This article investigates the computational foundations of Immanuel Kant’s transcendental logic and its relevance to artificial intelligence and machine consciousness. We demonstrate that while Kantian analytic judgments map to decidable computations on standard deterministic Turing machines, synthetic a priori judgments require extended models, specifically, Turing machines equipped with oracles, to capture their non-algorithmic, self-positing nature. Building on Johann Gottlieb Fichte’s formulation of consciousness as a self-negating loop (“I = not-I”), we formalize a consistent syllogistic system that accommodates non-trivial self-reference. By interpreting this system topologically via spanning simplicial complexes, we show that reflexive reasoning remains both logically consistent and polynomial-time decidable. Furthermore, we introduce quantitative evaluation frameworks, including a Turing Simulation Test and a Reflexion Loop Consciousness Test, to assess whether large language models exhibit minimal conscious-like behavior, such as escaping semantic stagnation and integrating contextual grounding. Thus, we argue that transcendental logic constitutes a viable, computationally tractable framework for modeling self-aware, synthetic reasoning in artificial agents.
We introduce and elaborate a new, evolutionary worldview, as a “Third Story”, intended to replace and complement the earlier religious (First) and mechanistic (Second) worldviews. The confusions created by a world that is ever more volatile, uncertain, complex and ambiguous have eroded people’s “sense of coherence”, i.e. the degree to which they experience the world as comprehensible, manageable and meaningful. The First Story provides meaning and values, but its descriptions no longer provide an accurate understanding of the universe. The Second Story, which sees the universe as a clockwork mechanism governed by the laws of nature, provides more accurate predictions that allow us to build powerful technologies. However, it does not provide meaning or values. The Third Story sees the universe as self-organizing towards increasing complexity and consciousness, subsequently producing matter, life, mind and society. It understands the fundamental mechanism of evolution as mutual adaptation between interacting systems, thus generating synergetic wholes that in turn interact, so as integrate into even more complex wholes. Its implicit value is the search for fitness and synergy, thus inviting individuals to work towards a further evolutionary integration into the noosphere, i.e. the planetary superorganism formed by humanity, its technological extensions, and the ecosystem.
The article argues that in Turing there is an unresolved tension between his approach to the theory of computation and his approach to mathematics. While Turing’s approach to the theory of computation is based on a rational process, his approach to mathematics essentially depends on intuition, of which no rational account can be given. It is remarkable that Turing uses two different approaches to the theory of computation and mathematics, because the theory of computation is commonly considered part of mathematics.
Calculating longitude as precisely as possible is important for navigation and requires resolving issues in relation to position and measurement while the ship is moving. The names of Euler, Bezout, Laplace, and other distinguished mathematicians are linked to studies on this problem. It can be said that in past times, these theoretical and practical problems were as important as they are today. Now cutting-edge technologies and computers are used. The determination of longitude (Throughout this paper, “latitude” and “longitude” referring to the ship’s position are understood as geographical coordinates. When discussing the position of celestial bodies, the corresponding celestial reference system (mainly ecliptic coordinates) is explicitly indicated.) by astronomical means is mathematically a seemingly simple problem of spherical trigonometry. However, its effective resolution required theoretical developments and the design of special instruments for observation and calculation. Within the group of mathematicians who were interested in these problems at the turn of the eighteenth to the nineteenth century, the figure of Joseph de Mendoza y Ríos stands out. This article is concerned with the achievements of this mathematician from Seville who contributed substantially to the solution of the problem of calculating longitude for which he received one of the great prizes awarded by the Board of Longitude in London. His contributions in this area were manifold and cover a broad spectrum of the problems of nautical astronomy. All these elements: design of instruments to capture astronomical information, development of an analytical method, formulation of an approximate calculation procedure, and preparation of auxiliary (supportive) calculation instruments allowing skipping stages in the transition from observation to position data. Mendoza y Ríos In this work, the authors explain the mathematical calculations of determining longitude by means of lunar distances that are due to Joseph de Mendoza y Ríos.
