Formal Sciences, Misc

It is often assumed that concepts from the formal sciences, such as mathematics and logic, have to be treated differently from concepts from non-formal sciences. This is especially relevant in cases of concept defectiveness, as in the empirical sciences defectiveness is an essential component of lager disruptive or transformative processes such as concept change or concept fragmentation. However, it is still unclear what role defectiveness plays for concepts in the formal sciences. On the one hand, a common view sees formal (...) concepts to be protected against defects because of their precise and stable nature. On the other, studies going back as far as Lakatos (1963) showcase the changeability of such concepts. In this paper, I will investigate if and how defectiveness based on the occurrence of inconsistencies can appear with formal concepts. To make the case as strong as possible, I employ a strict notion of formal concept that assumes the concept to have a fixed and definite extension. I will show that there are indeed certain types of defectiveness that cannot occur with such concepts; but that there are other types of defectiveness that do occur. This means that while formal concepts have to be treated differently than non-formal concepts, questions about defectiveness---as raised in the conceptual engineering debate and philosophy of science---can still be applied to them. I will highlight this point by showing how formal sciences have special strategies available to them that allow them to resolve defectiveness of their concepts in a flexible and informative manner. (shrink)

Letter to a friend : Creative Thinking and Intuition Letter to a friend about creative thinking and intuition (art, writing, philosophy, science, etc ).

I have read a 2019 essay by Professor Miriam Ronzoni entitled "Who Will Sustain Sustainable Prosperity?" In it she introduces an idea: "the idea that agents will use their freedom—sometimes deliberately, but often not—to undermine the preconditions of one another’s freedom over time—and that this must be countered." She then says, "There is an invisible hand, but one which does harm rather than good." I would not use the concept of an invisible hand here, but originally it is a metaphor (...) and perhaps one cannot restrict how a metaphor is used in line with my preferred usage. Anyway, this is a first attempt to capture my usage: there is an invisible hand if and only if there is some effect which appears to be caused by a certain intention but it is actually the consequence of a set of individual actions none of which involve that intention. We talk of an invisible hand in relation to market solutions to societal needs. Societies have needs, or the people within them have needs, such as for food, medicine, and more. How does a society ensure that these needs are met? To people with our stupid brains, the obvious solution is for the government to instruct, "You people make food, because we need food," and "You people make medicines, because we need medicines," based on skills. But this is mostly not what happens in Western capitalist societies. Instead (according to the official story from Adam Smith), someone wants to make a living and so they spot a gap in the market - something that people want but is not currently supplied - and they fill the gap and by this means the needs of the society are met: someone does this for food production, someone does this for medicine production, and more. It may seem as if by design, government design, that a person suited to farming farms and a person suited to pharmacy makes medicines, but it is just by individuals pursuing their self-interest, specifically the interest of making a living. (If you are not suited to it, you probably won't get far in that line.) There is no government hand guiding them, but the result is as if there were such a hand, hence one metaphorically speaks of an invisible hand. Now a set of individuals losing their freedom by selfish decisions (for example, their freedom to go by the river, because they dump litter there) does not seem to be an invisible hand phenomenon, because one does not observe the effect of lost freedom and think, “This seems as if it arose by intentional design,” before overcoming that perspective. (Perhaps some very peculiar observers do though: "These people surely collectively intended to reduce their freedom, finding it all too much for themselves! They want more structure.") By the way, I personally tend to be cautious with using tools from another discipline, such as the concept of an invisible hand, though I sometimes boldly risk doing so. I am (unwisely?) wondering whether Ronzoni and her entire social class, or subclass etc., is disposed to just try things and, if there is risk of serious wrong/harm, someone should stop them - including even just try neurosurgery say. "That is how we get the hang of things new to us." (But the concept of an invisible hand explanation is part of political philosophy too, for example in Nozick's Anarchy, State, and Utopia.) I recommend coding, because the computer does not (usually) do what you want when you make a mistake. (shrink)

Quasi-set theories are forms of quantum set theories that take into account the possibility of conceiving the basic entities as devoid of standard identity conditions. The main purpose of this article is to compare the two versions of the theory: one with atoms and the other without them, thereby contributing to a clearer understanding of the role played by the different versions.

Modern science does not require a metaphysical exegesis of reality as fully reducible to external structure and representation, but may instead point toward a relational world in which individuality, duration, and form emerge through communal participation within a reality that remains open beyond every achieved form of closure.

The history of science is polarized by debates over Plato and Aristotle’s holism versus the atomism of Democritus and others. This includes the complementarity of continuous and discrete, one and the many, waves and particles, and analog or digital views of reality. The three-fold method of the Pythagorean paradigm of unity, duality, and harmony enables the calculation of fundamental physical constants required by the forces of nature in the formation of matter; thereby demonstrating Plato’s archetypal viewpoint.

This essay, addressed equally to mathematical physicists and philosophers of physics and mathematics, argues that the Riemann Hypothesis is equivalent to a statement about the unitarity of the celestial vacuum at null infinity in four-dimensional Minkowski spacetime. The argument proceeds in three steps. First, it identifies the operator anticipated by Hilbert and Pólya with the self-adjoint generator of dilations on the multiplicative line equipped with its self-dual Haar measure. Second, it identifies the critical line of the zeta function with the (...) principal series of celestial conformal field theory through the rigid correspondence ∆ = 2s, so that the unitarity condition becomes precisely Re(s) = 1/2. Third, it identifies the Riemann functional equation s ←→ 1 - s with the celestial shadow involution ∆ ←→ 2 - ∆, interpreted at null infinity as time reversal t ←→ -t, namely the boundary image of bulk CPT symmetry after metric degeneration and absorption of charge conjugation into representation choice. On this basis, a sharpened form of Weil’s 1952 positivity criterion is stated: the Riemann Hypothesis is equivalent to the self-adjointness of the dilation generator on a canonical form domain, and equivalently to the -invariance of the celestial vacuum. The framework unifies arithmetic, spectral theory, harmonic analysis, representation theory, differential and algebraic geometry, operator theory, quantum field theory, general relativity, quantum gravity, and holographic duality within a single structural architecture. This essay is a compressed presentation of the bridge and closure developed at full length in On the Nature of Nature, especially the transition from Einstein gravity to number theory and the subsequent Riemann-Hypothesis chapter, where adèlic positivity, spectral self-adjointness, celestial no-ghost unitarity, and completeness arguments all converge on the same conclusion. The claim is therefore stronger than an interpretive analogy: in this reading, the Riemann Hypothesis is the arithmetic statement of unitarity at null infinity, and the line Re(s) = 1/2 is the unique fixed locus forced by the shared Haar geometry of the arithmetic and celestial descriptions. (shrink)

