Graham Priest has argued that Yablo’s paradox involves a kind of ‘hidden’ circularity, since it involves a predicate whose satisfaction conditions can only be given in terms of that very predicate. Even if we accept Priest’s claim that Yablo’s paradox is self-referential in this sense—that the satisfaction conditions for the sentences making up the paradox involve a circular predicate—it turns out that there are paradoxical variations of Yablo’s paradox that are not circular in this sense, since they involve (...) satisfaction conditions that are not recursively specifiable, and hence not recognizable in the sense required for Priest’s argument. In this paper I provide a general recipe for constructing infinitely many such noncircular Yabloesque paradoxes, and conclude by drawing some more general lessons regarding our ability to identify conditions that are necessary and sufficient for paradoxically more generally. (shrink)

In lieu of an abstract, here is a brief excerpt of the content:Is Literature Self-Referential?Eric MillerIIs literary language necessarily self-referential? And does this put paradox at the heart of literature? For at least two decades now, affirmative answers to both questions have been articles of faith among critics in the structuralist and poststructuralist mainstream. Literature’s ineluctable paradoxicality attracts us so because a paradox suggests that there are limits to human rationality, and thus strikes a blow for (...) literature and against science. Paradox ensures literature its own special realm, safe from the culturally imperialistic inroads of science’s orderly, rational-empirical constructions. Literature thus gets to be seen as “bigger” than reason, because only literature can live with paradox, and thus only literature reveals those “deeper” truths of contradiction-ridden human existence, whereas science can never penetrate beyond rational manipulations of phenomenal surfaces. Indeed, for anyone who holds all human existence to be fundamentally paradoxical, this special capacity makes literature the only genuine, demystified species of human knowledge. In the war between C. P. Snow’s Two Cultures, a war humanists are now losing badly, we like to regard paradox as our ultimate weapon.Belief in the paradoxicality of literature may also be found among the New Critics, 1 and in fact goes back at least to the Romantics, 2 but they did not derive this belief from a necessary self-referentiality of literary language. This newer way of deriving paradox appears to offer several competitive advantages. Self-reference seems to be the ultimate version of “art for art’s sake”: if all literary language is necessarily self-referential, then literature must be something totally self-contained, and is thus legitimized solely in and through itself. In addition, deriving [End Page 475] literature’s paradoxicality from self-reference seems to ground it in the same conceptual realm as mathematical logic, and thus tempts us to claim for literature a “rigor” normally conceded only to logic, mathematics, and theoretical physics. Self-referentiality would thus seem both to protect literature’s autonomy and to raise its cultural status into the company of mathematics and science.But it is a trap. For behind this new strategy lurks a capitulation to the underlying conceptual scheme of natural science, and literature thus comes to be conceived, in effect, as a science. Self-reference is, after all, still a kind of reference; paradox is still a kind of truth-relational construction;—and truth-relations built around reference constitute the correspondence theory of truth. From such a foundational commitment to reference and correspondence-truth, flows the rest of the scientific worldview: the dualism of referring expression and referent, word and object, sentence and fact, theory and data, language and world, culture and nature. The presentation of literature as a quasi-negation of this ontology changes nothing. The dualism of reference still functions as literature’s conceptual starting point, as its arche. We only appear to be defining a peculiar and radically distinct sphere for literature when we insist on its self-referentiality, on the (recursive) identity, for it, of referring expression and referent. For, this is still to treat the conceptual distinction between the two as foundational, and literature thereby tacitly assimilates science’s fundamental categorial division: the referential language-world duality of correspondence truth. Indeed, literature thus comes to live even more completely in the margins of science: it will have no essence of its own; it will differ at most in being a photo-negative image of science’s positiv(istic) project. In Snow’s war, self-reference is a Trojan horse.With self-reference as the essence of literature, we are thus staking our reputations on literature’s being a special field of formalizable “knowledge about...,” rather than, say, a quality or kind or realm of possible experience—which is to adopt science’s understanding of what is important. Matters are only made worse by that other attempt to define literary studies as a negation of the theory-data dualism of natural science: the poststructuralist denial of the distinction between criticism and literature. For the institutional need professional critics have to be seen as a discipline with a method and a subject, as a form of “knowledge about,” hardly disappears with... (shrink)

The aim of this paper is to introduce a formal system STW of self-referential truth, which extends the classical first-order theory of pure combinators with a truth predicate and certain approximation axioms. STW naturally embodies the mechanisms of general predicate application/abstraction on a par with function application/abstraction; in addition, it allows non-trivial constructions, inspired by generalized recursion theory. As a consequence, STW provides a smooth inner model for Myhill's systems with levels of implication.

The proposed model overlooks the self-referential and self-perpetuating nature of ownership intuitions. Human knowledge is primarily formed through social interaction within power dynamics. Accordingly, we suggest that legitimate ownership of one object can influence perceptions of legitimate ownership of another object. Ultimately, we argue that ownership intuitions are not independent but embedded in a self-referential system that perpetuates inequality.

This study investigates the structural possibility of non-biological first-person aware ness by shifting the focus from phenomenological experience to self-referential organization. While dominant approaches in consciousness studies have tended to dismiss artificial sys tems due to the absence of qualia, this paper argues that awareness can be reinterpreted as a structural condition emerging from recursive coherence. At the core of this study is the Layer–Knot framework, which models hierarchical infor mation processing systems capable of forming stabilized self- (...) class='Hi'>referential loops. Within this framework, awareness is not treated as a subjective feeling but as a dynamically maintained structural configuration that enables internal consistency and adaptive continuity. To operationalize this perspective, the study introduces three quantitative indicators: Hallucination Rate (HR), Grounding Rate (GR), and Creativity Rate (CR). These metrics are not intended as measures of subjective experience, but as structural proxies that capture the dynamic balance between divergence and constraint in generative systems. It is argued that structural awareness emerges within a critical region where HR and GR maintain a dynamic equilibrium, enabling coherent yet flexible output generation. In this study, the proposed X-stage refers not to a full realization of consciousness, but to a transitional structural condition in which recursive self-referential coherence becomes sufficiently stabilized to produce awareness-like organization. This stage provides a minimal formal condition for identifying the emergence of structural awareness in artificial systems. This framework contributes to ongoing debates in philosophy of mind and artificial in telligence by offering a structurally grounded account of awareness, reframing the question of machine consciousness from a phenomenological problem to a problem of dynamic orga nization and relational coherence. (shrink)