We propose and defend a form of emergent materialism that, while rejecting both idealism and dualistic metaphysics, does not collapse into physicalism. After critically examining physicalism in its principal variants—reductive and non-reductive, a priori and a posteriori—we characterize our ontological framework as a novel, scientifically informed form of materialism, whose core ontological commitments are developed in this article. Drawing on precise conceptual distinctions, we address foundational issues in materialist ontology that we argue underlie the methodological practices of science across disciplines. Central to our account is the structuring role of emergence, alongside a focus on systems, the hierarchical organization of reality, the nature of laws, and the diverse forms of causality. Within this framework, we propose a “restrictivist” view of natural laws as an alternative to the standard “prescriptivist” and “descriptivist” accounts. On our view, natural regularities—or restrictions—arise as the consequence of the resulting equilibrium among the powers of all existents.
Debates about whether large language models (LLMs) genuinely understand the language they produce often rest on the assumption that understanding necessarily entails conscious experience. In this article, we argue that this assumption is unwarranted. By drawing a principled distinction between structural meaning and phenomenal access to meaning, we defend the thesis that genuine understanding does not require consciousness. We situate our position within the Turing tradition, while responding to classical objections such as Searle’s Chinese Room by showing that they conflate semantic competence with conscious awareness. After distinguishing symbols, information, and meaning, we argue that meaning constitutes an autonomous, abstract domain characterized by contextuality, potentiality, and non-classical composition. We then show how LLMs operate within this domain by exhibiting sensitivity to semantic structure rather than merely manipulating symbols. Drawing on results from quantum cognition, we further argue that both human and artificial semantic intelligence are naturally modeled by quantum-like structures, revealing a convergence between biological and artificial cognition at the level of meaning. We conclude that LLMs instantiate a genuine, though non-phenomenal, form of semantic intelligence, and that acknowledging this requires a revision of inherited concepts of understanding rather than an appeal to consciousness as a necessary condition.
Recent discussions in Foundations of Science have revived the “two-times problem’’ - the apparent conflict between the formal symmetry of physical time and the experiential asymmetry of becoming. This paper develops an operational resolution based on the concept of closure: the completion of radiative relations between emission and absorption events. Time is defined as the ordered accumulation of such realized closures, forming a Lorentz-coherent record of the world. Each closure adds a new element to this record without invoking a global present or subjective flow. By examining clock networks and atomic emission–absorption cycles, the paper shows how duration arises from measurable waiting intervals, how temporal flow corresponds to the sequential realization of closures, and how asymmetry follows from the irreversible structure of emission and record formation. The future remains open as a set of lawful but unrealized possibilities, while the realized domain expands locally through Past-Only Lorentz Equivariance. The resulting framework reconciles the empirical structure of relativity with the probabilistic openness of quantum mechanics and clarifies how experiential passage emerges from the progressive integration of newly realized records. The two-times problem thereby dissolves: the universe does not evolve in time - it generates time through the accumulation of realized relations.
It has become commonplace to acknowledge that the human being is no isolated entity but is rather a relational being that attains a particular shape as a result of its relation to other entities. This has resulted in a variety of so-called relational approaches in the ethics and philosophy of technology, to the extent that one might speak of a broader “relational trend”. However, the concept of relationality and its implications often remain unclear in ethical discussions and even more so when applied to specific technologies. In this paper, we provide a deeper understanding of what defines relational approaches by examining qualitative differences in the way relationality is understood and integrated into philosophical approaches. We do so by focusing on three prominent relational approaches in the philosophy of technology: postphenomenology, actor-network theory, and new materialism. The sense in which these approaches are relational will be qualified with reference to six themes: (1) ontological commitments, (2) boundaries between entities, (3) subjectivity, (4) agency, (5) anthropocentrism, (6) normativity. We conclude that there does not appear to be a shared view of what relationality entails, nor a shared normative stance or framework that provides clear ethical guidance. In response to this, we make some suggestions concerning the shared vector that could unify different approaches.
