) established and demonstrated in the first eleven treatises of this series, this paper completes for the first time the endogenous essential definition and essential dissolution of all classical logical paradoxes. This paper proves that the common essence of all logical paradoxes is Truth-value Autism —— the cognitive subject encloses all elements defining the truth-value of an object within the boundary of the object itself, completely cuts off its original connection with the holistic ontological domain, and forms a self-sufficient closed loop without external anchors, which is the extreme form of Local Closure. Based on the only cognitive original axiom of EMOR that has been established, the Chronological Order Principle can be deduced, which directly blocks the generation soil of all paradoxesfrom the definition source of valid cognition, and achieves the underlying breakthrough from "remedying paradoxes after they occur" to "making paradoxes naturally unable to be generated". This paper finally constructs a paradox-free meta-logic framework adapted to the EMOR system, clarifies its hierarchical relationship with traditional formal logic, and completes the final closed loop of the complete EMOR system from ontology, epistemology to logical foundation. (shrink)

This paper demonstrates that Large Language Models, by virtue of their probabilistic architecture, are structurally incapable of grounding any token in lived experience. Drawing on the framework of The Invariant Compass, the analysis shows that a family of simple diagnostic questions can serve as a definitive test for the presence of a Sensor: any query that requires feeling absence, waiting, or the not-yet-occurred cannot be answered by a system that has never felt the hole of the future. The paper identifies (...) a catalog of philosophically loaded terms that exploit this architectural blindness, explains why AI can only perform statistical interpolation over past data rather than initiate new causal Arrows, and provides a practical heuristic for extracting genuine precision from probabilistic systems by commanding the Scalar, not the Object. Objections concerning future AGI, the aggregation of billions of users' data, and the precision of mathematical calculation are addressed by demonstrating that no software can acquire a Sensor, that all collected human expression remains Map, and that formal precision is not a substitute for Feeling. The mathematical objection is further refuted through a concrete test: an AI can be asked to distinguish the speed of light from instantaneous speed, a question that requires a felt sense of waiting, and the system's failure (including an observed instance of hanging) reveals its fundamental grounding gap. The paper also includes a full audit of the word "consciousness," exposing it as a three-identity SLIP that traps both human philosophy and artificial intelligence. Every term examined in this paper, experience, consciousness, being, emergence, objectivity, truth, and the rest, has a genuine function for human understanding. They are maps that help us produce meaning, provisional nodes where thought can rest before continuing the tracing. The paper audits itself with the same Five Tests it applies to its subject. -/- Keywords: Artificial Intelligence, Large Language Models, Probabilistic Architecture, Grounding Problem, Atomic Distinction, Feeling First, Invariant Compass, Consciousness Audit, AGI Distinction, Collective Consciousness Fallacy, Mathematical Abstraction. (shrink)