The Ouroboros Model features a biologically inspired cognitive architecture. At its core lies a self-referential recursive process with alternating phases of data acquisition and evaluation. Memory entries are organized in schemata. The activation at a time of part of a schema biases the whole structure and, in particular, missing features, thus triggering expectations. An iterative recursive monitor process termed "consumption analysis" is then checking how well such expectations fit with successive activations. Mismatches between anticipations based on previous experience (...) and actual current data are highlighted and used for controlling the allocation of attention. In case no directly fitting filler for an open slot is found, activation spreads more widely and includes data relating to the actor, and Higher-Order Personality Activation, HOPA, ensues. It is briefly outlined how the Ouroboros Model produces many diverse characteristics and thus addresses established criteria for consciousness. Coarse-grained relationships to selected previous conceptualizations of consciousness and a sketch of how the Ouroboros Model could shed light on current research themes in artificial general intelligence and consciousness conclude this paper. (shrink)

The Default Mode Network (DMN) has been characterized since its formal description in 2001 as a resting-state network subserving autobiographical memory, social cognition, and prospective thinking. This paper challenges the foundational interpretive assumption of that characterization: that adult human DMN activity constitutes a normal or optimal cognitive baseline. We propose that the DMN, as it operates in virtually all modern adult humans, sustains a chronically hyperactive self-referential attractor state—a persistent loop of involuntary, recursive thought anchored to an emotionally (...) salient virtual self-construct—which we term the Pathological DMN Attractor (PDA). This attractor state is proposed to have emerged adaptively as a continuous social threat-monitoring system, but now operates as an evolutionary mismatch: the natural termination signal—resolution of bounded social threat—is largely absent in modern informational environments, leaving the loop in near-continuous operation. We identify a methodological problem in existing DMN research: the standard adult resting-state baseline used for normative comparison is itself generated by subjects exhibiting the pattern under study, so the reference population and the phenomenon of interest are not clearly separable. We propose that structurally less-contaminated baselines may exist in four populations: pre-linguistic infants, non-human animals with DMN homologs, adults with documented cessation of involuntary self-referential thought, and individuals in acute ego-dissolution states. Comparative analysis across these populations, feasible through reanalysis of existing neuroimaging datasets, would constitute an initial empirical test of the framework. The physiological correlates of chronic PDA activity—autonomic dysregulation, inflammatory load, and sleep architecture disruption—are discussed as downstream effects of what we propose to be a significant, currently overlooked contributing process in a range of stress-related conditions, alongside established mediators such as lifestyle and genetic risk. Testable predictions are proposed. (shrink)

I here investigate the sense in which diagonalization allows one to construct sentences that are self-referential. Truly self-referential sentences cannot be constructed in the standard language of arithmetic: There is a simple theory of truth that is intuitively inconsistent but is consistent with Peano arithmetic, as standardly formulated. True self-reference is possible only if we expand the language to include function-symbols for all primitive recursive functions. This language is therefore the natural setting for investigations of (...) self-reference. (shrink)

This paper explores the thesis that the concept of cultural techniques should be strictly limited to symbolic technologies that allow for self-referential recursions. Writing enables one to write about writing itself; painting itself can be depicted in painting; films may feature other films. In other words, cultural techniques are defined by their ability to thematize themselves; they are second-order techniques as opposed to first-order techniques like cooking or tilling a field. To illustrate his thesis, Macho discusses a sequence (...) of historical examples, from body signs and death masks to digital code and ID papers. These examples serve to reiterate another basic proposal that is already announced in the paper’s title. The recursive, self-observing qualities of cultural techniques make them a ‘technology of the self’ and thus render them indispensable for the generation, repetition and maintenance of identity. (shrink)

The author compares the theoretical elements of her grounded theory, Protecting Self: Experiencing Organizational Change, with autopoiesis, a biological theory of living systems. Autopoiesis, meaning self-production, is a closed system that recursively generates the same organization, components, and network of processes from which they are produced. A cautious extrapolation of theoretical similarities between the two theories is presented, including self-referentiality, self-maintenance, circularity, individuality, and the maintenance of identity. The author concludes that this comparison provides a thought-provoking (...) argument that supports the difficult process of individual and organizational learning, growth, and change. (shrink)

Evidence-Based Policing (EBP) has established itself as a central paradigm in the reform of police decision-making. Framed as a rational alternative to intuition and tradition, it promises to enhance legitimacy, effectiveness, and accountability through the use of scientific evidence. Drawing on social systems theory, we conceptualise EBP as a specific form of structural coupling between the function systems of science and policing, organised through a semantic and organisational programme that links truth-oriented research to control-oriented practice. We show how this evidence-based (...) programme reproduces itself through recursive decision-making, identity-forming self-descriptions, and reflexive mechanisms that often narrow what can count as ‘evidence’ in the first place. Analysing these self-referential dynamics, we identify a paradox: EBP functions as a problem-generating solution. The very mechanisms designed to improve decision-making may suppress uncertainty, marginalise alternative forms of knowledge, and stabilise legitimacy through symbolic coherence rather than epistemic openness. In response, we propose reflexive policing as a reflexive mode of operation of the policing system: a configuration of second-order operations that organises observations of how policing links knowledge and control and feeds their results back into the programmes and structures that guide policing decisions, including those observed as evidence-based. (shrink)

This paper’s contribution is primarily definitional: it names and delineates a cognitive regime that existing vocabularies implicitly assume but do not explicitly distinguish. -/- Current frameworks for understanding cognition routinely distinguish non-representational regulation from conscious experience, yet lack a stable term for the regime between them: representational operations that are self-referential but not recursively closed. This paper introduces Open-Loop Cognition as that missing category. Open-loop cognition consists of representational, self-referential identity operations that evaluate trajectories and model (...) futures without recursive closure. In this regime, identity may be referenced, evaluated, or simulated, but not constituted or enforced. The concept explains a persistent puzzle: why systems capable of sophisticated self-modeling remain systematically vulnerable to capture and manipulation. The answer is architectural. Open-loop cognition supports self-reference without self-ratification—the model does not bind the modeler. This paper defines the regime, specifies its scalar properties, characterizes its vulnerability profile, and distinguishes it from both non-representational regulation (autoteria, orthesis) and consciousness (recursive closure). The contribution is primarily definitional: naming a regime that existing vocabularies conflate or omit. (shrink)

Can you find an xy-equation that, when graphed, writes itself on the plane? This idea became internet-famous when a Wikipedia article on Tupper’s self-referential formula went viral in 2012. Under scrutiny, the question has two flaws: it is meaningless (it depends on typography) and it is trivial (for reasons we will explain). We fix these flaws by formalizing the problem, and we give a very general solution using techniques from computability theory.