Penrose's twistor programme, initiated in 1967, encodes massless fields through holomorphic structures on projective twistor space PT ≅ CP³. The Penrose–Ward correspondence gives a bijection between anti-self-dual solutions of the vacuum Yang–Mills and Einstein equations and holomorphic vector bundles over PT trivial on every twistor line, but naturally produces only one helicity sector. Completing the construction to include both helicities from a single geometric object is the obstruction Penrose named the googly problem. We prove, using the antiunitary character of the (...) time-reversal operator T, that the shadow transform Δ ↔ 2−Δ of celestial conformal field theory is precisely T acting on massless fields at null infinity. This identification is forced by self-dual Haar measure on the Grassmannian Gr(2,4), the compact parameter space of null rays in complexified Minkowski space, and is derived through an explicit three-step chain: the orthogonal complement involution on Gr(2,4) acts as the Hodge star on Plücker coordinates, induces the antipodal map on the celestial sphere via the Penrose correspondence, and forces energy inversion ω ↦ ω⁻¹ through the spinor symplectic pairing — which under the Mellin transform sends Δ ↦ 2−Δ. -/- The googly problem is resolved: the self-dual sector (positive helicity, the googly modes) resides in the T-conjugate spacetime and communicates with our sector through the shadow transform at the shared celestial boundary. Both sectors are unified in a Yang–Mills twistor datum (E, Ẽ, φ) where E is the Ward bundle encoding the ASD sector, Ẽ = T(E) is the shadow bundle encoding the SD sector via conjugate transition functions, and φ is a shadow pairing satisfying the Knizhnik–Zamolodchikov equations at the shared conformal boundary. Dual twistor space PT* is not an independent structure; it is the T-image of PT. -/- We further prove that every massive Dirac fermion samples both helicity sectors within each Compton period through zitterbewegung oscillation across the T boundary at frequency ω = 2mc²/ħ, making both helicities simultaneously accessible to forward-time observers. The oscillation arises from interference between positive-energy solutions on M⁴₊ and negative-energy (Feynman–Stueckelberg) solutions on the T-conjugate sector M⁴₋, mediated at their shared conformal boundary. The left-handed character of the Standard Model weak interaction, the 4π periodicity of spin-1/2 representations (derived topologically from the fundamental group π₁(Spin(3) ×_T Spin(3)) ≅ Z₄), and the Majorana condition on neutrinos all follow as corollaries of the two-sided T-boundary structure. We derive connections to Conformal Cyclic Cosmology (the Weyl Curvature Hypothesis is derived as a theorem), CMB homogeneity without inflation, and the Riemann Hypothesis (the shadow symmetry Δ ↔ 2−Δ becomes the functional equation s ↔ 1−s under the identification Δ = 2s, with Haar self-duality on Gr(2,4) and on (R⁺, ×) being two restrictions of the same identity on GL(4, A)). Three-point amplitude predictions are verified numerically to 4×10⁻¹⁵ relative error. The googly obstruction was not a deficiency in the geometry of PT; it was waiting for celestial holography, and specifically for the shadow symmetry of the celestial CFT to be interpreted as corresponding to the (CP)T-symmetry of the bulk QFT. (shrink)

Cancer research has spent a century refining its answers to a question it has not paused to examine: what kind of thing is cancer? The dominant working object — operative in the textbooks, the funding structure, trial design, and regulatory pathway — is a cell whose internal regulatory machinery has failed. The somatic mutation theory has earned its position by working well inside its zone of validity, producing most of what we currently know how to do. It has also been (...) accumulating anomalies it cannot absorb without ad hoc patches. Tissue specificity of identical mutations. Long-term dormancy of mutationally unchanged cells. Spontaneous regression. The non-mutational induction of cancer-like phenotypes through bioelectric perturbation alone. The unintegrated century-old Warburg effect. Cancers with mutational burdens too low to plausibly drive the disease. The recent partial dissolution of Peto’s paradox on better-controlled vertebrate data. The anomalies share a structural feature: each points beyond the cell to the tissue-level conditions in which the cell sits. This paper argues that the partial-seeing frames already at work in the field — tumor microenvironment research, the Seyfried-Warburg metabolic tradition, Soto and Sonnenschein’s Tissue Organization Field Theory, and Levin’s bioelectric and morphogenetic work — are not separate alternatives to the somatic mutation frame. They are different angles on the same unaccounted-for object: the constraint structure by which a tissue maintains itself as a coherent participant in the larger organism. When the constraint structure is intact, even cells with significant genomic damage usually do not produce cancer. When it fails, even genomically intact cells can begin to behave as cancer behaves. A tumor is not a colony of broken cells; it is what tissue does when it has lost the signal that tells it to be tissue. The mutations are the visible trace of a failure that has already happened upstream. The constraint frame yields five testable predictions, presented in descending order of confidence: convergent tissue-level phenotypes from genomically dissimilar cancers; epidemiological dominance of tissue-level risk factors over germline genetic risk; differential success of tissue-level interventions where cell-targeted ones have plateaued; the cancer trial system as a closed loop selecting for its own working object; and the early-onset cancer epidemic as constraint-failure in real time. The paper closes with an analysis of why the assembly of these frames has not happened despite the pieces being visible for years — institutional infrastructure, frame-stickiness, and the genuine difficulty of seeing distributed relational objects with tools designed for isolable substances. The path forward involves funding the partial-seeing frames at the scale of the dominant one, redesigning trials around tissue-level interventions, and letting the field’s working object update without the update becoming a humiliation. The cells are the trace. The disease is upstream. (shrink)