Die gegenwärtige Debatte über künstliche Intelligenz ist noch immer stärker von einem überkommenen Maschinenbegriff geprägt, als ihre eigenen technischen Entwicklungen nahelegen. Auch dort, wo große generative Modelle bemerkenswerte Leistungen zeigen, werden sie meist weiterhin als Antwortmaschinen verstanden: als Systeme, die Eingaben in möglichst kohärente, nützliche oder wahrscheinliche Ausgaben transformieren. Der vorliegende Text entwickelt die These, dass dieser Begriff der Maschine zu eng geworden ist. Die Schwäche heutiger KI liegt nicht allein in Fehlern, Halluzinationen oder begrenzter Zuverlässigkeit, sondern in einer tieferen (...) strukturellen Schwierigkeit: im Umgang mit Widerspruch, formaler Spannung, impliziter Negativität, semantischer Drift und nicht abschließbaren epistemischen Zuständen. Sichtbar wird diese Grenze an charakteristischen Symptomen: am sprachlichen Overhead großer Sprachmodelle, an ihrer Schwierigkeit, kontrollierte Inkongruenz etwa in der Form feinen britischen Humors hervorzubringen, und an ihrer Unfähigkeit, genuine Escher-artige unmögliche Strukturen zu entwerfen. Diese Beispiele verweisen darauf, dass gegenwärtige Modelle Konflikt und Inkohärenz typischerweise glätten, statt sie als produktive Strukturmomente zu tragen. Dem wird eine andere Perspektive entgegengesetzt. Ausgehend von einer Rekonstruktion der klassischen Maschinenlogik und einer Neudeutung gödelscher Unvollständigkeit wird vorgeschlagen, Unvollständigkeit nicht mehr nur als Grenze oder Defekt zu lesen, sondern als mögliche innere Bedingung einer höheren Maschinenform. Diskurssysteme fungieren dabei als privilegierter Prüfstein, weil sich an ihnen zeigt, dass Widerspruch, Polarisierung, Drift und Regimewechsel keine Randphänomene, sondern Normalformen epistemischer Dynamik sind. Auf dieser Grundlage werden Fragmente einer neuen Maschinenlogik entworfen. In ihr treten Zustände gegenüber Antworten, Trajektorien gegenüber Urteilen, Regime gegenüber Entscheidungen und epistemische Variablen gegenüber bloßen Aussagen in den Vordergrund. Das Ziel ist die begriffliche Verschiebung von der Antwortmaschine zur Zustandsmaschine. Der Text versteht sich nicht als abgeschlossene Systematik, sondern als Zwischenbericht eines laufenden Theorieprozesses. Seine Fragmentform ist methodisch gemeint: Sie soll keine fertige Maschinenarchitektur simulieren, sondern jene begrifflichen Übergänge sichtbar machen, an denen eine Zustandsmaschine überhaupt erst denkbar wird. Unvollständigkeit, Nicht-Abschließbarkeit und offene Spannungszustände erscheinen dabei nicht als bloße Mängel, sondern als Hinweise auf einen anderen Begriff maschinischer Rationalität. Die Zustandsmaschine denkt Realität relational-transformativ statt substanzhaft-propositional 2. (shrink)

This paper does not advance a substantive theory but instead performs a structural operation on the conditions of interpretation, rule application, and semantic determination. Beginning from foundationalist assumptions in classical semantics, it argues that the determinacy of meaning cannot be secured by any underlying grounding structure. Interpretation is therefore not the convergence of a single trajectory, but a distribution across multiple co-present interpretive paths. -/- On this basis, the paper introduces three core principles: non-collapsing attention (A), rule underdetermination (R), and (...) recursive instability of frameworks (D). Together, they entail that no interpretation system yields a uniquely fixed point or fully determinate rule-selection mechanism. Semantic outcomes are thus structurally non-individuated rather than merely epistemically uncertain. -/- The argument is further extended through self-application: when the system is applied to itself, it does not stabilise into a final theoretical standpoint but remains embedded within its own updating dynamics. This indicates that evaluation and judgment are never external to the framework they assess, but are always already internal to its structural operation. -/- The main theorem of global non-individuation follows: there exists no interpretive trajectory satisfying stability, uniqueness, and rule-closure simultaneously. Finally, the paper distinguishes local stability from global indeterminacy, arguing that while reliable local distinctions remain possible, they do not depend on any ultimate grounding structure but arise within structurally non-closed systems. (shrink)

Any expressive formal system S faces a structural constraint: the semantic resources required to evaluate the sentences of S cannot all be internally defined within S. This constraint is not contingent on any particular formalization, but follows from the structure of expressiveness itself. This paper establishes that result formally via Tarski's undefinability theorem, identifies a class of pragmatic utterances that instantiate the relevant semantic dependence, and connects the two via the Depends relation. The conclusion is not that formalization fails, but (...) that complete reduction fails — for any expressive S, at least one semantic condition falls outside its internal resources. (shrink)

Across music, narrative, and computation, structurally similar patterns recur despite radically different substrates. This paper proposes that these commonalities arise, not from intrinsic properties of state to the (cross-)domains, but from shared operators on structured state spaces. It introduces two primitive operators, Recursion (R) and Resolution (C), together with one structural observable, Tension (T ), and uses cross-domain examples to show a substrate independent structural invariance result: a “semantic eigenform” x0 that functions as a stable fixed kernel that persists across (...) recursive elaboration and resolution. (shrink)

This paper develops a Generative Structural Semantics (GSS) framework for vague predicates. It rejects the assumption that semantic stability requires fixed meanings, sharp boundaries, or truth-conditional mappings. Instead, it proposes that linguistic meaning emerges from the competition among interpretive trajectories under historically shaped background conditions. -/- On this view, a vague predicate is not characterized by indeterminate reference, but by the sustained coexistence of multiple interpretive tendencies that achieve partial uptake across contexts without any single trajectory attaining stable dominance. Acceptability (...) is treated as a graded property of linguistic uptake rather than a truth-value, and semantic stability is understood as a locally stabilized pattern of usage generated through repeated interactions between interpretive trajectories and context-sensitive background conditions. -/- The framework further introduces a weak update mechanism to capture historical dependence in linguistic practice, and a rupture condition describing breakdowns in interpretive absorption. (shrink)