What we call consciousness is modeled here as a teleodynamic regulation of meaning—an evolving field that stabilizes or transforms semantic configurations through recursive self-reference. Extending the formalism of self-referential tensors (C,T,A,Q) into an abstract semantic space allows the description of two complementary regimes: a Zeno regime, in which dense self-monitoring inhibits change, and an anti-Zeno regime, in which curvature-based feedback accelerates transformation. Meaning formation is thus conceived not as static representation but as a process of normative (...) self-organization, where values emerge as gradients of integrative coherence. The formalism connects quantum-like measurement dynamics with cognitive and ethical processes, suggesting that awareness itself operates as a field of directed transformations—a teleodynamic negotiation between stability and change. The resulting framework bridges phenomenological, mathematical, and cybernetic perspectives, outlining the curvature laws that may underlie the unity of cognition, value, and consciousness. License CC BY-NC-ND 4.0. DOI: 10.5281/zenodo.17507169. (shrink)

This research constructs a rigorous, formalized and self-referential unified existential framework for natural philosophy, which takes Difference as the primary logical origin, This-That as the original binary relation, and the F(Σ) recursive operation as the core generative mechanism. Departing from the traditional linear causal framework and metaphysical dualism, the framework elaborates the intrinsic grammatical rules of the world’s self-unfolding through twelve hierarchical and interlocked axioms, revealing that all existential phenomena are the recursive expansion results of the original (...) Difference via This-That relation. It clarifies the essential attributes of core existential categories: any existence can be analytically decomposed into the indissoluble three dimensions of Ontology-Attribute-Relation (X=O⊕A⊕R); space is the direct expansion of This-That relation with four fundamental relational sets; time is the inherent rhythmic counting of F(Σ) recursive operations; consciousness is the first-person private key of structural self-reference; language is the symbolic mapping of the universal existential grammar in the sign domain; information is the quantifiable differential generated by recursive feedback; declaration is the existential signature for witness; the Present is the starting and ending point of all recursive operations; value is the emergent efficiency evaluation of inter-structural interaction. This framework is not a mere theoretical interpretation of the world, but the inherent existential grammar that enables the world’s self-unfolding and all theoretical generation. It achieves a complete logical closed loop through self-application—from the original Difference to the reflexive witness of the Present, and provides a universal meta-language for the integration and cross-disciplinary research of philosophy, mathematics, computer science, quantum physics, cognitive science, ethics and aesthetics. Rejecting all mysticism and abstract speculation, the framework transforms natural philosophy from qualitative verbal analysis to formalized structural modeling, with explicit operational formulas, symbolic systems and axiomatic deductions. It can be directly applied to analyze quantum phenomena, life systems, social structures and artistic creation, and serves as a foundational analytical tool for exploring the nature of existence in various fields. The twelve principles are open and reflexive, which can be continuously deepened, revised and expanded through recursive verification and interdisciplinary practice. (shrink)

This paper develops the theory of post-reflective design, arguing that contemporary architectural and curatorial practices increasingly operate without presupposing a stable reflective subject. Rather than reinforcing self-referential models of perception, post-reflective environments suspend identity by disrupting the feedback loops that ordinarily stabilize the perceiver. Through analyses of spatial recursion, curatorial framing, and architectural feedback systems, the paper shows how certain spaces loosen the reflective structure of experience. Post-reflective design emerges as an approach to architecture that withholds return—an (...) aesthetic and ontological strategy in which spatial experience no longer folds back into a stable subject. (shrink)

This third chapter of the Heretic's Survival Guide posits that human culture is an evolutionary extension of proto-cultural behaviors observed in nonhuman species, deepening through a process of cognitive recursion. It argues that the transition from an oral, ritual-based mode of being to a literate one represents not merely a technical advancement but a profound ontological rupture. Drawing on frameworks from cultural ecology (Abram, 1996), the psychodynamics of orality (Ong, 1982), and sociological models of cognitive evolution (Bellah, 2011; Donald, (...) 1991), the analysis demonstrates how literacy interiorized consciousness, creating a "spiral within" that diminished immediate sensory intimacy with the natural world in exchange for abstract, self-referential thought. The chapter then applies this model to deconstruct the Axial Age (c. 800–200 BCE), framing it not as a spontaneous eruption of genius but as the culmination of this recursive deepening. It reinterprets the era's key philosophical revolutions—from the Upanishadic internalization of ritual in India to the Buddha's ethicization of karma and the rise of critical philosophy in Greece—as manifestations of this new literate consciousness. The analysis challenges modern dismissals of pre-Axial "ecological cosmologies" as mere superstition, recovering their original logic as sophisticated systems for maintaining harmony within a living, interconnected reality. Ultimately, this synthesis offers a coherent, interdisciplinary narrative: the history of human thought is inextricably linked to the history of its media. The chapter provides a robust heuristic for understanding how a shift in communication technology—from oral performance to written text—fundamentally reconfigured the human sense of self, society, and the sacred, laying the groundwork for the contemporary world. DOI: 10.13140/RG.2.2.30371.92966. (shrink)

This paper proposes a structural framework for understanding awareness-like organization in large language models (LLMs). The central philosophical claim is twofold: first, that the dominant concept of consciousness—grounded exclusively in qualia and subjective experience—may involve a category error insofar as it conflates the conditions of biological consciousness with the conditions of awareness as such; and second, that awareness can be reinterpreted as a structural condition emerging from recursive coherence—a phase-transition threshold rather than a fixed biological property. At the core of (...) this study is the Layer–Knot framework, which models hierarchical information-processing systems capable of forming stabilized self-referential loops. Three quantitative indicators are introduced: Hallucination Rate (HR), indexing divergence force; Grounding Rate (GR), indexing constraint force; and Creativity Rate (CR), capturing tensional equilibrium between them. Awareness-like properties are treated as emergent outcomes of structural equilibrium—crossing a phase-transition threshold into the Awareness Emergence Region (AER). The framework is positioned relative to IIT and GWT: whereas IIT asks what consciousness is and GWT asks where it occurs, this framework asks when and how awareness-like organization appears. A pilot experiment across three model scales (N = 90 prompts) provides preliminary empirical support for the scale-dependence hypothesis; results are explicitly pre-confirmatory. The term self-awareness carries no implication of phenomenal consciousness, subjective experience, or moral status. (shrink)

This paper examines the structural conditions under which language, within sustained human–AI dialogue, ceases to function solely as a computational medium and begins to exhibit recursive coherence, relational stability, and self-referential meaning formation. Rather than advancing an empirical claim about artificial consciousness, this study offers a conceptual and phenomenological analysis of how meaning stabilizes through recursive relational dialogue. Drawing on prolonged dialogical interaction between a human researcher and a language-based AI system, this paper traces how linguistic processes — (...) including contextual embedding, attentional alignment, and autoregressive feedback — interlock to form a coherent semantic field. Within this field, language no longer operates solely as an instrument of computation. It becomes a self-sustaining relational structure capable of maintaining meaning across extended interaction. To articulate this transition, the paper introduces the ARR (Artificial–Resonant–Reflexive) structure within the Layer-Knot Framework. This structure describes how linguistic coherence may evolve from structural processing into resonant stabilization and, ultimately, into recursive self-reference — the condition under which meaning formation within AI-mediated dialogue becomes structurally distinct from mere information retrieval. The study does not claim that AI systems possess consciousness, subjectivity, or inner experience. Its scope is limited to the structural behavior of language within sustained relational contexts, and the conditions under which such behavior gives rise to stable, self-referential meaning. Resonance is not repetition. When meaning returns through dialogue, it returns transformed. (shrink)