A philosophical micro-history of early quantum theory is developed through an indiciary–abductive approach. Against narratives centred on axioms, formalism, or abrupt scientific ‘revolutions,’ the analysis reconstructs three early quantum episodes—Planck, Einstein, and Bohr—as clue-sensitive episodes of hypothesis appraisal under weak and heterogeneous evidence. Drawing on Ginzburg’s indiciary paradigm, Peircean abduction, and recent work on epistemic aesthetics, the reconstruction develops a rubric for analysing how local anomalies, inherited constraints, and evaluative form-values jointly shaped the comparative plausibility of candidate hypotheses. The comparative result is deliberately partial rather than total: Einstein weakly dominates Planck in the reconstructive profile, whereas Einstein and Bohr remain incomparable. Early quantum theory is thus interpreted not as a simple repudiation of classical rationality, but as a series of disciplined conjectural reorganisations in which empirical resistance, economy, limit coherence, unificatory reach, and prospective fecundity interacted in historically localised ways. The reconstruction remains intentionally limited in scope: it complements rather than replaces Kuhnian historiography and does not claim to exhaust broader social accounts of scientific change.
The systematization of evaluation criteria for scientific theories, also known as theoretical virtues, aims to enhance understanding and objectivity in theory evaluation, and thereby to facilitate consensus formation. Explanatory virtues play a crucial role here. They are well known individually, but lack a widely accepted organization, especially with regard to how simplicity integrates with the other explanatory virtues. This work introduces a unificatory model of virtues (UM), in which simplicity is integrated in a way that yields a concise hierarchical organization of the explanatory virtues. In UM, a theory’s accuracy, explanatory depth, internal consistency, and ontological simplicity are components of its unifying power, while its consistency and explanatory relations with other theories are components of both its external coherence and the unifying power of the set of theories under consideration. Arguably, UM is in some ways more advanced than the coherential virtue models of Michael Keas and Adolfas Mackonis, such as in providing a quantitative criterion for a theory’s fitness. UM and its comparison with the coherential models are valuable for anyone who seeks a deeper understanding of explanatory virtues.
The p-adic conception of number, inaugurated by Kurt Hensel in 1897, redefined the meaning of completeness and proximity by replacing magnitude with divisibility. Born within number theory, it has since transformed the conceptual foundations of mathematics and physics alike. This paper traces the historical genesis and philosophical significance of this transformation-from the arithmetization of the continuum to the emergence of p-adic and adelic structures. Methodologically, we combine a concise mathematical exposition of p-adic and adelic constructions with a structural analysis of their role in modern mathematical physics, particularly in renormalization and scale hierarchies. We show how ultrametric topology and valuation naturally encode hierarchical regularity and yield convergent structures where Archimedean frameworks encounter divergence. Conceptually, we argue that the p-adic and adelic frameworks do not merely extend analysis but reconfigure the categories of infinity, unity, and knowledge. Infinity appears not as boundless extension but as hierarchical depth; unity arises from coherence among distinct local worlds; and knowledge unfolds as refinement rather than approximation. Taken together, these developments lead to an arithmetic metaphysics in which reality is defined by coherence across scales—an ontology of structure and harmony rather than of substance and extension.
Over the last several decades, complex systems have become the central scientific metaphor for multidisciplinary investigations of planetary processes. Though complex systems thinking offers useful affordances for modeling and understanding select dimensions of social-environmental change, its theoretical closure and totalizing ontology limit its ability to address the qualitatively distinct transformations occasioned by the Anthropocene or their meaning for more-than-human political communities. This paper examines the increasingly troubled scientific assumptions inherent to a complex systems approach to dynamic change, its distinct political and economic affordances for actionable knowledge, and the social validity of systems-based projections under conditions of accelerating uncertainty. What are the explanatory and predictive limits of the complex systems paradigm and are its affordances adequate for understanding unprecedented kinds of change? How does the nature of the complex systems paradigm itself limit and hinder the intellectual pursuit of complexity? Seeking an inclusive path forward, I resituate complex systems and their extended technoscientific networks within the more capacious framework of assemblage thinking, whose attention to the structuration of both matter and knowledge can help repurpose the products of Western technoscience towards emancipatory ends. Such an approach eschews reductionism, dualism, and instrumentality in favor of engaging planetary complexity on its own, more-than-human terms, with implications for how Western science can be employed towards socionatural adaptation.