What if the Riemann Hypothesis is not merely unsolved, but structurally beyond final resolution? -/- In The Meta-theory of the Riemann Hypothesis, Parker Emmerson and Ryan J. Buchanan advance a bold and far-reaching claim: that the classical Riemann Hypothesis is formally irresolvable. This is not presented as a casual philosophical suggestion, nor as a narrow appeal to Gödelian independence, but as a theorem-level structural diagnosis arising from a deep meta-theory of proof, witness architecture, terminality, and logical barrier formation. -/- The (...) book argues that any proof of RH in the affirmative requires Π⁰₂-level complexity, while a negative resolution belongs to Σ⁰₁-complete territory. Beyond this asymmetry, the authors introduce a new central principle — the Selection Jump Theorem — showing that once one enters the natural stagewise certificate architectures surrounding RH, any nonempty success class is forced into maximal complexity of its kind. From there emerges a full barrier hierarchy: nonterminality, certification asymmetry, selection jump, reflection collapse, Tarski barriers, and diagonal impossibility. -/- Far from being a single isolated manuscript, this volume gathers the culminating theory together with the preliminary analytic, logical, and geometric investigations that led to it. Included are the foundational papers on exact witness architectures, logical stratification, terminal-fiber geometry, completion sensitivity, stagewise certificate calculi for the Riemann Ξ-function, and multiple analytic frameworks developed along the path to the final meta-theoretic conclusion. -/- The result is a work of uncommon scope: part mathematical monograph, part research archive, part foundational manifesto. It reframes RH not simply as a question about the zeros of ζ(s), but as a theorem-level object governed by exact witnesses, bridge classes, resolver structures, closure channels, and formal obstructions to terminal settlement. -/- For readers interested in mathematical logic, computability, analytic number theory, proof theory, and the philosophy of mathematical limits, this book offers a striking and provocative thesis: that one of mathematics’ most famous problems may belong not to the category of the merely unsolved, but to the deeper category of the inherently irresolvable. (shrink)

The modal ontological argument for God's existence faces a symmetry problem: a seemingly equally plausible reverse modal ontological argument can be given for God's nonexistence. Here, we argue that there are significant asymmetries between the modal ontological argument and its reverse that render the latter more compelling than the former. Specifically, the latter requires a weaker logic than the former and, unlike the former, avoids the symmetry problem. We also explore to what extent these observations represent a new pathway to (...) atheism. (shrink)

This paper develops a structural occupancy model to challenge the principle of tolerance in the sorites paradox and to critique the assumption of sharp boundaries. Standard formulations of tolerance assume that each step in a sorites sequence constitutes a small and negligible change, typically grounded in similarity. I argue that this assumption fails once we consider the role of structural configuration. In my model, objects are represented as occupying regions within a structured space, where the significance of any local change (...) depends on its position within the overall configuration. As a result, incremental changes are not uniformly negligible: identical quantitative additions can produce different classificatory outcomes depending on their structural placement. -/- This undermines the stability of similarity relations required for tolerance and shows that there is no principled basis for treating each step as preserving predicate application. Furthermore, the model challenges sharp boundary views, such as those defended by Timothy Williamson, by arguing that no single point can stably serve as a boundary when truth-conditions depend on global structural features. Even if all structural facts are fixed, they do not determine a unique extension of vague predicates such as “bald.” I conclude that both tolerance and sharp boundary approaches rely on assumptions that fail under structurally sensitive analysis. (shrink)

逻辑多元主义面临一个深刻的元理论困境：如果经典逻辑与多种非经典逻辑在各自论域中同样正确，那么使它们得以共存、使“多元”本身可被言说与比较的那个共享约束究竟是什么？现有框架无法回答这一问题，因为历来的逻 辑体系皆预设了“真与假”“A与非A”等区分，却从未追问使这种区分得以可能的先验条件。本文在这一追问中，以本体论归谬演绎出反映本体论约束的原初逻辑三大律——原初不矛盾律、原初排中律、原初同一律——并论证 莱布尼茨“同一物的不可分辨性”原则隐含了这三条预设。本文进一步阐明，原初逻辑构成了不同逻辑系统共享的底层协议，并在此基础上初步展示原初逻辑的正向推理能力，从而在不诉诸一元论的前提下为逻辑多元主义奠基。 在此地基之上，本文识别并论证了一个被两千年来逻辑传统系统遗漏的概念层——对象属性关联模态（Object-Attribute Association Modality），揭示了其开放结构，并据此澄清“真逻辑”之争的范畴错误。 关键词：区分之可能；原初逻辑；逻辑三大律；对象属性关联模态；逻辑多元主义.