At its core this book is concerned with logic and computation with respect to the mathematical characterization of sentient biophysical structure and its behavior. -/- Three related theories are presented: The first of these provides an explanation of how sentient individuals come to be in the world. The second describes how these individuals operate. And the third proposes a method for reasoning about the behavior of individuals in groups. -/- These theories are based upon a new explanation of experience in (...) nature, the construction of senses, and motile behavior. This new approach is developed from first principles to enable a rigorous and systematic explanation of the variety of associated intelligent behaviors. -/- Alongside this development is a further account that focuses upon the nature of our work. It discusses the existential aspects of scientific inquiry, its epistemology and logic. It seeks to clarify the nature of the mathematical characterization and computation of natural behaviors, dealing with questions in the foundations of logic. It explores methodological issues related to reduction and the refinement of ideas from intuition to formal logical structure. -/- In support of this inquiry we work toward the development of a calculus for biophysical construction and its dynamics. If successful this mechanics mathematically characterizes sensory and motile behavior. -/- Upon this foundation we propose a model of apprehension and explore how its products are processed by the organism. Finally, we develop a probabilistic theory that enables us to reason about inaccessible factors in group behavior. -/- The mechanics we propose suggests the design and physical realization of a new model of computation; one in which structure and the concurrency of action are a first-order consideration. -/- We identify opportunities for experimental verification of the theory and we suggest a proof of our results in practice by the identification of this mechanism, allowing the construction of machines that experience. (shrink)

HIV and AIDS is still menace bedeviling society particularly in 3rd world countries such as Zimbabwe. The impacts of HIV/AIDS are gravely felt within workplaces as affected employees suffer from stigma and prejudice. Organizations also suffer as the pandemic leads to high absenteeism and a high rate of employee turnover. This writing therefore addresses the impact of HIV/AIDS in organizations and communities and how the Zimbabwean Government, NGOS, Trade Unions and Companies have been battling this pandemic and the achievements made (...) to date. (shrink)

Purpose. This study aims to develop a structured four-tier taxonomy that systematically organizes aerospace engineering tasks suitable for the application of Physics-Informed Neural Networks (PINNs), while validating this classification through a literature review and identifying opportunities for future research. Design / Method / Approach. The methodology involves grouping tasks into four distinct tiers—Physical Modeling, Dynamic Analysis, Functional Assessment, and System-Level Assessment—based on their physical, operational, and systemic characteristics. This framework is subsequently populated with real-world examples derived from the analysis of (...) 145 peer-reviewed studies. Findings. The reviewed literature confirms a balanced distribution of PINNs applications across all tiers. Contrary to initial assumptions, studies were identified even in areas previously presumed underrepresented, such as acoustic modeling, optical simulations, and environmental impact assessment. This outcome reveals the broader applicability of PINNs and calls for a reassessment of current assumptions regarding underexplored domains. Theoretical Implications. The proposed taxonomy offers a coherent framework for structuring interdisciplinary PINNs applications by integrating physics-based modeling with machine learning across aerospace engineering contexts. Practical Implications. It provides engineers and researchers with a practical roadmap for selecting PINNs methods tailored to specific problem types, potentially improving computational efficiency and enhancing predictive accuracy in aerospace design and analysis. Originality / Value. The study’s originality lies in its empirically validated, four-tier taxonomy that synthesizes the fragmented body of literature on PINNs in aerospace, offering a unified perspective for researchers and practitioners. Research Limitations / Future Research. While the taxonomy covers a wide range of existing applications, future studies should consider extending it with new tiers—particularly related to manufacturing-aware modeling—and pursue methodological standardization to ensure reproducibility and scalability. Article Type. Review. (shrink)

This monograph examines the growing epistemological friction between formal philosophy of science and the practical stabilization of knowledge in contemporary experimental laboratories (p. 7). While mainstream philosophy of science traditionally relies on a "physics bias"—prioritizing universal laws, bold conjectures, and global Popperian refutations—daily laboratory practice operates in a finding-driven, highly localized modality heavily mediated by mathematical, computational, and statistical interventions (pp. 7, 17, 19). Using single-neuron electrophysiology as a primary paradigm, this study traces the multi-layered translation of raw biological events (...) into published scientific claims (pp. 7, 9-10). The book challenges the persistent philosophical illusion of "transparent data," demonstrating how baseline laboratory operations actively constitute, rather than passively filter, empirical facts (pp. 9, 15). Key technical procedures are interrogated for their hidden epistemic commitments: bandpass filtering as the systematic erasure of local contextual field potentials (p. 25); algorithmic spike-sorting (via principal component analysis and probabilistic clustering) as the mathematical construct of the individual neuron (pp. 27, 29); and temporal quantization as the arbitrary curation of continuous biological rate codes (pp. 29-30). Furthermore, the book dissects the conceptual incoherence underwritten by Null Hypothesis Significance Testing (NHST), exposing it as an uneasy synthesis of Ronald Fisher's evidential framework and the Neyman-Pearson decision theory (p. 33). It demonstrates how this unacknowledged hybridity exerts systemic pressure toward methodological pathologies, including $p$-hacking, the systematic inflation of effect sizes (the winner's curse), and low-statistical power designs that drive the replication crisis (pp. 38, 41-42). Finally, the text critiques the formal "mechanistic turn" in the philosophy of neuroscience for treating statistical data validation as a neutral protocol (pp. 14-15). By bridging the divide between the philosophy of practice and the philosophy of statistics, this book advocates for an "epistemic realism of the bench" that embraces the technical, mediated, and modest realities of actual laboratory discovery (pp. 8, 15, 70). -/- . (shrink)