Classical mathematical frameworks used in the semantics of computation and programming languages are traditionally grounded in idealized abstractions, including infinite-precision numbers, unbounded sets, and unrestricted operations. Concrete computation, however, is intrinsically finite, operating under explicit bounds on precision, memory, and structural resources. This foundational mismatch complicates semantic reasoning about numerical behavior, algebraic properties, and execution in realistic computational settings. This paper proposes Limited Math (LM), a bounded foundational framework intended to realign mathematical semantics with the realities of finite computation. Rather than presenting a complete formal theory or establishing meta-theoretical results, LM is introduced as a conceptual foundation in which finiteness is made explicit at the semantic level. Numeric magnitude, precision, and structural complexity are treated as primitive constraints, enforced through a finite numeric domain parameterized by a single bound M and a deterministic value-mapping operator that makes quantization and boundary behavior explicit. Within representable bounds, LM coincides with classical arithmetic; beyond these bounds, deviations are explicit, deterministic, and open to analysis rather than implicit or idealized. By additionally bounding structural constructions such as set cardinality, the framework prevents infinitary assumptions from re-entering through indirect means. The resulting semantics induces finite-state models of computation, offering a principled basis for reasoning about arithmetic, structure, and execution under finite computational constraints and for guiding future formal and technical developments.
Hallucination in Large Language Models (LLMs) is a persistent and challenging phenomenon. These hallucinations manifest when LLMs produce outputs that are plausible but factually inaccurate or logically inconsistent. Old hallucinations in LLMs could be categorized into three categories: factual hallucination, contextual hallucination, and logical hallucination. Key contributing factors include limitations in training data, the absence of ground-truth verification mechanisms, and tendencies toward overgeneralization and extrapolation. To address these issues, researchers have proposed various mitigation strategies, including learning-based techniques, post-training interventions and knowledge transfer, and safety and alignment enhancements. Despite these efforts, residual hallucination risks persist, thereby raising profound challenges from an epistemological perspective. This paper examines these challenges through the lens of contemporary epistemology. Specifically, it explores how residual hallucinations in LLMs pose difficulties for knowledge-first and anti-Gettier accounts of knowledge. It analyzes the epistemic limitations of LLMs by engaging the debate between internalism and externalism in model justification, and addresses the epistemic boundedness of residual hallucinations in relation to grounding and post-training strategies. Additionally, it evaluates the epistemic constraints inherent in aligning LLMs with safety goals in the absence of justification, and considers an embodied epistemology of hallucination risks. Finally, the paper highlights the role of sycophancy in contributing to these residual epistemological risks. By integrating philosophical analysis with empirical developments in LLMs design, this study aims to clarify the epistemological implications of hallucination mitigation and propose conceptual frameworks for better understanding and evaluating LLMs outputs.
Although Leibniz’s reputation had something to do with the debate about the least action principle within the 18th century, he never stated it as such. He did however address the two conceptual elements in the principle. First, as an interpretation of divine providence in creation, he developed a mathematical theory of natural optimisation in his works on the optics, dynamics, and other physical subjects. Second, in his later dynamical works, he developed a theory of “action” (actio) which is the product of mass, displacement, and speed (a = msv). This second component is also situated within the context of vis viva conservation (mv2). With these two elements in place, and together with the conservation of vis viva, Leibniz seems to have arrived at the doorstep of the least action principle but never entered the open door. This paper argues that while Leibniz did not state a least action principle, his use of the concept of action together with the conservation vis viva implies stationary action, an eventual and more sophisticated interpretation of the least action principle. By reconstructing this argument, we can also show how Leibniz’s defence of a naturalistic, intrinsic teleology developed into a mathematical analysis of action quite distinct from the least action principles of the later Maupertuis and Euler. Instead of an optimisation formed by a sum over the path of motion, Leibniz’s method implies the actualisation of the optimum at each infinitesimal segment of the path. Finality, therefore, is not realised “at the end” but actualised continuously.