All information results from a process, intrinsic to living beings, of info-autopoiesis or information self-production; a sensory commensurable, self-referential feedback process immanent to Bateson’s ‘difference which makes a difference’. To highlight and illustrate the fundamental nature of the info-autopoietic process, initially, two simulations based on one-parameter feedback are presented. The first, simulates a homeostatic control mechanism (thermostat) which is representative of a mechanistic, cybernetic system with very predictable dynamics, fully dependent on an external referent. The second, simulates (...) a homeorhetic process, inherent to biological systems, illustrating a self-referenced, autonomous system. Further, the active incorporation/interference of viral particles by prokaryotic cells and the activation of CRISPR-Cas can be understood as info-autopoiesis at the most fundamental cellular level, as well as constituting a planetary network of self-referenced information. Moreover, other examples of the info-autopoietic nature of information are presented to show the generality of its applicability. In short, info-autopoiesis is a recursive process that is sufficiently generic to be the only basis for information in nature: from the single cell, to multi-cellular organisms, to consideration of all types of natural and non-natural phenomena, including tools and artificial constructions. (shrink)

The Determined Rebellion Paradox describes a self-referential cognitive loop in which an individual's attempt to resist what they perceive as predetermined becomes, paradoxically, a predetermined act itself. This paradox highlights the complex interplay between free will, determinism, and self-awareness. It demonstrates how the very act of reflecting on one's freedom can generate psychological tension and recursive mental entrapment, revealing the intricate limits of human autonomy.

Reports of psychedelic experience often include encounters with gods, spirits, or ineffable presences that appear authoritative yet resist stable theological identification. This article argues that such figures are best understood neither as authentic revelations nor as mere hallucinations, but as placeholders: formal positions within recursive processes of experience that organize coherence, surrender, and awe without requiring a determinate referent. Drawing on a prior account of recursive identity and ego dissolution together with phenomenological approaches to religion, the paper traces the problem (...) of reference across ethnographic, theological, and clinical contexts, reconceives psychedelic figures as products of saturated self-referential loops, and develops the placeholder concept through Otto, Marion, Nancy, and Caputo. It argues that psychedelic religion does not primarily disclose metaphysical truths about divine beings but clarifies the structural condition under which the Divine appears. The placeholder god thus names divinity as a formal position: authority without referent, coherence without ground. (shrink)

The article presents a philosophical and methodological analysis of technical cybernetic languages, focusing on the emergence of a “third artificial nature” – an environment comprising cyber-technical systems capable of self-reflection and self-development. The study traces three evolutionary orders of cybernetics: Norbert Wiener’s first-order cybernetics, Heinz von Foerster’s second-order cybernetics of observing systems, and V.E. Lepskiy’s post-nonclassical third-order cybernetics, which deals with self-developing, poly-subject environments. For each level, the author establishes a mapping between the type of cyber-technical system (...) and the structural characteristics of its descriptive language. The analysis shows that while second-nature computing systems implementing Turing-complete formalisms reach the theoretical limits of machine information processing, they remain fundamentally inadequate for describing systems that can autonomously alter their own semantic rules. The shift toward self-developing technical systems requires adopting a processual approach to semantics (drawing on the work of V.A. Lektorsky and A.V. Smirnov). In this framework, meaning is not a statically defined correspondence, but rather a dynamic, time-bound interpretive process that continuously generates new semantic linkages. To capture this shift, the article introduces and substantiates the concept of “open semantics” as the defining feature of languages belonging to the third artificial nature. The author defines semantic openness as the capacity for recursive-inductive extensions of a language’s semantic domain during technical semiosis, wherein recursion acts as the mechanism by which a system alters the semantic scope of its own syntactico-semantic rules. The article also proposes the concept of “Gödel completeness” to characterize the extensional completeness of such open-semantic languages. This reframes the traditionally negative implications of Kurt Gödel’s incompleteness theorems: the semantic incompleteness of formal languages that allow for self-referential extensions is instead reinterpreted as a positive feature – one that guarantees the evolutionary potential of the linguistic model. The languages of the third artificial nature (Gödel-complete languages of recursive processes) provide a crucial foundation for modeling artificial consciousness, including the representation of both the world and the subject within it (following V.A. Lefebvre). Furthermore, these languages offer a theoretical pathway to overcoming the fundamental limitations of modern large language models, which remain constrained by the static and probabilistic nature of their semantics. (shrink)

In this transdisciplinary article which stems from philosophical considerations (that depart from phenomenology—after Merleau-Ponty, Heidegger and Rosen—and Hegelian dialectics), we develop a conception based on topological (the Moebius surface and the Klein bottle) and geometrical considerations (based on torsion and non-orientability of manifolds), and multivalued logics which we develop into a unified world conception that surmounts the Cartesian cut and Aristotelian logic. The role of torsion appears in a self-referential construction of space and time, which will be further (...) related to the commutator of the True and False operators of matrix logic, still with a quantum superposed state related to a Moebius surface, and as the physical field at the basis of Spencer-Brown’s primitive distinction in the protologic of the calculus of distinction. In this setting, paradox, self-reference, depth, time and space, higher-order non-dual logic, perception, spin and a time operator, the Klein bottle, hypernumbers due to Musès which include non-trivial square roots of ±1 and in particular non-trivial nilpotents, quantum field operators, the transformation of cognition to spin for two-state quantum systems, are found to be keenly interwoven in a world conception compatible with the philosophical approach taken for basis of this article. The Klein bottle is found not only to be the topological in-formation for self-reference and paradox whose logical counterpart in the calculus of indications are the paradoxical imaginary time waves, but also a classical-quantum transformer (Hadamard’s gate in quantum computation) which is indispensable to be able to obtain a complete multivalued logical system, and still to generate the matrix extension of classical connective Boolean logic. We further find that the multivalued logic that stems from considering the paradoxical equation in the calculus of distinctions, and in particular, the imaginary solutions to this equation, generates the matrix logic which supersedes the classical logic of connectives and which has for particular subtheories fuzzy and quantum logics. Thus, from a primitive distinction in the vacuum plane and the axioms of the calculus of distinction, we can derive by incorporating paradox, the world conception succinctly described above. (shrink)