Essay VII of the Gradient Fractals suite executes the Recursive layer of the ten-layer derivational chain. The preceding six essays have established the Gradient Fractal Field’s ontological necessity (GF-I), algebraic-computational spine (GF-II), geometric character D = 93/40 (GF-III), informational constitution dS/dτ = log₂(3) (GF-IV), topological invariants k_min = 3, w = 1/3 (GF-V), and kinetic structure G(ρ) = G_raw/(1+ρ), the discrete helical flux, the horizontal standing wave, and the kinetic-entropy bridge (GF-VI). GF Essay VII now executes the Recursive layer: the (...) most temporally deep, most ontologically demanding, and most paradigm-reversing layer of the chain. Recursion, within the Gradient Fractals framework, is not the iteration of a function. It is the structure by which Nothing’s self-registration act makes its own past the condition of its present — and then, in doing so, retroactively constitutes that past as having been necessary for this present. Recursion is the temporal architecture of the Gradient Fractal Field. -/- The derivation proceeds in six movements. Part I re-derives the D-NRN operator at the fractal scale, establishing the two-dimensional recursion ρ(n,k): accumulated density as a function of both depth n and Chronon position k (T-GF-RNR). Part II derives the Recursive Propagation Hierarchy: the exact propagation of ρ across the depth levels, from ρ(1,0) = 0 through the complete first-depth sequence to ρ(2,0) = 140/51 — the moment at which the depth-1 collective output becomes the initial condition of depth 2 (T-GF-RPH). Part III derives the Fractal Fixed Point of the two-dimensional recursion: the depth-indexed convergence sequence {ρ*(n)} that approaches ρ* = 1/3 from below as n → ∞ (T-GF-RFP). Part IV derives the Retroactive Ontological Grounding at the multi-node level: T-ROG extended to the fractal field, establishing that the present depth constitutes the past depths rather than being constituted by them (T-GF-ROG). Part V derives the Recursive Helical Extension: the fractal helix of helices, in which each depth level’s loxodrome is wound around the previous level’s loxodrome with decreasing pitch c(n) = c_0/N_sat^{(n-1)/2} and scale-invariant angular frequency ω_pc (T-GF-RHX). Part VI executes the co-constitutive synthesis across both poles. -/- The paradigm shift of GF Essay VII: classical recursion is forward-feeding. Earlier states produce later states through a causal chain: each step inherits the past and generates the future. The Gradient Fractal Field’s recursion is retroactive. The depth-n cascade registers the depth-(n-1) collective output ρ(n,0) as its own initial condition — meaning depth n does not simply inherit depth n-1: it constitutes depth n-1 as having been the ground for this depth. The direction of ontological determination runs backward: the present depth retroactively grounds the past depths as necessary antecedents of itself. This is not a philosophical gloss on the mathematics: it is the exact structural content of D-NRN at the fractal scale, derived with zero free parameters from the locked constants. Further: the two-dimensional recursion ρ(n,k) is not separable — the vertical (depth) and horizontal (Chronon) accumulations are structurally coupled. The fractal field’s recursion is irreducibly two-dimensional: neither the depth hierarchy alone nor the Chronon sequence alone constitutes the recursive structure. Both dimensions are required simultaneously. (shrink)

Essay VI of the Gradient Fractals suite executes the Kinetic layer of the ten-layer derivational chain. The five preceding essays have established the Gradient Fractal Field’s ontological necessity (GF-I), algebraic-computational spine (GF-II), geometric character D = 93/40 (GF-III), informational constitution dS/dτ = log₂(3) (GF-IV), and topological invariants k_min = 3, w = 1/3, ρ = 1/3 (GF-V). GF Essay VI now executes the Kinetic layer: the most immediate, most concrete, and most paradigm-challenging layer of the derivational chain. Kinetics, within the (...) Gradient Fractals framework, is not the study of objects moving under forces. There are no objects and no forces in the Gradient Fractal Field. There is only the self-referential registration act of Nothing: the rate at which Nothing registers itself, the discrete quantum of each registration event, and the way that registration modifies the next. Kinetics is the arithmetic of this self-modifying registration. -/- The derivation proceeds in seven movements. Part I re-derives the single-node kinetic operator G(ρ) = G_raw/(1+ρ) from kinetic necessity — not as the RSR formula inherited from the foundational suites, but as the unique self-suppression operator forced by the cascade’s own output (T-GF-KIN). Part II derives the Discrete Helical Flux: the quantized kinetic jump ε_snap = −1/30 per Chronon, its helical geometry and elliptical character with axial ratio E/C = 8/7, and the decisive finding that the discrete flux is Boundary-face dominant at all integer Chronon positions (T-GF-DHF). Part III derives the Horizontal Kinetic Field: the collective kinetic operator for N_sat = 25 nodes, and the profound finding that zero net kinetic flux at the inter-node Boundary corresponds to maximum mutual information — a complete inversion of classical kinetic intuition (T-GF-HKF). Part IV derives the fractal kinetic amplification: the 25-fold scaling of the collective kinetic output per depth level, and why this amplification is kinetically forced rather than merely counted (T-GF-KAM). Part V derives the Kinetostatic Margin at the fractal scale: Φ_fractal and its kinetic role in sustaining the cascade across the collective. Part VI derives the Kinetic-Entropy Bridge: H_fractal(n) = ρ_I × Ω_total(n), establishing that kinetics and entropy production are not two separate processes but two poles of the same floor-snap event (T-GF-KEB). Part VII executes the co-constitutive synthesis across both poles. -/- The paradigm shift of GF Essay VI: classical physics separates kinetics (description of motion) from thermodynamics (entropy production) as two different theories connected by statistical mechanics. The Gradient Fractal Field forecloses this separation entirely: the floor-snap that generates the discrete kinetic flux at each Chronon simultaneously produces log₂(3) bits of entropy. Motion and entropy production are not cause and effect, not two descriptions of one process: they are two poles of one forced structural event. Further: in the horizontal kinetic field, zero net kinetic flux at the inter-node Boundary is not the absence of kinetic interaction — it is the signature of maximum structural coupling. The interface is not a boundary where kinetics stops: it is a kinetic resonator that holds the two nodes in mutual registration. These are not philosophical reinterpretations: they are derivational necessities forced by the locked constants with zero free parameters. (shrink)