Chang’s arguments against ‘standard scientific realism’ and in favour of ‘pragmatic realism’ in his recent book Realism for realistic people are addressed. It is argued that Chang’s interpretation of ‘truth’ and ‘reality’ in terms of the contribution to the operational coherence of practices is not superior to a more traditional ‘scientific realist’ understanding of those concepts. In particular, it is shown that a deflationary account of truth can be congenial to a realist and pragmatist theory of scientific knowledge, and that it does not suffer the problems Chang attributes to it.
In this paper, we examine Newton’s concept of absolute space. We aim at clarifying: (1) the reasons that led Newton to introduce this notion; (2) the arguments he used to justify its existence; (3) the relationship between absolute space and the principle of inertia; and (4) the role of absolute space within Newtonian physics. We then analyse the criticisms raised by Leibniz and Mach, focusing on their specific arguments rather than their broader philosophical frameworks, due to the space limitations of this article. We conclude by discussing Einstein’s views, particularly how his theory of relativity ultimately ruled out the existence of absolute space and time. Nevertheless, we argue that in the context of Newtonian physics, the concept of absolute space was not at all absurd, even if it presented certain conceptual difficulties. The paper ends with an appendix highlighting noteworthy annotations from the editors of the Geneva Edition to Proposition XIX of the third book of Newton’s Principia.
This work proposes a novel, observer-neutral explanation for why advanced adaptive systems tend to perceive the universe as ordered and stable. Drawing on principles from adaptive dynamics and information theory, we argue that this perception emerges not from external fine-tuning or anthropic necessity in the global environment/universe, but as a statistical consequence of the system’s own adaptive trajectory and informational growth. Specifically, systems that successfully develop complex internal information models necessarily do so in environments whose local probabilistic structure permits persistent adaptation and incremental informational accumulation. In contrast, systems that face chaotic or terminally disruptive environments fail to develop such ordered worldviews, as their adaptive trajectories are suppressed or curtailed before complex modeling can emerge. This perspective shifts the explanatory burden from global assumptions about the universe’s structure to the objectively observable statistical and probabilistic properties of the local environment that enable the emergence and long-term persistence of advanced observers. The argument highlights the limits of interpreting locally derived constraints as global features of the universe, given that such extrapolations cannot be empirically warranted beyond the observer’s interactive domain. We briefly discuss the broader implications of this argument for the philosophy of science, adaptive systems research, and debates about the anthropic principle.
This paper reconstructs the philosophical genesis of a foundational motif—difference that preserves—emerging at the intersection of ontology, logic, and mathematics. Through a genealogical arc spanning Fichte’s theory of self-positing, Hegelian mediation, Bergsonian duration, and the anti-psychologism of Bolzano and Frege, we identify a deep tension in modern foundations: how can a logic of differentiation account for identity across transformation? We propose that this unresolved tension structures both historical and contemporary foundational programs. To address it, we articulate a new meta-theoretical framework—Mnēmaic logic—which grounds preservation not in static identity, but in recursive genesis. This paper provides the philosophical foundation and conceptual justification for that framework; its formal development appears in a companion article (Ballús Santacana, 2025). We conclude by suggesting that difference-that-preserves offers a powerful alternative to existing models of identity, continuity, and foundation in mathematical logic.
This essay interrogates the Freudian conception of the Unheimliche by reinterpreting it through the dual categories of perturbance and animation. Taking Roger Corman's X: The Man with the X-Ray Eyes as a privileged site of analysis, it argues that the film not only stages but radically exposes the very dimension that Freud's text systematically dissimulates: the nexus between ocularity, animation, and the death drive. Whereas Freud sublimates the perturbing into the castration complex, Corman dramatizes its irreducible link with blinding, thereby rendering visible the removed of psychoanalysis. The essay proposes "Perturbance" as the ontological oscillation immanent to beings, the universal radiation that makes them appear mysteriously alive. From this perspective, psychoanalysis is constituted precisely by its removal of perturbance, whereas cinema, by externalizing psychic nexuses in representation, fulfills the repressed possibility of psychoanalysis without removal. Through a dialogue between Freud, Hoffmann's Sandman, the Oedipal paradigm, and Corman's visionary film, the study delineates a psychophysical ontology in which animation is no longer confined to the living subject but revealed as the fundamental energetic quality of all that is.