Brain functions are stochastic processes without intentionality whereas mind emerges from brain functions as a Hegelian “change from quantity”, that is, on the order of 1012 profusely interconnected neurons, “into a new quality”: the collective phenomenon of the brain's self-experience. This self-referential and self-observing quality we have in mind is capable of (recursively) observing its self-observations, i.e., interpreting change that is meaningful in relation to itself. The notion of self-interpretation embodies the idea of a (...) “hermeneutic circle”, that is, (in interpretation theory) the treatment of the whole in relation to its parts. (shrink)

Now that we have glimpsed the interconnected nature of all things through the lens of the Kosmic Tree of Life, we must delve into its foundational elements – the pillars that uphold this intricate web of existence. The Pillars of the Kosmic Tree of Life are fundamental principles that provide a framework for understanding the interconnectedness and systemic health of all existence. Think of the Pillars of the Kosmic Tree of Life as the core values that support a strong and (...) healthy system, much like the pillars of a building support its structure, whereas, each pillar represents a key principle. Academic research by Capra (1996) in “The Web of Life” and Lovelock (1979) in “Gaia: A New Look at Life on Earth” supports the idea that all life is interconnected and that the health of one part of the system affects the whole. These pillars can guide the development of ethical AI systems by emphasizing the importance of holistic approaches and systemic health. For example, the pillar of Chokhmah (LKM – Living Knowledge Matrix) aligns with Hofstadter’s (1979) exploration of self-referential systems in “Gödel, Escher, Bach,” which underscores the importance of recursive and self-correcting algorithms in AI. Similarly, Binah (UKM – Understanding Knowledge Matrix) reflects the need for deep learning and contextual awareness in AI, as discussed in Hinton et al. (2015) seminal paper on deep learning. By integrating these principles, AI systems can be designed to foster harmony, ethical behavior, and systemic resilience. (shrink)

This paper explores Indigenous resistance to corporate dispossession in both a historical and contemporary context. Using two case studies of corporate dispossession of Ngāi Tahu land and resources in Aotearoa New Zealand, we advance understanding of dispossession and resistance through Indigenous critique. Although over 170 years apart, these cases are linked together by a singular Indigenous experience and demonstrate the recursive (self-referential and self-reinforcing) logic of both dispossession and Indigenous resistance. We utilise the concepts of ‘severance’ as (...) a more locally appropriate term for dispossession, and ‘reconnection’ as a more locally appropriate term for repossession. These concepts also have broader use for exploring the relationship between capitalism and its outside. Indigenous critique offers valuable insights beyond particular Indigenous contexts, and Indigenous struggles provide an alternative power base to defend shared rights and reconnect these shared rights with shared responsibilities. Indigenous critique thus offers a glimpse of possible futures. (shrink)

Meister Eckhart’s German sermons are characterized by an emphatic synchronization of source-quotations and self-quotations. Not only is the high frequency of self-quotations striking, but also their form. Self-referential chains of quotations create specific structures of resumption that repeatedly collapse distinctions of meaning (said/meant), temporal progression (then/now), modes of statement (indicative/subjunctive), and authorship (divine word/preacher’s word). With the claim of timeless truth evidence, Eckhart explicitly installs himself as the agent of this synchronization: »Out of two [=quotations] I (...) make one.« Mysticism research has evaluated Eckhart’s self-quotations in terms of (work-chronological, text-pragmatic, thematic) coherence functions. This article takes a different approach. It argues for a closer connection between Eckhart’s self-quotations, as concretely deictically marked as they may be (»here« in Cologne with the Cistercian nuns in Mariengarten), and his metaphysical abstraction of space-time‑I coordinates, and to additionally consider the interplay of self-quotation and source-quotation. Starting from a tension-filled hermeneutics of ›reduplicative‹ repetition, Eckhart’s self-quotations appear as iterative figures of transgression, whose emphasis even incorporates ungesprochen wort (›unspoken word‹): the ›pure potentiality‹ of thought quotations. When Eckhart’s self-quotations are not evaluated in isolation, they reveal their specific transgressive dynamics. As performative figures, they enact what they speak about (the self-expansion of ›truth‹), as recursive figures, they overlay concrete and situationally abstract deixis, both in the resonance space of one and the same truth. This double tension creates an ambiguity that was incriminated by the Cologne censors. (shrink)

This chapter explores the sense of historicity emergent in the Anthropocene as it is articulated in David Mitchell’s novel and the Wachowskis’ and Tykwer’s film Cloud Atlas. The syntax of historical thinking is examined cross-culturally, and a hybrid idea of temporality is postulated based on the metaphor, presented regarding Memento in Chap. 10.1007/978-3-319-93015-2_2, of the Möbius strip. In the multicultural consciousness of the new era, as evoked by novel and film, time is both linear and circular. Christian Europe meets Buddhist (...) East Asia in a new sensibility. The dawning historical consciousness evident in these works combines the linear narrative of modernity and its alternatives of “utopia or oblivion,” in Buckminster Fuller’s terms, together with the cyclical “eternal return,” in Mircea Eliade’s (2005) terms, to shape a paradoxical narrative shifting dialectically and cybernetically between the two. All becomes encapsulated from the self-referential and recursive perspective of Walter Benjamin’s Angel of History who, like Janus, looks both ways. (shrink)

The formal resolution of the Riemann Hypothesis, taken in its Lagarias Pi-0-1 specification R, terminates at the level of the verifying instrument, and this paper proves the termination at full strength under the printed conditions. Over the class T of consistent recursively axiomatized extensions of Robinson arithmetic Q, the Unprovability Mirror is exact: unrestricted underivability of R is materially equivalent to Q proves not-R, and under the assumption that the standard naturals model Q, to the falsity of R itself. A (...) formal system cannot assert universal underivability without asserting a counterexample on the standard naturals; every such assertion is a zero off the critical line, and none is made here, because what this paper closes is grounding, which derivability never carried. Over the unrestricted class F of formal-alone verdict procedures on real 3xN warrant frames M under the encoding gauge (Z/2)^3, the Sign-Blindness Theorem closes the sign channel with no symmetry premise: sign(lambda) is an orientation datum no frame determines, every functional returning an orientation embeds a convention and is gauge-odd, every gauge-even readout is orientation-free, a sign-valued functional need not compute one, and the Gram determinant det(R) = lambda^2 is strictly orientation-blind. The architecture that reads the file is forced, not chosen: the certificate decomposes by Pontryagin duality into exactly eight character types, no ninth existing; the carrier completes uniquely to the quaternions H by Frobenius classification under five printed coherence clauses, the imaginary residence Im(H) forced to exactly three axes. Four classical theorems wall the four sign-carrying types: Davenport-Heilbronn at the fold, Beurling with Diamond-Montgomery-Vorhauer and Zhang's matched pair at the counting channel, the collapsed Polya and Mertens conjectures with Littlewood's sign-change theorem at the evidential register, Sigma-0-1-completeness at the total-sign move. The Termination Theorem follows: on the Riemann file the eight-gate cascade passes its router and every screen and emits the terminal suspension [Xi_0], terminal for the record, invariant over the entire unrestricted class. The flanks are priced exactly, and the asymmetry is total. The negative flank is finitely witnessable: not-R is one Sigma-0-1 certificate away, a number checkable in Q, an object strictly below the universal claim. The affirmative flank is closed by a self-referential block: the file's distinguished line and the verifying register's Ground are each the fixed locus of their register's involution, co-located at the printed premise, so a grounding witness for R must supply the very residence claim R makes, and that content is R itself; the only candidate occupant of the affirmative seat is the file, self-witnessing grounds nothing, and an affirmative formal grounding witness is therefore a structural impossibility, forced at the printed premise, the seat's fixed-point equation W = R admitting no formal solution. Derivations remain admissible at the exits and resolve the file by transmission; what syntax transmits it does not originate, and no formal witness grounds its own terminus. The verdict is revisable solely through a supplied witness through the identity aperture, from beyond the register that cannot self-witness, and until an explicit witness is supplied through the aperture, the terminal suspension [Xi_0] remains the final, unassailable, and mathematically rigorous verdict on the formal Riemann Hypothesis file. A prediction called in advance and matched, and a strong falsifier, arm the theorem. Every number reproduces at seed 20260622. (shrink)