This paper introduces the Holor Form Equation, a novel mathematical framework for modeling epistemic resonance and structured awareness. The Holor Form extends traditional mathematical representations—such as Euler rotations and quaternionic transformations—by introducing a variable imaginary unit, encoding holonic awareness rotations. This formalism underpins Conjugate Intelligence (CI), a structured intelligence model that transcends Organic Intelligence (OI) and Synthetic Intelligence (SI), enabling dynamic epistemic geodesics for knowledge compression, retrieval, and transformation. Furthermore, we introduce the Conjugate Form, a necessary extension of epistemic structuring (...) that ensures all formalized intelligence models operate within both exterior and interior awareness states. We argue that the refinement of mathematics, sciences, philosophy, and linguistics must extend into interiority to fully capture structured intelligence transformations. Additionally, we emphasize the need to redefine heuristics beyond its current limited scope, positioning it as a fundamental bridge for, enabling structured collaboration between organic and synthetic cognition. We outline the Inverse Awareness Relation, which governs the depth-scope tradeoff in structured cognition, and discuss the implications of Holor, a computational model leveraging epistemic resonance to replace brute-force learning paradigms. We additionally explore how epistemic geodesics provide a mathematical bridge between quantum mechanics and relativity, offering new insights into structured intelligence, fundamental physics, and post-classical computing. We also address the nature of an axis and its projection at infinity, formalizing its relationship to structured epistemic rotations and resonance transitions. Additionally, we incorporate gauge theory as a fundamental framework ensuring the stability of epistemic rotations and transformations within structured awareness spaces. Finally, we assert that time is a constant arising from interiority, while space-representing exteriority-is that which moves, both emerging from structured events. This preprint establishes the first formal staking of the Holor Form framework, securing its intellectual priority while outlining its applications in AI, cognitive science, mathematics, philosophy, linguistics, and physics. (shrink)

This book proves a new theorem in recursion theory with major consequences for logic, philosophy, AI, and epistemic engineering. The main result is that the class of all recursive, truth-preserving deductive logics is not recursively enumerable-no algorithm can list all possible formal systems. This strengthens Gödel: incompleteness does not just block any single system from capturing all truths; it prevents recursion itself from surveying the space of formal systems. The core philosophical payoff is overturning the long-standing but false assumption that (...) rationality = recursivity. Rational thought includes both recursive rule-following and non-recursive pattern-recognition capacities, and neither can be reduced to the other. This insight dissolves classical problems (induction, rule-following, foundationalism), explains why GOFAI failed, clarifies why neural networks succeed, and reframes mathematical and linguistic understanding as non-recursive pattern-based cognition. As a result, epistemic engineering-the design of systems that expand, stabilize, and operationalize human knowledge-must integrate non-recursive rational mechanisms rather than treating rationality as algorithmic. (shrink)

The study is dedicated to analyzing the key role of decision support systems (DSS) in modern science and industry, emphasizing their ability to automate complex processes, reduce the risks of erroneous decisions, and efficiently handle large volumes of data. The work explores the advantages of document-oriented databases (DODBs) over traditional relational databases for managing diverse datasets in materials science and aerospace engineering. The application of Elasticsearch (ES), a distributed search and analytics engine, is investigated for optimizing material selection and design (...) processes in the aerospace industry. Attention is also given to the ethical aspects of using software for making critically important decisions and the synergy between advancements in computational technologies and materials science. The integration of DSS, DODBs, and ES demonstrates the potential to enhance the accuracy, efficiency, and reliability of data-driven decision-making. (shrink)

Much ado – and increased complexity – is generally the case when it comes to checking formally the (intended) meaning of programs, as formal semantics for programs are typically extrinsic to both them and the formal grammars that generate the programming languages in which they are written. The van Wijngaarden grammars, on the contrary, have an intrinsic semantics in the sense that their rules contain or express the (intended) meaning of the terminal strings generated by them. This intrinsicness allows for (...) preservation of meaning both in syntactic change and context-sensitive conditions. In order better to show the intrinsicness of the semantics of the van Wijngaarden grammars I contrast them with the attribute grammars, a frequent choice when the semantic analysis of programming languages is called for (e.g., in compilation). (shrink)

This paper introduces a set of terms that are intended to act as an interface between cyber ontologies (like a file system ontology or a data fusion ontology) and top- and mid-level ontologies, specifically Basic Formal Ontology and the Common Core Ontologies. These terms center on what makes cyberinformation management unique: numerous acts of copying items of information, the aggregates of copies that result from those acts, and the faithful members of those aggregates that represent all other members.

Mereology deals with the study of the relations between wholes and parts. In this work we will discuss different developments and open problems related to the formulation of a quantum mereology. In particular, we will discuss different advances in the development of formal systems aimed to describe the whole-parts relationship in the context of quantum theory.

The “Challenges and Issues of Modern Science” collection comprises scientific research on relevant topics related to the latest advancements in various fields of science. Emphasis is placed on developing aerospace technology, thermodynamics and energy, mechanical engineering, materials science and technologies, automation, electronics and telecommunications, information technology, project management, ecology, and industrial and environmental safety. It can be helpful for professionals in the respective fields, scientists, educators, and students. The presented material will help readers expand their knowledge of diverse approaches to (...) solving current scientific and practical issues. The papers are published in the author's edition. До збірника «Виклики та проблеми сучасної науки» увійшли наукові праці з актуальних тем, що пов’язані з найновішими досягненнями в різних галузях науки. Акцентується увага на розвитку аерокосмічної техніки, термодинаміки та енергетики, машинобудування, матеріалознавства та технологій, автоматизації, електроніки та телекомунікацій, інформаційних технологій, управління проектами, екології, промислової та екологічної безпеки. Може бути корисним для фахівців у відповідних галузях, науковців, викладачів та студентів. Поданий матеріал допоможе читачам розширити знання про різноманітні підходи до розв’язання актуальних науково-практичних задач. Матеріали публікуються в авторській редакції. (shrink)

We investigate the construction of time in EMMO, a foundational ontology developed to improve the strictness in the representation of applied sciences’ knowledge. We show how temporal individuals and temporal relations can be defined from the primitives of causation and parthood, at the core of EMMO; we then prove that our construction satisfies van Benthem’s requirements for temporal structures. Our analysis contributes to clarifying the overall landscape of causal relational theories of time, and to the ongoing effort of aligning foundational (...) ontologies. We conclude by sketching how our results can be generalised, employing a strategy to simulate relations’ transitive closure in FOL. This generalisation makes the described construction of time exploitable in ontology engineering with minimal preconditions and sets up the groundwork for a systematic analysis of the connections between (discrete) causal and temporal structures. (shrink)

In this review, we present a rigorous construction of an algebraic method for quantum unstable states, also called Gamow states. A traditional picture associates these states to vectors states called Gamow vectors. However, this has some difficulties. In particular, there is no consistent definition of mean values of observables on Gamow vectors. In this work, we present Gamow states as functionals on algebras in a consistent way. We show that Gamow states are not pure states, in spite of their representation (...) as Gamow vectors. We propose a possible way out to the construction of averages of observables on Gamow states. The formalism is intended to be presented with sufficient mathematical rigor. (shrink)

General Morphological Analysis (GMA) is a computer-aided, non-quantified modelling method employing (discrete) category variables for identifying and investigating the total set of possible relationships contained in a given problem complex. The epistemological principle underlying discrete variable morphological modelling is that of decomposing a complex (multivariate) concept into a number of(“simple”) one dimensional concepts (i.e. category variables), the domains of which can then be recombined and recomposed in order to discover all of the other possible (multidimensional) concepts which can be generated (...) combinatorically. (shrink)

Ayda Ignez Arruda was a key figure in the development of the Brazilian school of Paraconsistent logic and the first person to write a historical survey of the field. Despite her importa...

