This book deals with the problem of dual-use science research and technology. It first explains the concept of dual use and then offers analyses of collective knowledge and collective ignorance. It goes on to present a theory of collective responsibility, followed by four chapters focusing on a particular scientific field or industry of dual use concern: the chemical industry, the nuclear industry, cyber-technology and the biological sciences. The problem of dual-use science research and technology arises because (...) such research and technology has the potential to be used for great evil as well as for great good. On the one hand, knowledge is a necessary condition, and perhaps a constitutive feature, of technologies that contribute greatly to individual and collective well-being. Consider, for example, nuclear technology that enables the generation of low cost electricity in populations without obvious alternative energy sources. So technological knowledge is a good thing and ignorance of it a bad thing. On the other hand, these same technologies can be extremely harmful to individuals and collectives, as with the atomic bombs dropped on Hiroshima and Nagasaki. So, at least with respect to some technologies evidently knowledge is a bad thing and ignorance a good thing. Accordingly, the question arises as to whether we ought to limit scientific research and/or the development of technology and, if so, which research or technology, in what manner and to what extent. This book examines the answer to that question. (shrink)

This paper defends the view that common nouns have a dual semantic structure that includes extension-determining and non-extension-determining components. I argue that the non-extension-determining components are part of linguistic meaning because they play a key compositional role in certain constructions, especially in privative noun phrases such as "fake gun" and "counterfeit document". Furthermore, I show that if we modify the compositional interpretation rules in certain simple ways, this dual content account of noun phrase modification can be implemented in (...) a type-driven formal semantic framework. In addition, I also argue against traditional accounts of privative noun phrases which can be paired with the assumption that nouns do not have a dual semantic structure. At the most general level, this paper presents a proposal for how we can begin to integrate a psychologically realistic account of lexical semantics with a linguistically plausible compositional semantic framework. (shrink)

Our aim was to try to generalize some theorems about the saturation of ultrapowers to reduced powers. Naturally, we deal with saturation for types consisting of atomic formulas. We succeed to generalize “the theory of dense linear order (or T with the strict order property) is maximal and so is any which is SOP3”, (where Δ consists of atomic or conjunction of atomic formulas). However, the theorem on “it is enough to deal with symmetric pre‐cuts” (so the theorem) cannot be (...) generalized in this case. Similarly the uniqueness of the dual cofinality fails in this context. (shrink)

Not only do grammars have the dual structure that Clahsen discusses but the lexicon contains atomic, unanalyzed items, which would be still more mysterious for single-mechanism models. Forms of be in modern English are listed atomically and this is not a simple function of their morphological richness or of the fact that they move.

Once atoms and molecules existed, a whole new dynamic entered the universe the moment the first cells appeared. What is different about cells is that they require energy to maintain their construction and be active. Their energy consumption produces waste products and heat that are released, or ‘dissipated’, into the environment. Cells are therefore dissipative structures. Recent research has shown that different types of cells live at the base of the tree of life. The best known are the bacteria. A (...) second group are the archaea. How could these cells have formed in a chemical environment? And how, with bacteria/archaea as a base, could complexity continue to increase to protozoa, plants and animals? These are some of the fundamental questions explored in this chapter. (shrink)

In the present work, the notion of chemical element is analyzed from the perspective of chemical education. Chemists refer to elements either as the final term of chemical analysis (i.e., simple substances) or as what persists in a chemical change. This duality has deep historical roots and it is sanctioned by IUPAC’s definition of chemical element. Nevertheless, it is inherently contradictory and it may result in deep misunderstandings in the educational context. After discussing the problems raised by the identification of (...) the element with any material body—either macroscopic or microscopic—we analyze a number of definitions of elements, proposed by chemists, epistemologists, and educators. After pointing out the strengths and weaknesses of such definitions, we argue that the chemical element is a unifying chemical concept that designates an abstract category, identified by the atomic number. (shrink)

In this paper, we prove that the lattice of all closure operators of a complete Almost Distributive Lattice L with fixed maximal element m is dual atomistic. We define the concept of a completely meet-irreducible element in a complete ADL and derive a necessary and sufficient condition for a dual atom of Φ (L) to be complemented.