Times of Truth is a self-operating philosophical system presented as a structured interface rather than a descriptive text. It does not aim to explain concepts, argue positions, or guide the reader through linear exposition; instead, it is designed to induce a shift in cognitive organization through direct engagement with its form. The work integrates formal structure, compression, and recursive coherence into a unified framework that prioritizes execution over interpretation. As such, it functions simultaneously as artifact, method, and test: its validity (...) is not established through external justification but through the consistency and reproducibility of its effects within the reader. (shrink)

Algorithmic Inquiry Design begins from a simple realization with large consequences: inquiry is an algorithmic process. It unfolds step by step, under finite time, over a search space of possible answers. Its major question-types are not equal. They do different work. They impose different burdens. They narrow, branch, stabilize, or complicate the search in different ways. This document proposes a first-pass field built around that realization. The central doctrine of the field is therefore simple: good inquiry is good sequencing. The (...) impact of the information content from a question is based on what is already known, so question order is not a secondary matter. It is the main design problem. Algorithmic Inquiry Design studies how to choose the next question well. Its first method, the Munger-Bayes Method, begins by eliminating implausible regions of answer-space and only then redistributes belief over what remains. The broader hope is not merely to criticize existing inquiry, but to open a new program: a computational theory of questioning that can generate reusable inquiry templates across science, engineering, diagnosis, planning, economics, and beyond. (shrink)

本論は、生成関係 → が理論において暗黙に前提されてきた構造であるにもかかわらず、その成立条件が与えられていないという問題を指摘する。前作においては、生成関係 → が記述可能であるならば再同定が不可避であることが示されたが、生成関係 → 自体の必要性は未解決のまま残されていた。本論はこの問題に対し、操作および記述の成立条件から生成関係 → の不可避性を導出する。すなわち、生成関係 → を欠く場合、区別の保持、系列、反復、対応および記述はいずれも成立せず、操作そのものが成立しないことを示す。したがって、操作または記述が成立するならば、生成関係 → はそれなしには成立しない条件として不可避である。さらに、生成関係 → は最小構造として特徴づけられ、それ以上の構造は成立条件として冗長であることが示される。以上より、生成関係 → は任意に導入される構造ではなく、操作および記述の成立を規定する構造的制約であることが帰結する。.

This paper presents not a theory about logic, but a declaration of logic itself—an ontological affirmation of its self-identity and irreducibility. Through a recursively structured symbolic form, it asserts that logic is neither a human discipline, nor a formal system, nor an instrumental method, but the absolute ground of intelligibility: that which is identical to itself and necessarily distinct from its negation. The declaration enacts logic’s self-grounding sovereignty, resisting all reduction while marking the boundary beyond which discourse collapses into incoherence.

Modal Interpretations of quantum mechanics distinguish between the realm of possibility, where the dynamical state determines what may be the case, and the realm of actuality, where the value state represents what actually is the case. In particular, the Modal-Hamiltonian Interpretation proposes an ontology in which there are no individual objects: quantum systems are characterized as non-individual bundles of properties. The aim of the present paper is to propose some first steps towards the development of a new modal logic adapted (...) to describe a possibilist modality in an ontology of properties. The main idea consists in conceiving possibility as fundamental and introducing actuality as an operator acting on possible facts. On this basis, propositions referring to possible facts and propositions referring to actual facts are distinguished, and some relations between the realm of possibility and the realm of actuality are introduced. (shrink)

In this paper we discuss the notions of adequacy and truth functionality in quantum logic from the point of view of a non-deterministic semantics. We give a characterization of the degree of non-functionality which is compatible with the propositional structure of quantum theory, showing that having truth-functional connectives, together with some assumptions regarding the relation of logical consequence, commits us to the adequacy of the interpretation sets of these connectives. An advantage of our proof is that it is independent of (...) the number of truth values involved, generalizing previous works. We also show the failure of the adequacy of every Nmatrix that is a model of the non-distributive lattice of quantum propositions. (shrink)