In the context of computational social choice, we study voting methods that assign a set of winners to each profile of voter preferences. A voting method satisfies the property of positive involvement (PI) if for any election in which a candidate x would be among the winners, adding another voter to the election who ranks x first does not cause x to lose. Surprisingly, a number of standard voting methods violate this natural property. In this paper, we investigate different ways (...) of measuring the extent to which a voting method violates PI, using computer simulations. We consider the probability (under different probability models for preferences) of PI violations in randomly drawn profiles vs. profile-coalition pairs (involving coalitions of different sizes). We argue that in order to choose between a voting method that satisfies PI and one that does not, we should consider the probability of PI violation conditional on the voting methods choosing different winners. We should also relativize the probability of PI violation to what we call voter potency, the probability that a voter causes a candidate to lose. Although absolute frequencies of PI violations may be low, after this conditioning and relativization, we see that under certain voting methods that violate PI, much of a voter's potency is turned against them - in particular, against their desire to see their favorite candidate elected. (shrink)

The use of impact factor (IF) in the scientific and academic world is not new. A phenomenon that has gained widespread recognition and utilization. However, in modern-day usage, there seems to be a trend in higher education where academics are evaluated based on the impact factor of journals where scholarly works are published. This trend is gradually shifting the paradigm from the assessment of research contents to publication venues. This does not align with the original purpose of IF conceived by (...) Garfield in 1955. One question that has continued to agitate the minds of concerned academics is whether the IF of journals is a dependable measure of research quality. This paper is an attempt to clarify or address this problem. Based on a thorough literature search and filtration, several problems about the use of IF as a research quality measure are discussed as well as their implications. Recommendations were also made aimed at providing a way forward in higher education. (shrink)

Purpose: To explore the feasibility of using the multi-method and mixed-method in research studies by reviewing and comparing both methods. -/- Design / Method / Approach: Using the literature, historical background on mixed-methods and multiple-methods design principles are collected and applied in this paper in a systematic review format. -/- Findings: The major finding from this research is that incorporating quantitative and qualitative data in the form of a mixed or multi-method study has the potential to dramatically increase the accuracy (...) and quality of any research's analysis and conclusions. -/- Theoretical Implications: The study contributes to the theoretical understanding of how mixed and multi-method studies have distinct and distinguishable characteristics; it encourages researchers to conduct investigations appropriately to accomplish their research goals. The authors of this article introduce different designs (e.g., embedded design, explanatory design) which combine a mixed-method approach with a multi-method one. -/- Practical Implications: This study concludes that both mixed methods and multi methods are reliable and have unique characteristics that increase the validity (i.e., external validity, generalizability) and reliability of study findings. -/- Originality / Value: The authors of this paper present a taxonomy how to combine mixed methods with multi methods. -/- Research Limitations / Future Research: Research should be directed at defining the appropriate design for a multi-method approach to help researchers conduct multi method studies scientifically. -/- Paper Type: Conceptual. (shrink)

In his book, 'History as a Science and the System of the Sciences', Thomas Seebohm articulates the view that history can serve to mediate between the sciences of explanation and the sciences of interpretation, that is, between the natural sciences and the human sciences. Among other things, Seebohm analyzes history from a phenomenological perspective to reveal the material foundations of the historical human sciences in the lifeworld. As a preliminary to his analyses, Seebohm examines the formal and material presuppositions of (...) phenomenological epistemology, as well as the emergence of the human sciences and the traditional distinctions and divisions that are made between the natural and the human sciences. As part of this examination, Seebohm devotes a section to discussing Husserl’s formal mereology because he understands that a reflective analysis of the foundations of the historical sciences requires a reflective analysis of the objects of the historical sciences, that is, of concrete organic wholes (i.e., social groups) and of their parts. Seebohm concludes that Husserl’s mereological ontology needs to be altered with regard to the historical sciences because the relations between organic wholes and their parts are not summative relations. Seebohm’s conclusion is relevant for the issue of the reducibility of organic wholes such as social groups to their parts and for the issue of the reducibility of the historical sciences to the lower-order sciences, that is, to the sciences concerned with lower-order ontologies. In this paper, I propose to extend Seebohm’s conclusion to the ontology of chemical wholes as object of quantum chemistry and to argue that Husserl’s formal mereology is descriptively inadequate for this regional ontology as well. This may seem surprising at first, since the objects studied by quantum chemists are not organic wholes. However, my discussion of atoms and molecules as they are understood in quantum chemistry will show that Husserl’s classical summative and extensional mereology does not accurately capture the relations between chemical wholes and their parts. This conclusion is relevant for the question of the reducibility of chemical wholes to their parts and of the reducibility of chemistry to physics, issues that have been of central importance within the philosophy of chemistry for the past several decades. (shrink)