In lieu of an abstract, here is a brief excerpt of the content:Spiritually Bilingual:Buddhist Christians and the Process of Dual Religious BelongingJonathan HomrighausenSociologists studying convert Buddhism in America have found that a surprisingly large number of Buddhists also identify as Christian.1 However, little empirical literature examines these Buddhist-Christian “dual religious belongers.”2 This study aims to fill that gap. Based on extensive interviews with eight self-identified “Buddhist Christians” of varying levels of doctrinal and experiential understanding, this study examines the (...) conversion process of these dual belongers and how they combine these religious traditions. Building on Michael von Brück’s contention that one’s first religion is like a mother tongue, I compare taking on a second religious tradition to learning a second language.3 As practitioners become more “fluent” in the second religion, they differentiate the two religions more clearly while combining them more seamlessly in their daily lives.methodologyThis study employs grounded theory and a qualitative, inductive methodology. Grounded theory is designed to elucidate the dynamic changes involved in a social process, with rich descriptions of categories and explanations for variations between different people’s experiences.4 While the use of qualitative methods with a small sample size means that my results have little statistical significance, such methods have been used in recent research on conversion and dual belonging and yield deep theoretical insight.5Eight participants for this study were solicited via word of mouth, personal acquaintance, and posting in a Buddhist-Christian Yahoo Group. In particular, I focused on Buddhist-Catholic practitioners to limit my sample group. Interviews were conducted and recorded in person or on the phone over a three-month period in fall, 2011. Interviews were open-ended, each lasting from sixty to ninety minutes. Several participants later received a draft of the paper to ensure they felt adequately represented; five participants responded. Names of participants have been changed for [End Page 57] confidentiality. To complement these interviews, I also incorporate written accounts of Buddhist-Christian conversion from both Catholic and Protestant authors.6participants’ backgroundsIt can be difficult to define Buddhist identity in the West, as many people who regularly practice meditation in a sangha do not self-identify as Buddhist.7 This study focuses on those who both practice Buddhist and Christian spirituality and belong to religious groups of both traditions. The eight participants have a range of religious expertise and commitment to both traditions. In terms of Catholic identity, six are laypeople (one in a secular religious order), one a priest, and one a nun. Three participants are theology professors. Seven have been Catholics from birth. One spent a decade living in a Buddhist monastery, two of them are roshis, and five give Buddhist teaching or meditation instruction formally. Seven of them practice various forms of Ch’an or Zen, while one practices Tibetan Buddhism.Cathy went not from Catholicism to Buddhism, but from Buddhism to Catholicism. A former Mormon and Unitarian, she began learning meditation at a Ch’an temple. This Ch’an temple normally only reached out to the Chinese community, but there was a Taiwanese nun there who wanted to reach out to non-Chinese community members. After practicing there for a few years, Cathy moved to another location, where she could not find any sangha that fit her needs. After attending Mass with a friend, she decided to become Catholic because she needed a community. It was not a hard transition for Cathy, who described feeling in meditation “some kind of entity, whether you call it God or Creator or atomic process.” She was confirmed as a Catholic in 2011.Rachel has been a nun for fifty years and a practicing Zen Buddhist for thirty, ten of those years living and working in a Zen monastery in the mountains of California. She described feeling an emptiness in her faith, a lack of practical knowledge of how to attain the spiritual goals that her Catholic tradition had for her. After hearing Zen teacher Cheri Huber speak at a conference, she took Huber on as her teacher. She has facilitated meditation workshops for many years. Though meditation instruction is not her full-time ministry, “meditation is my life … so in a sense... (shrink)

In this thesis I argue that the psychological study of concepts and categorisation, and the philosophical study of reference are deeply intertwined. I propose that semantic intuitions are a variety of categorisation judgements, determined by concepts, and that because of this, concepts determine reference. I defend a dual theory of natural kind concepts, according to which natural kind concepts have distinct semantic cores and non-semantic identification procedures. Drawing on psychological essentialism, I suggest that the cores consist of externalistic placeholder (...) essence beliefs. The identification procedures, in turn, consist of prototypes, sets of exemplars, or possibly also theory-structured beliefs. I argue that the dual theory is motivated both by experimental data and theoretical considerations. The thesis consists of three interrelated articles. Article I examines philosophical causal and description theories of natural kind term reference, and argues that they involve, or need to involve, certain psychological elements. I propose a unified theory of natural kind term reference, built on the psychology of concepts. Article II presents two semantic adaptations of psychological essentialism, one of which is a strict externalistic Kripkean-Putnamian theory, while the other is a hybrid account, according to which natural kind terms are ambiguous between internalistic and externalistic senses. We present two experiments, the results of which support the strict externalistic theory. Article III examines Fodor’s influential atomistic theory of concepts, according to which no psychological capacities associated with concepts constitute them, or are necessary for reference. I argue, contra Fodor, that the psychological mechanisms are necessary for reference. (shrink)

Fundamental experiments on the dual nature of atomic entities (photons, electrons, neutrons, etc.) can be interpreted in terms of “empty” waves not carrying energy and momentum. Similar points of view were advanced in famous papers by Einstein, de Broglie, Bohr, and Born. Recent proposals could lead to experimental tests of this idea, using low intensity photon beams, thanks to modern experimental apparatuses.