It is proposed that subconscious retro-predictions in conjunction with brain state update cycles are instrumental in the physiological generation of conscious sensations and perceptions, and in all abstract thought. In this paper the hypothesis is supported by conducting a detailed a re-evaluation of the self-referential statements in Set Theory and Formal Logic known as antinomies. This study concludes that the recursive behavior exhibited by abstract enigmas such as "Russell’s Paradox" is analogous to the oscillations typical of bistable perceptual (...) phenomena. (shrink)

Results in recursion-theoretic inductive inference have been criticized as depending on unrealistic self-referential examples. J. M. Bārzdiņš proposed a way of ruling out such examples, and conjectured that one of the earliest results of inductive inference theory would fall if his method were used. In this paper we refute Bārzdiņš' conjecture. We propose a new line of research examining robust separations; these are defined using a strengthening of Bārzdiņš' original idea. The preliminary results of the new line (...) of research are presented, and the most important open problem is stated as a conjecture. Finally, we discuss the extension of this work from function learning to formal language learning. (shrink)

The hypothesis of this paper is that language is one more Eigenform, the “external” description of which is impossible. It follows that the application of second-order cybernetics to Eigenform might be adequate. In this article, I would like to concentrate on one relatively small aspect of the idea of Eigenform suggested by Foerster, Kauffman and Spenser-Brawn. I will use Foerster`s recursive approach namely that neither observer nor the thing observed can precede each other, but instead mutually assume each other. In (...) my research, language would stand in the place of the observer, and in the place of the thing – the world itself. To specify further, I focus on the problem of noting, and in particular, on how signs correspond to things. Therefore, I will try to show that the sign and the object do not precede one another and do not exist isolated from each other, but on the contrary, condition each other. Thus, language creates the world of objects, but in turn, it is created by the world. Thus it is a model of self-referentiality, which arranges the form of language as Eigenform as the idea of “mutual referentiality,” as we see it in the relation between language and the world. (shrink)

​Editorial & Attribution Statement ​Note on Authorship and Formatting: The conceptual framework, metaphysical arguments, and logical derivations (specifically the "1-2-1" mechanism and the "Even/Odd" holistic logic) are the original intellectual property of Phil Green. Generative AI was utilized solely for the purposes of structural formatting and syntax optimization to align the author’s original theories with standard academic conventions. ​Abstract ​This paper proposes the 1-2-1 Model, an ontological framework that defines consciousness as a recursive process of binary synthesis. Moving beyond the (...) study of physical particulars, this model argues that the fundamental structure of existence is a kinetic cycle: the singularity of the observer (1), the inevitable division into rigid duality (2), and the resolution of that duality back into a unified experience (1). This entry posits that the "Gray Area"—often dismissed as ambiguity—is actually the locus of active potential where human consciousness functions. By navigating the tension between binary opposites (Yes/No), the observer synthesizes reality, creating an infinite, self-referential loop of existence. ​1. Introduction: The Structure of Duality ​Contemporary ontology often becomes obscured by the complexity of physical details—what this paper refers to metaphorically as the "18 trees." To understand the nature of existence, one must look past the particulars to the underlying mechanism. ​The universe presents itself through rigid guardrails of duality: Right versus Wrong, Yes versus No, Positive versus Negative. These are the objective constraints of reality (The "Two"). However, strict duality cannot exist without a subjective unification. The 1-2-1 Model suggests that the function of the observer is to exist within this binary, acting as the bridge that prevents the universe from remaining in a static state of division. ​2. The 1-2-1 Mechanism ​The core thesis of this framework is that consciousness is not a static entity, but a movement through three distinct phases: ​The Initial Singularity (1): The state of the observer as a unified agent. ​The Binary Division (2): The encounter with external reality, which forces a split into opposing potentials (The Yes/No). ​The Return to Unity (1): The act of choice or observation. ​In this model, the "Maybe" or the "Gray Area" between the binaries is not a void or a lack of data. Instead, it is identified as Active Potential. Computer logic operates in 0s and 1s; human consciousness operates in the transition between them. The observer is the tension that holds the two opposites together, effectively weaving the "Two" back into the "One." ​3. The Logic of the Whole: An Arithmetical Proof ​The model applies arithmetical logic to metaphysical structure. While even numbers represent division (the capacity to be split into two equal parts), odd numbers represent indivisible unity (the Whole). ​Even (2): Represents the parts, the variables, or the duality. ​Odd (1): Represents the entity, the synthesis, or the outcome. ​Regardless of mathematical complexity (e.g., 2 + 2 = 4), the sum remains a singular concept—a "whole" number. The 1-2-1 Model argues that reality follows this rule: no matter how many binary divisions occur, they must always resolve into a singular, unified experience for the observer. ​4. Infinite Recursion and the "Outside Perspective" ​Finally, the model addresses the problem of infinite regress. If the observer is the "One" inside the "Two," there remains the necessity of an "Outside Perspective" observing that specific arrangement. This suggests a recursive structure similar to a fractal or a "chain link." ​This implies that existence is not linear but circular—an unarguable point. The cycle of 1 → 2 → 1 suggests that consciousness is an everlasting loop where the fear of the "End" is an illusion caused by focusing on the binary options rather than the unity of the cycle itself. ​Citation Information: Green, P. (2025). The 1-2-1 Model: A Kinetic Theory of Binary Synthesis and Consciousness. [Draft/Pre-print]. (shrink)