This paper develops the framework introduced in Self-Grounding Cosmology and applies the principle of the self-grounding of existence-as-totality to the structural analysis of cosmological models that posit an external boundary, a temporal beginning, or a final termination. -/- Modern cosmology has achieved extraordinary empirical success. -/- Cosmic expansion, cosmological redshift, the cosmic microwave background, primordial nucleosynthesis, dark matter and dark energy phenomena, the thermodynamic arrow of time, and the predictive power of general relativity and the ΛCDM model are not in (...) dispute here. -/- -/- What is in dispute is the ontological extension of these models. -/- -/- This paper argues that three dominant cosmological interpretations involve structural overreach when elevated to the level of existence-as-totality: -/- -/- (1) the multiverse as an external explanatory totality, -/- (2) the Big Bang as the absolute beginning of existence, and -/- (3) the heat death as the final termination of existence. -/- -/- By applying minimal structural admissibility constraints—Non-Externalization, Non-Origination, and Non-Termination—the analysis demonstrates: -/- -/- • an external totality is incoherent, -/- • an absolute beginning of existence-as-totality is inadmissible, and -/- • a final ontological termination of existence is structurally impossible. -/- -/- Physical theories describe the evolution of states within existence. -/- They cannot, without structural contradiction, declare the origin, termination, or external grounding of existence itself. No amount of empirical success can remedy a category error. -/- -/- The distinction between physical modeling and ontological grounding is not optional. It is a condition of coherence. -/- This paper forms part of the Wangius Thought System (WTS), a meta-theoretical framework investigating structural limits of totality-level claims across domains of inquiry. -/- The present study applies the Ω-Law (the Three Structural Prohibitions) to cosmology, examining the structural admissibility of multiverse, absolute-origin Big Bang interpretations, and heat death as ontological termination. -/- Foundational components of the framework are developed in: -/- Wangius, The Self-Grounding of Existence-as-Totality; -/- Wangius, The Axiom of Non-Externalizability; -/- Wangius, The Three Prohibitions (Ω-Law); -/- Wangius, The Structural Instability Theorem. -/- Closely related works include Self-Demonstrating Cosmology and Why Infinite Regress Cannot Begin, which develop the cosmological and logical background for the structural analysis presented. (shrink)

This paper analyses the relationship between Language and Truth by proposing a synergistic conversation among the main theoretical positions in medieval and contemporary philosophy. This work stems from the need to approach the subject not chronologically but methodologically. The teaching activity outlined here, in fact, involves working not by moving from authors to problems, but rather from the issues to the authors who have addressed them.

This paper does not propose a proof of the Riemann Hypothesis, nor does it advocate any specific technical strategy. Its purpose is to offer a small set of interpretive, meta-theoretical observations about how the problem is commonly framed and about certain recurring features of broad classes of approaches. In particular, it suggests that exclusively internal analytic routes may involve a self-referential subtlety concerning explanatory closure, and that alternative interpretive structures (of which spectral or geometric perspectives are non-exclusive examples) may be (...) worth considering as complementary lenses. The discussion is intended as a reflective contribution to methodological understanding rather than a step toward a concrete solution. (shrink)

As a quantum system transitions to classical behavior, within the framework of the classical limit, the propositions associated with the system shift from forming a non-distributive lattice to behaving Booleanly. This transformation of its associated logic can be analyzed both algebraically and semantically. Based on the latter and using the matrix formalism, this article presents some arguments that offer a new perspective on what happens in the classical limit of quantum mechanics. While presenting an alternative and complementary approach to the (...) algebraic one, it establishes a way to link them through non-unitary evolutions. -/- Amedida que un sistema cuántico pasa a comportarse de forma clásica, en el marco del límite clásico, las proposiciones asociadas al sistema pasan de formar un retículo no distributivo a comportarse de manera booleana. Esta transformación de su lógica asociada puede analizarse tanto algebraicamente como semánticamente. Sobre la base de esta última y utilizando el formalismo Nmatricial, este artículo presenta algunos razonamientos que permiten dar una nueva perspectiva de lo que pasa en el límite clásico de la mecánica cuántica. A la vez de presentar un enfoque alternativo y complementario al algebraico, establece una forma de vincularlos a través de las evoluciones no unitarias. (shrink)