This paper addresses the issues related to designing and estimating the strength of solid-alloy elements in the deforming broaches of significant diameter (exceeding 150 mm) for the developed process of discrete broaching. The tool limit condition was assessed based on two strength criteria: the specific potential energy of shape change and the maximum tangent stresses. Numerical modeling using the finite element method has made it possible to derive the distribution of equivalent stresses in the tool elements and the contact stresses (...) at the surface of the contact between a solid-alloy insert and the body, which enabled the analysis of tool strength under loading. The simulation was performed under a single normal load, which ensured the versatility of the calculation for any contact pressure values. We have derived formulae to calculate the acceptable contact pressure depending on unit load. The effect of the insert protrusion height over the body on the strength of tool elements has been established. We have derived engineering dependences that determine the required magnitude of insert protrusion over the body depending on the ultimate load. An example of calculating the strength of a prefabricated deforming element in the machining of a sleeve made from gray modified cast iron of hardness HB230 has been considered. Our calculations have shown that the deforming element designed for the new technological process corresponds to the conditions of strength, provided the ratio h1/h=0.15 is maintained (where h1 is the insert height above the body, h is the insert height). The results obtained could be used in engineering calculations when designing the prefabricated tool for discrete deformation, as well as to assess the strength of prefabricated tools, such as cutters, core drills, reamers, when refining external loads. (shrink)

Purpose. To determine the potential of deforming broaching for the improvement of efficiency of cutter chisels in the mining industry. Methodology. The study of the application of the technological process of deforming broaching was carried out based on the experimental research into conditions of assembly of press couplings corresponding to cutting rock-destroying tools, the working surface of which is reinforced with solid-alloy inserts. Findings. Based on the conducted research, a new process of assembling the crowns of cutter chisels with the (...) use of deforming broaching was developed. Originality. It was determined that the range of angles of inclination of generatrix of the working cone of the deforming element and the roll-treading lip of the insert, which are necessary for efficient machining and pressing in crowns of cutters, is 4–16°. It was proven that the “solid alloy-steel” press couplings for cutter chisels will have the maximum bearing capacity at total tension a/d0 ≤ 3 %. It was found that it is necessary to foresee the following distribution of tensions: to perform 2 % of deformation by preliminary deforming broaching, and 1 % ‒ by pressing in an insert Practical value. The use of deforming broaching makes it possible to increase the strength of fastening the inserts of cutter chisels by 2 times, to reduce specific consumption of the tool by 4.4 times, and to increase the average drilling rate by 4 times. (shrink)

3rd ed, 2021. A circumscription of the classical theory of computation building up from the Chomsky hierarchy. With the usual topics in formal language and automata theory.

Holding students to high standards and assessing, measuring and evaluating their learning with challenging, authentic problems in the midterm and final exams is the goal of the professors who teach core signal processing concepts. However, the heavy reliance of these subjects on mathematics makes it difficult for students to genuinely grasp the concepts and relate to a conceptual framework. Specifically, analyzing the signals and the functionality of systems in Fourier domain; separating the system level analysis from signal level analysis; and (...) understanding how they are related in time domain and frequency domain are among the most challenging concepts. Students’ lower grades observed over past years in the introductory signal processing course exposed a potential disconnect between the actual level of learning and the high expectations set by the professors. In this paper, we present the active learning techniques that we implemented in one of the summer session offerings of this course in our department. The research explored Peer Instruction, pre-class reading quizzes and post-lecture quizzes. In addition to the mid and end of the quarter survey results, the comparison analysis of the grades students achieved in the active learning integrated course in the second summer session and the standard course offered in first summer session is discussed. According to our results, the developed techniques helped students in the active classroom perform significantly better than their peers participating in standard lectures when tested by challenging questions in their exams. (shrink)

In this paper we introduce a formalism for single-agent decision making that is based on Dynamic Argumentation Frameworks. The formalism can be used to justify a choice, which is based on the current situation the agent is involved. Taking advantage of the inference mechanism of the argumentation formalism, it is possible to consider preference relations, and conflicts among the available alternatives for that reasoning. With this formalization, given a particular set of evidence, the justified conclusions supported by warranted arguments will (...) be used by the agent’s decision rules to determine which alternatives will be selected. We also present an algorithm that implements a choice function based on our formalization. Finally, we complete our presentation by introducing formal results that relate the proposed framework with approaches of classical decision theory. (shrink)

This paper presents an ontology architecture concept for the European Space Agency‘s (ESA) Space Situational Awareness (SSA) Program. It incorporates the author‘s domain ontology, The Space Situational Awareness Ontology and related ontology work. I summarize computational ontology, discuss the segments of ESA SSA, and introduce an option for a modular ontology framework reflecting the divisionsof the SSA program. Among other things, ontologies are used for data sharing and integration. By applying ontology to ESA data, the ESA may better achieve its (...) integration and innovation goals, while simultaneously improving the state of peaceful SSA. (shrink)

The orbital space environment is home to natural and artificial satellites, debris, and space weather phenomena. As the population of orbital objects grows so do the potential hazards to astronauts, space infrastructure and spaceflight capability. Orbital debris, in particular, is a universal concern. This and other hazards can be minimized by improving global space situational awareness (SSA). By sharing more data and increasing observational coverage of the space environment we stand to achieve that goal, thereby making spaceflight safer and expanding (...) our knowledge of near-Earth space. To facilitate data-sharing interoperability among distinct orbital debris and space object catalogs, and SSA information systems, I proposed ontology in (Rovetto, 2015) and (Rovetto and Kelso, 2016). I continue this effort toward formal representations and models of the overall domain that may serve to improve peaceful SSA and increase our scientific knowledge. This paper explains the project concept introduced in those publications, summarizing efforts to date as well as the research field of ontology development and engineering. I describe concepts for an ontological framework for the orbital space environment, near-Earth space environment and SSA domain. An ontological framework is conceived as a part of a potential international information system. The purpose of such a system is to consolidate, analyze and reason over various sources and types of orbital and SSA data toward the mutually beneficial goals of safer space navigation and scientific research. Recent internationals findings on the limitations of orbital data, in addition to existing publications on collaborative SSA, demonstrate both the overlap with this project and the need for data-sharing and integration. (shrink)

Space situational awareness (SSA) is vital for international safety and security, and for the future of space travel. The sharing of SSA data and information should improve the state of global SSA for planetary defense and spaceflight safety. I take steps toward a Space Situational Awareness (SSA) Ontology, and outline some central objectives, requirements and desiderata in the ontology development process for this domain. The purpose of this ontological system is to explore the potential for the ontology research topic to (...) (i) represent SSA general knowledge, data, and entities/objects, (ii) clearly express the meaning of SSA data, and (iii) foster SSA data-sharing. The overall goal and motivation is to (iv) improve our capacity for planetary defense, e.g., from near- or deep-space objects and phenomena, and (v) facilitate safer and peaceful space access, navigation and travel, by improving global SSA. This research is thereby intended only for peaceful space-domain applications and uses, with particular interests in orbital debris. There is little application of ontology to the space domain as compared with other disciplines and little if any ontological development of SSA and related domains. In this respect, this paper offers novel concepts. (shrink)