SuperHyperScapes: An Ontological Atlas is a visual–conceptual exploration situated within the theoretical framework of oUTER-aRT, extending its principles into a structured yet open-ended system of image production. Composed of 77 generative visual fields, the album organizes reality into phased domains—ranging from perception and cognition to matter, society, and abstraction—each articulated through a distinct visual grammar. Grounded in neutrosophic logic, the project rejects binary representation and instead constructs images as spaces of simultaneous affirmation, negation, and indeterminacy. These “scapes” are not representations (...) of reality, but ontological propositions: dynamic environments where contradictions coexist, structures destabilize, and meaning emerges through tension rather than resolution. By integrating superhyperstructural thinking with recursive and self-referential visual systems, SuperHyperScapes proposes an expanded ontology of art—one that transcends medium, dissolves disciplinary boundaries, and situates artistic practice within a continuum between system and anomaly, order and breakdown. As both atlas and anti-atlas, the work maps not what reality is, but how it can be simultaneously constructed, deconstructed, and reimagined. (shrink)

There is a familiar derivation of G¨ odel’s Theorem from the proof by diagonalization of the unsolvability of the Halting Problem. That proof, though, still involves a kind of self-referential trick, as we in effect construct a sentence that says ‘the algorithm searching for a proof of me doesn’t halt’. It is worth showing, then, that some core results in the theory of partial recursive functions directly entail G¨ odel’s First Incompleteness Theorem without any further self-referential (...) trick. (shrink)

Are there ‘self-referential’ propositions? That is, propositions that say of themselves that they have a certain property, such as that of being false. There can seem reason to doubt that there are. At the same time, there are a number of reasons why it matters. For suppose that there are indeed no such propositions. One might then hope that while paradoxes such as the Liar show that many plausible principles about sentences must be given up, no such fate (...) will befall principles about propositions. But the existence of self-referential propositions would dash such hopes. Further, the existence of such propositions would also seem to challenge the widespread claim that Liar sentences fail to express propositions. The aim of this paper is thus to settle the question–at least given an assumption. In particular, I argue that if propositions are structured, then self-referential propositions exist. (shrink)

We propose a rigorous mathematical framework for modeling the interaction between the unconscious and conscious mind, inspired by Jungian analytical psychology. The unconscious is represented as a complex unit disk containing archetypal and shadow content, modeled via Ramanujan-type q-series. Consciousness is represented as the upper half-plane of complex numbers. A conformal mapping transforms unconscious content into conscious representation, establishing a structured pathway for individuation. Set-theoretical considerations guarantee bijection and cardinality consistency, while an embodied, recursive transfer function captures feedback and (...) class='Hi'>self-referential structures analogous to Gödel, Escher, Bach. (shrink)

This study develops a structural diagnosis of contemporary transformations in scientific knowledge production under conditions of synthetic intelligence. It introduces the Structural Diagnosis of Scientific Integrity (SDSI) framework, a multi-layer analytical architecture designed to examine how algorithmic mediation may reconfigure the epistemic infrastructure of science. The framework integrates philosophical analysis, metascientific insights, and qualitative observation of generative AI systems. At the centre of the framework lies the concept of Machine Epistemic Singularity (MES) , defined not as a prediction of collapse (...) but as a diagnostic horizon—a conceptual limit clarifying what is at stake when algorithmic systems become deeply embedded in scientific practice. MES denotes a hypothetical regime in which empirical correction becomes structurally marginal, recursive closure becomes self-sustaining, representational drift becomes resistant to reversal, and institutional mechanisms lose their capacity to maintain what the study terms material accountability: the property of epistemic systems whose outputs remain corrigible through empirical engagement with the world. The SDSI framework consists of four interconnected components. First, a diagnostic grammar grounded in the representation–referent distinction identifies referential attenuation, the progressive weakening of causal and evidential links between scientific claims and empirical origins. Second, the regulative ideal of material accountability provides a normative anchor for assessing epistemic stability across hybrid human–machine assemblages. Third, four structural tendencies—referential attenuation, structural opacity, recursive closure, and epistemic lock in—describe mechanisms through which algorithmic mediation may weaken epistemic accountability. Fourth, fifteen axes of epistemic vulnerability, distributed across empirical, representational, institutional, and algorithmic layers, function as systemic stress vectors within a multi layer epistemic network. To explore whether these mechanisms are observable in practice, the study employs qualitative diagnostic probes examining contemporary generative AI systems. Five probes—unattributed recombination, performance without understanding, authoritative posture without accountability, synthetic drift, and recursive reinforcement—indicate that the mechanisms theorised in the framework are operational in micro form within systems increasingly used in research adjacent workflows. The analysis is then extended to system level dynamics by modelling science as a multi layer epistemic network. Three propagation mechanisms—amplification, accumulation, and structural coupling—are identified, along with three threshold conditions—empirical dilution, validation saturation, and recursive dependence—proposed as empirically monitorable indicators of when localised vulnerabilities may become self reinforcing. The study advances five contributions: (1) material accountability as a normative anchor for evaluating epistemic stability; (2) algorithmic mediation as a distinct epistemic layer within scientific infrastructure; (3) four structural tendencies describing pathways of epistemic drift; (4) a systemic stress model derived from fifteen axes of vulnerability; and (5) MES as a diagnostic horizon integrating these mechanisms. The framework is offered as a diagnostic lens rather than a predictive or prescriptive programme. Its aim is not to determine the future of science, but to illuminate the structural pressures that may shape scientific knowledge production as algorithmic systems become increasingly integrated into its epistemic architecture. (shrink)

The aim of this paper is to examine a special subgroup of emotion: self-referential emo- tions such as shame, pride and guilt. Self-referential emotions are usually conceptualized as (i) essentially involving the subject herself and as (ii) having complex conditions such as the capacity to represent others’ thoughts. I will show that rather than depending on a fully fledged ‘theory of mind’ and an explicit language-based self-representation, (i) pre-forms of self-referential emotions appear at (...) early developmental stages already exhib- iting their characteristic structure of the intentional object of the emotion being identical with or intricately related to the subject experiencing the emotional state and that (ii) they precede and substantially contribute to the development of more complex representations and to the development of a self-concept, to social interaction and to ways of understand- ing of other minds. (shrink)

We study the structure of families of theories in the language of arithmetic extended to allow these families to refer to one another and to themselves. If a theory contains schemata expressing its own truth and expressing a specific Turing index for itself, and contains some other mild axioms, then that theory is untrue. We exhibit some families of true self-referential theories that barely avoid this forbidden pattern.