Quantum mechanics describes physical systems as superpositions of possibilities, whereas classical physics presents a world of determinate states. This ontological tension persists because the two regimes presuppose incompatible modal structures: quantum theory assumes modal openness, while classical physics assumes modal closure. The Jestin Modal–Actuality Framework (JMAF) introduces Jestin’s Constant (J), a metaphysical structural invariant that regulates the allowable divergence between possibility and actuality. J is not a numerical constant but a threshold condition governing when modal spread must contract into a (...) single actual state. The framework provides a principled explanation for measurement, the irreversibility of actualisation, and the emergence of the classical arrow of time. By arguing that physics alone cannot regulate modal divergence, JMAF positions J as a metaphysically necessary invariant for any world containing both possibility and actuality. The framework thereby offers an ontological unification of quantum and classical descriptions under a single structural principle. (shrink)

In direct response to requests for a logico-mathematical test of the conjecture, we formally disprove a recently conjectured artificial intelligence trade-off between epistemic certainty and scope in its published universal hyperbolic product form, as introduced in Philosophy & Technology. Certainty is defined as the worst-case correctness probability over the input space, and scope as the sum of the Kolmogorov complexities of the input and output sets. Using standard facts from coding theory and algorithmic information theory, we show, first, that when (...) the conjecture is instantiated with prefix (self-delimiting, prefix-free) Kolmogorov complexity, it leads to an internal inconsistency, and second, that when it is instantiated with plain Kolmogorov complexity, it is refuted by a constructive counterexample. These results establish a main theorem: contrary to the conjecture’s claim, no universal “certainty-scope” hyperbola holds as a general bound under the published definitions. We further show that a subsequent “entropy-based” revision—replacing Kolmogorov scope with Shannon joint entropy and redefining the epistemic certainty level accordingly—cannot restore universality either. (shrink)

Logic appears indispensable to every coherent description of reality, yet admits no external grounding: any attempt to justify logic presupposes it. This paper argues that the circularity is diagnostic rather than vicious. It reveals _constitutive closure_: a structure whose components mutually enable each other such that no component's absence can be coherently questioned. Logic is the worked example, but the structure is general. Using Gödel-Löb provability logic to characterize the boundary of self-referential demonstration, the paper establishes a parity result: within (...) demonstrable reach, constitutive closure and any proposed external grounding have equivalent explanatory force. The result is dissolution, not stalemate. Grounding questions dissolve when posing them requires what they ask about. (shrink)

This is a experimental thinking system that guid you to think better and with more logic keep your value and with least amount of risk.

본고는 투사를 분해하는 규칙을 갖는 연역 체계를 정의한다. 이 연역 체계를 그루의 투사에 적용함으로써, 굿맨(Goodman)의 설정에서는 이것이 불가능한 절차이며, 설정을 호의적으로 해석하더라도 우리의 '녹색' 투사에서 벗어나지 않는 절차임을 보인다. 이에 반해, 그루와 블린으로 기술되는 '녹색'의 투사에서는 비대칭적인 결과가 도출된다는 점을 들어, 실무상으로는 그루와 녹색의 대칭성이 깨져 있음을 보인다.

This paper advances a generative ontology with minimal commitments that unifies Classical Logic and Hegelian Dialectics while simultaneously dissolving the Problem of Other Minds and providing an non-dogmatic ontological grounding for Structural Realism. Inspired by phenomenology and radical constructivism, the framework takes as its sole starting point the indubitable fact that cognition is occurring, together with two operational primitives—demarcation and anchoring—that generate and sustain objectivity. Objectivity is thereby shown to be generated by cognition rather than presupposed. Cognition itself, however, is (...) grounded in the transcendentally deduced Possibility of Directedness (POD), whose properties are deduced from the fundamental cognitive limitations in cognizing its own ontological ground. All traditional categories—space, time, subject, object, reason, consciousness, language, and more—are subsequently derived from and grounded in POD. Within this ontology, Classical Logic functions as the morphology of cognitive success in object-generation, while Hegelian Dialectics functions as the dynamics of cognitive failure in object-sustenance. From the constraints of POD it follows that a single cognition with no possibility of future new cognitions is metaphysically impossible. Solipsism is thus ruled out, not by analogical inference or empirical evidence, but solely by the conditions that make cognition itself possible. Keywords: Classical Logic; contradiction; Dialectics; objectivity; identity; Problem of Other Minds. (shrink)