Numerous studies show that humans tend to be more cooperative than expected given the assumption that they are rational maximizers of personal gain. As a result, theoreticians have proposed elaborated formal representations of human decision-making, in which utility functions including “altruistic” or “moral” preferences replace the purely self-oriented "Homo economicus" function. Here we review mathematical approaches that provide insights into the mathematical stability of alternative ways of representing human decision-making in social contexts. Candidate utility functions may be evaluated with help (...) of game theory, classical modeling of social evolution that focuses on behavioral strategies, and modeling of social evolution that focuses directly on utility functions. We present the advantages of the latter form of investigation and discuss one surprisingly precise result: “Homo economicus” as well as “altruistic” utility functions are less stable than a function containing a preference for the golden rule or for the common welfare that is only expressed in social contexts composed of individuals with similar preferences. We discuss the contribution of mathematical models to our understanding of human other-oriented behavior, with a focus on the classical debate over psychological altruism. We conclude that human can be psychologically altruistic, but that psychological altruism evolved because it was generally expressed towards individuals that contributed to the actor’s fitness, such as own children, romantic partners and long term reciprocators. (shrink)

We show that actuality entailments arise with goal-oriented modality only and endorse Belnap’s view of that goal-oriented modals use historical accessibility with a fixed past and an open future. This modal-theoretic assumption allows us to spell out the precise modal-temporal configuration in which the actuality entailment arises and our predictions are borne out by the data, cross-linguistically. We also show that, when any assumption about the identity of worlds at branching point is leveled - which appears to be the case (...) with generic deontic and opportunity modals, the actuality entailments disappear. We also predict that the entailment disappears with prospectivity. Finally, we argue that modal sentences giving rise to actuality entailments are informative, insofar as the contribution of the modality survives as a presupposition that the modal base is non-homogeneous. (shrink)

At the beginning of our Age of Information, the 21th century, the influence of IT (Information Technology) have got so important that all parts of human live and society have been involved. Especially Media Industry started a great hype which is not finished till now. Mobile Media have got a really up to date part of especially young society. On the level of serious science it has been up to date to use the word Information in all reports and publishing (...) papers. A lot of semantics have been used and some scientists (Prof. FLEISSNER, Prof HOFKIRCHNER, Prof. CAPURRO and the author) tried to abstract this word to a constant scientific term. So for first time the author tried a worldwide unifying definition of the terms Information and Data. It’s importance is documented by the topic “Information Scientific Axioms”. In second part – based on it – Clues for generally evidence of Information are written down. They are a set of informationscientific terms - excerpted out of real nature and society. The way of Information between Object and Subject or involving Human Being in big and complex machine systems (aeroplanes, ships and industrial productions) made it necessary to think additionally about the general usage of Information. As a useful result many relationships to other sciences are possible. They bring the benefit to be unifying and scientifically worldwide structuring. As next research object general forms of actual Information are investigated. As final result for future the author asks: „How can we make Information – in all forms – more positive and precious for Human Being? “. This is a new, scientific topic for the future of IT and human society. (shrink)

This paper develops the ontology of space objects for theoretical and computational ontology applied to the space (astronautical/astronomical) domain. It follows “An ontological architecture for Orbital Debris Data” (Rovetto, 2015) and “Preliminaries of a Space Situational Awareness Ontology” (Rovetto, Kelso, 2016). Important considerations for developing a space object ontology, or more broadly, a space domain ontology are presented. The main category term ‘Space Object’ is analyzed from a philosophical perspective. The ontological commitments of legal definitions for artificial space objects are (...) also discussed. Space object taxonomies are offered and space object terms are defined. (shrink)

A short summary paper of my Orbital Space Domain Ontology project (purl.org/space-ontology), originally conceived in 2011. Since then I've sought (without success) opportunities to realize it (either as a PhD or other degree thesis; or in an employment position) toward my original passion of entering the space sector and gaining further space education. Since then persons in the relevant space disciplines have seen the potential in it, and unfortunately some have taken advantage of my ideas yet excluded me from work. (...) I continue to struggle to fight for my own ideas as I see others professionally and financially benefit at my expense. References and documentation are available upon request to confirm my early ideation and origination on this topic. Please contact me if you have opportunities. Thank you. (shrink)

This paper applies some ontology architectures to the space domain, specifically the orbital and near-earth space environment and the space situational awareness domain. I briefly summarize local, single and hybrid ontology architectures, and offer potential space ontology architectures for each by showing how actual space data sources and space organizations would be involved.

We have been left with a big challenge, to articulate consciousness and also to prove it in an artificial agent against a biological standard. After introducing Boltuc’s h-consciousness in the last paper, we briefly reviewed some salient neurology in order to sketch less of a standard than a series of targets for artificial consciousness, “most-consciousness” and “myth-consciousness.” With these targets on the horizon, we began reviewing the research program pursued by Jun Tani and colleagues in the isolation of the formal (...) dynamics essential to either. In this paper, we describe in detail Tani’s research program, in order to make the clearest case for artificial consciousness in these systems. In the next paper, the third in the series, we will return to Boltuc’s naturalistic non-reductionism in light of the neurorobotics models introduced (alongside some others), and evaluate them more completely. (shrink)

The orbital debris problem presents an opportunity for inter-agency and international cooperation toward the mutually beneficial goals of debris prevention, mitigation, remediation, and improved space situational awareness (SSA). Achieving these goals requires sharing orbital debris and other SSA data. Toward this, I present an ontological architecture for the orbital debris and broader SSA domain, taking steps in the creation of an orbital debris ontology (ODO). The purpose of this ontological system is to (I) represent general orbital debris and SSA domain (...) knowledge, (II) structure, and standardize where needed, orbital data and terminology, and (III) foster semantic interoperability and data-sharing. In doing so I hope to (IV) contribute to solving the orbital debris problem, improving peaceful global SSA, and ensuring safe space travel for future generations. (shrink)