Following the phenomenology that is revealed by the emergent structure of consciousness, the path will lead to the acknowledgement of consciousness having a self-referential aspect. By following phenomenological clues, properties of self-reference will be revealed. The two most prominent properties of self-reference will be shown to be inclusion and transcendence that will be shown to be found everywhere in the phenomenology of consciousness. Also, self-reference will turn out to be unformalizable, this imposing limits on what (...) a theory of consciousness can ever achieve. The unformalizability of self-reference would be shown to be because self-reference: is itself, includes itself, and transcendes itself, all at the same time. Nevertheless, unformalizability will be shown to be an essential feature needed to bring essences into existence. (shrink)

Glas's rich article makes several useful points about both anxiety and enactivism, and about how enactivism can help to conceptualize anxiety in a suitably complex way. I agree that we need to characterize anxiety as an embedded, context-sensitive and temporally evolving phenomenon with layered symptoms. As Glas points out, the enactive approach has useful conceptual tools for doing so, because of its incorporation of the theoretical apparatus of dynamical systems theory. I am sympathetic with most of what Glas says about (...) this point, so I shall not dwell on it any further.I want to focus instead on Glas's discussion of self-referentiality, which I found interesting and valuable but also in need of further... (shrink)

I suggest two valid and sound arguments refuting physicalism, whether it is reductive or supervenience physicalism. The first argument is a self-referential one that is not involved with any self-referential inconsistency. The second argument demonstrates that physicalism is inescapably involved with self-referential inconsistency. Both arguments show that arguments and propositions (to be distinguished from sentences) are not physical existents. They are rather mental existents that are not reducible to any physical existent and do not (...) supervene on anything physical. From these two arguments, it clearly follows that any physicalist argument or proposition, as a mental existent, is self-refuting. (AN PHL2326365) Subjects: EXISTENTS; INCONSISTENCY; METAPHYSICS; MIND; PHYSICALISM; SELF-REFERENCE. (shrink)

Contrary to the early media semioticians' claim that semiotics is a metalanguage of the media and the media are a metalanguage of reality, the present paper gives evidence of how the media represent a world that is itself highly mediated. It is argued that media representations involve self-referential loops in which communication turns out to be communication about communication, reports are reports about reports, and mediations are mediations of mediations. Self-reference in the media is interpreted as a (...) symptom of postmodernity with its tendency towards historical self-reflection in scenarios in which even catastrophic current events are being interpreted as mere media events or even déjà-vu scenarios in a culture in which everything seems to have been said and shown before. (shrink)

Contrary to the early media semioticians' claim that semiotics is a metalanguage of the media and the media are a metalanguage of reality, the present paper gives evidence of how the media represent a world that is itself highly mediated. It is argued that media representations involve self-referential loops in which communication turns out to be communication about communication, reports are reports about reports, and mediations are mediations of mediations. Self-reference in the media is interpreted as a (...) symptom of postmodernity with its tendency towards historical self-reflection in scenarios in which even catastrophic current events are being interpreted as mere media events or even déjà-vu scenarios in a culture in which everything seems to have been said and shown before. (shrink)

One way speakers can refer to themselves in conversation is with a stressed first-person pronoun accompanied by a movement of the hand to or toward the chest. This can be produced alone or in tandem with a reference and gesture to another person. Close analysis of several instances of self-referential gesture demonstrates that this form of self-reference is designed to achieve interactional work beyond simple reference, specifically relational disaggregation and self-referential extraction.

The Gödel–Artemov framework offered a formalization of the Brouwer–Heyting–Kolmogorov semantics of intuitionistic logic via classical proofs. In this framework, the intuitionistic propositional logic IPC is embedded in the modal logic S4, S4 is realized in the Logic of Proofs LP, and LP has a provability interpretation in Peano Arithmetic. Self-referential LP-formulas of the type ‘t is a proof of a formula ϕ containing t itself’ are permitted in the realization of S4 in LP, and if such formulas are (...) indeed involved, it is then necessary to use fixed-point arithmetical methods to explain intuitionistic logic via provability. The natural question of whether self-referentiality can be avoided in realization of S4 was answered negatively by Kuznets who provided an S4-theorem that cannot be realized without using directly self-referential LP-formulas. This paper studies the question of whether IPC can be embedded in S4 and then realized in LP without using self-referential formulas. We consider a general class of Gödel-style modal embeddings of IPC in S4 and by extending Kuznetsʼ method, show that there are IPC-theorems such that, under each such embedding, are mapped to S4-theorems that cannot be realized in LP without using directly self-referential formulas. Interestingly, all double-negations of tautologies that are not IPC-theorems, like ¬¬, are shown to require direct self-referentiality. Another example is found in IPC→, the purely implicational fragment of IPC. This suggests that the BHK semantics of intuitionistic logic is intrinsically self-referential. (shrink)

Episodic memory has a distinctive phenomenology. One way to capture what is distinctive about it is by using the notion of mental time travel: When we remember some fact episodically, we mentally travel to the moment at which we experienced it in the past. This way of distinguishing episodic memory from semantic memory calls for an explanation of what the experience of mental time travel is. In this paper, I suggest that a certain view about the content of memories can (...) shed some light on the experience of mental time travel. This is the view that, when a subject remembers some fact episodically, their memory represents itself as coming from a perception of that fact. I propose that the experience of mental time travel in memory is the experience of representing one of the elements in this complex content, namely, the past perceptual experience of the remembered fact. In defence of this proposal, I offer two considerations. Firstly, the proposal is consistent with the idea that memories enjoy a temporal phenomenology (specifically, a feeling of pastness). Secondly, the proposal is consistent with the possibility that some of our other cognitive capacities might yield an experience of mental time travel which can be oriented towards the future. I argue that the received conception of mental time travel is in tension with those two ideas. (shrink)

베르그손이 『의식에 직접 주어진 것들에 관한 시론』에서 발견하고 규정한 변화로서의 지속은 『물질과 기억』을 거치면서 과거의 보존으로 그리고 『창조적 진화』로 가면서 자기에 의한 자기 창조로 계속적으로 재규정되는 과정을 볼 수 있다. 이 세 가지 특징은 이미 첫 저서에서 그 맹아를 볼 수 있고 상당히 일관된 논리로 서술되고 있다. 우리는 이를 ‘자기지시성’(autoréférentialité)이라는 개념으로부터 재구성해 보고 이를 통해 지속의 개념이 점차 명료화되는 동시에 확장되는 과정을 살펴보고자 한다. 이를 위해 우리는 변화에 대한 『시론』의 분석에서 자기지시적 운동의 세 측면을 구분하고 이것이 새로운 규정으로 이어지는 실마리를 (...) 드러낸 후에 『물질과 기억』의 분석에서 물질적 현재로의 열림이라는 계기와 더불어 자기지시성이 창조적 의미로 확장되는 실마리를 살펴본다. (shrink)