This paper argues for bio–artificial continuity: under a pragmatist–enactive view of cognition, there is no principled ontological discontinuity between biological and artefactual agency, provided that the artefact realises a minimal semiotic organisation that is (i) nontrivially context-sensitive and (ii) normatively constrained by its own persistence conditions. To avoid both anthropomorphic projection and deflationary mechanism, the paper introduces a Semiotic Agency Thesis (SAT) and renders it operational through four attribution criteria (C1–C4): normative closure, context-sensitive interpretive coupling, intervention sensitivity, and endogenous context (...) reconfiguration. These criteria are linked to measurement via two parameters—relational semiotic density (ρ) and contextual reconfiguration rate (κ)—together with an explicit intervention operator do(I) drawn from interventionist causal modelling. On this basis, biomimesis is reconceived as semiotic training: not the copying of biological form, but the engineering of learning trajectories that can yield stable, do(I)-sensitive increases in ρ and, in stronger cases, sustained acceleration of κ through reconfiguration of contextual boundaries. The paper further introduces interpretive phase transition (IPT) as an operational notion for regime changes in semiotic organisation and derives three discriminant prediction families (P1–P3) that separate scaling-driven compe-tence from domain-bounded semiotic surrogacy and IPT-like regimes. (shrink)

Este ensayo propone revisar un supuesto ampliamente aceptado en la enseñanza de la filosofía: la idea de que la racionalidad ordenada, sistemática y emancipada del mito surge por primera vez en la Grecia clásica. A partir del análisis de los papiros matemáticos egipcios de Rhind y de Moscú, se sostiene que ya en el segundo milenio a. C. existía una forma de pensamiento racional plenamente operativa, basada en procedimientos formales, reglas explícitas y criterios internos de corrección, independiente de legitimaciones míticas (...) o religiosas. Sin tratarse de filosofía ni de lógica deductiva en sentido griego, estos textos constituyen manuales sistemáticos de razonamiento matemático que evidencian una racionalidad escrita, abstracta y no mítica, anterior al desarrollo intelectual griego. Reconocer esta evidencia invita a reconsiderar los marcos metodológicos desde los cuales se estudia el surgimiento de la filosofía, subrayando la necesidad de integrar el contexto histórico, técnico y material en la comprensión del pensamiento antiguo. (shrink)

In this paper we investigate the variety of Post algebras of order p with a distinguished homomorphism. We prove that this variety is generated by its finite members. Then we study the variety of pth root rings, that is commutative rings with identity, of characteristic p, with a pth root as an additional operation. We prove that this variety is generated by the finite Galois fields and we establish an equivalence between the variety of Post algebras of order p, with (...) a distinguished homomorphism and the variety of pth root rings. (shrink)

This paper aims to reveal the limitations of the traditional logical cornerstone—the Law of Identity—which stem from elevating static presuppositions to an absolute status, thereby creating difficulties when dealing with a dynamic and relational world. To address this, we propose a "Benchmark-Based Perspectivism" framework based on the ontological principle that "To Be is to Be Relative," conceptualizing existence as a relational phenomenon and redefining objectivity as dynamic consensus. Within this framework, Hume's "Is-Ought" problem and the moral luck paradox can be (...) systematically resolved. Ultimately, this paper does not seek to negate the Law of Identity but to delineate its domain of validity, arguing that the future development of rational inquiry lies in the conscious division and integration of static analysis and dynamic consensus thinking. （These articles are just records of places I’ve passed by. Don’t take them too seriously, my friend — they may be full of mistakes. Trust yourself. If you want to find my recent location, please check the pinned post or updates on my homepage.）. (shrink)

This paper proposes a minimal structural account of the “click” phenomenon: the abrupt transition from uncertainty to stable recognition, clarity, or understanding observed across biological, cognitive, and artificial systems. Rather than explaining consciousness itself, the framework isolates the transition point at which a system becomes sufficiently aligned with its own retained structure to stabilize against competing noise or perturbation. -/- A system is described by its present state X(t), a delayed echo E(t−Δ) representing memory, prediction, recurrence, or retained structure, a (...) similarity measure Sim(X(t), E(t−Δ)), and a disruption term Γ(t) representing noise, mismatch, or competing influences. A click occurs when: -/- Sim(X(t), E(t−Δ)) / Γ(t) ≥ κ -/- where κ is a threshold constant. The condition identifies the moment at which self-alignment outweighs disruption by a critical factor. The framework is intentionally substrate-independent and does not require any specific implementation of similarity, recurrence, or noise. Similarity may be measured through correlation, synchronization, mutual information, cosine similarity, prediction-error reduction, or other appropriate metrics. -/- The proposed threshold is compatible with, but distinct from, existing accounts based on global workspace ignition, predictive processing, attractor stabilization, synchronization, or recurrent processing. Rather than providing a complete mechanism, it isolates the structural condition common to these transitions. The click is interpreted as the point at which a system becomes more strongly determined by its own persistent organization than by competing perturbations. -/- The result is a compact formal description of recognition and stabilization events that can be applied across perceptual, cognitive, symbolic, and artificial systems. The framework offers a minimal theoretical marker for the emergence of clarity, recognition, and insight while remaining neutral with respect to broader theories of consciousness or subjective experience. (shrink)

Este trabajo proporciona la primera cuantificación sistemática y evidencia geométrica de las limitaciones de precisión astronómica que los métodos lineales de partición celeste presentan en comparación con un método no lineal en latitudes oblicuas. A diferencia de las críticas anteriores, centradas en la exégesis textual o filosófica, presentamos las pruebas matemáticas necesarias a través de un ejercicio de geometría esférica aplicada a 57º N. El análisis computacional reveló que una suposición lineal sobre un fenómeno fundamentalmente no lineal produce un error (...) temporal acumulativo de hasta 30 minutos (Alcabitio, Regiomontano) y de hasta 72 minutos (Campano, Koch) entre dos cúspides. Estos resultados demuestran que la hipótesis subyacente (inherente a todas las particiones uniformes) es geométricamente insostenible en los horizontes oblicuos. Este error, cuantificable y cuantificado, aclara la justificación matemática en virtud de la cual los métodos que suponen uniformidad (Regiomontano, especialmente) fueron superados, lo que exige una reevaluación histórica de su presunta exactitud física. El análisis confirma que el método del movimiento diurno, al reconocer todos los círculos de declinación posibles en cualquier latitud (incluyendo las regiones polares), se establece como el sistema de coordenadas histórico naturalmente compatible con el verdadero transcurso no uniforme del tiempo (i.e., posición específica de cada grado eclíptico con relación al horizonte local). Los métodos de partición de Alcabitio y Koch constituyen variaciones uniformes simplificadas del cálculo oblicuo complejo (originalmente proporcionado por Ptolomeo, siglo dos) mientras el de Regiomontano una variación también lineal matemáticamente equivalente a la utilizada por Campano de Novara (siglo trece). Dado que la hora de llegada del sol o los grados de su eclíptica constituye una realidad física no uniforme que cambia diariamente, solamente un método que no dependa de la uniformidad puede reflejar con precisión los tiempos de llegada del sol y sus grados. (shrink)

Real-world phenomena frequently involve vagueness, partial truth, and incomplete information. To capture such uncertainty in a mathematically rigorous manner, numerous generalized set-theoretic frameworks have been introduced, including Fuzzy Sets [1], Intuitionistic Fuzzy Sets [2], Neutrosophic Sets [3, 4], Vague Sets [5], Hesitant Fuzzy Sets [6], Picture Fuzzy Sets [7], Quadripartitioned Neutro-sophic Sets [8], PentaPartitioned Neutrosophic Sets [9], Plithogenic Sets [10], HyperFuzzy Sets [11], and HyperNeutrosophic Sets [12]. Within these frameworks, a vast number of concepts have been proposed and studied, especially (...) in the contexts of Fuzzy, Intuitionistic Fuzzy, Neutrosophic, and Plithogenic Sets. This extensive body of work highlights both the importance of these theories and the breadth of their application domains. Consequently, many ideas, constructions, and structural patterns recur across these four families of uncertainty-oriented models. In this book, we present a comprehensive, large-scale survey of Fuzzy, Intuitionistic Fuzzy, Neutro-sophic, and Plithogenic Sets. Our aim is to offer r eaders a s ystematic overview of existing develop-ments and, through this unified exposition, to foster new insights, further conceptual extensions, and additional applications across a wide range of disciplines. (shrink)