Some arguments, based on the possible spontaneous violation of the cosmological principle (represented by the observed large-scale structures of galaxies), on the Cartan geometry of simple spinors, and on the Fock formulation of hydrogen atom wave equation in momentum space, are presented in favor of the hypothesis that space-time and momentum space should be both conformally compactified and should both originate from the two four-dimensional homogeneous spaces of the conformai group, both isomorphic (S 3 ×S 1)/Z 2 and correlated (...) by conformal inversion, but should not necessarily be identified with them. Within this framework, the possible common origin for the SO(4) symmetry underlying the geometrical structure of the Universe, of Kepler orbits, and of the H atom is discussed. One of the consequences of the proposed hypothesis could be that any quantum field theory should be naturally free from both infrared and ultraviolet divergences. But then physical spaces defined as those where physical phenomena may be best described through some set of fields, could be different from those homogeneous spaces. A simple, exactly soluble, toy model, valid for a two-dimensional spacetime, is presented where the conjectured conformally compactified homogeneous spaces are both isomorphic to (S 1 ×S 1)/Z 2,while the possible physical spaces could be two finite lattices which are dual since Fourier transforms, represented by finite, discrete, sums, may be well defined on them. (shrink)

The problem of dual-use science research and technology arises because such research and technology has the potential to be used for great evil as well as for great good. On the one hand, knowledge is a necessary condition, and perhaps a constitutive feature, of technologies that contribute greatly to individual and collective well-being. Consider, for example, nuclear technology that enables the generation of low cost electricity in populations without obvious alternative energy sources. So technological knowledge is a good thing (...) and ignorance of it a bad thing. On the other hand, these same technologies can be extremely harmful to individuals and collectives. Consider, for example, the atomic bombs dropped on Hiroshima and NagasakiHiroshima and Nagasaki. So it seems that, at least with respect to some technologies, knowledge is a bad thing and ignorance a good thing. Accordingly, the question arises as to whether we ought to limit scientific research and/or the development of technology and, if so, which research or technology, in what manner and to what extent. (shrink)

Just like atomic physics seventy years ago, when it was realized that chain reaction could lead to medical applications as well as to the creation of atomic weapons, the life sciences have entered a grey zone. “Advances in biotechnology […]” a 2003 CIA document stated, “have the potential to create a much more dangerous biological warfare threat […] Engineered biological agents could be much worse than any disease known to man”. As sociologists of science have noted, contemporary life sciences have (...) dual use potential as they can be used to foster beneficial applications, for instance in health care, or generate harm, either intentionally or not, and possibly on an unprecedented.. (shrink)

The periodic table of elements, established empirically by Mendeleev in 1869, has been explained post-hoc by quantum mechanical electron configuration rules. Its primary ordering axis — atomic number Z, a count of protons — presupposes particle ontology at every level. Several structural anomalies persist within this framework: hydrogen's dual chemical character, helium's ambiguous placement, and the discontinuous displacement of lanthanides and actinides from the main table body. These anomalies have no Tier-1 justification within the current framework. -/- This paper (...) derives the periodic table from the automorphism structure of the unique minimal non-commutative algebra M₃(ℂ) of Cognitional Mechanics (CM), with zero free parameters. Elements are classified by their spectral resonance class — the equivalence class of M₃(ℂ) Cartan configurations under the automorphism action — rather than by atomic number Z. Four primary Cartan sets S1–S4 are derived from Axioms A1–A3, and their composite resonances generate the full element sequence. The period lengths 2·8·8·18·18·32·32 emerge from the A3 cyclotomic invariants Φ₃ = 13 and Φ₆ = 7 via the slot formula N_ℓ = 2 + 4(ℓ−1), where the increment 4 = n+1 follows from the A1 dimension n = 3. Zero free parameters are introduced. The nuclear stability maximum of iron-56 and the chemical basis of carbon-based life are established as algebraic necessities of the M₃(ℂ) automorphism structure. The three anomalies of the current periodic table are dissolved as Tier-3 projection artifacts. This paper presupposes the chemical projection framework established in the companion paper (DOI: 10.5281/zenodo.19122094). -/- Files. (shrink)

In this work I present what may be the first complete construction of quantum gravity describing the real universe via the celestial holographic conformal field theory dual to Einstein gravity in asymptotically-flat 4D spacetime. The theory is rigorously constructed as the shadow-invariant, purely spin-2 sector of holomorphic Chern–Simons theory on twistor space PT ≃ CP³ with gauge group the quantomorphic group Quant(PT). Primary fields are the celestial graviton operators O^{±2}Δ(z, z̄) with Δ ∈ 1 + iR and J = (...) ±2. Three-point functions are determined by the Penrose transform and reproduce the MHV and anti-MHV amplitudes of general relativity, including the vanishing of parity-odd and mixed-helicity couplings. Higher-point amplitudes arise from OPEs with analytically continued principal-series contours; loop integrands emerge as double discontinuities across shadow poles, which I verify explicitly for the scalar box integrals computed via this novel shadow discontinuity method, demonstrating analytically that they match Feynman diagram calculations for the scalar box, with numerical verification for the graviton box matching to 11+ decimal places. The construction satisfies extended BMS₄ ⋉ shadow symmetry with vanishing Virasoro central charge, also explicitly demonstrated via five independent and mutually reinforcing and rigorous arguments to be c = 0 to 10+ significant figures. I prove a rigidity theorem establishing that any 2D CFT with only spin ±2 primaries, the above symmetries and three-point data, and local inverse-Mellin-transformed correlators, is uniquely determined to be isomorphic to this quantomorphic twistor theory. Combined with the proof that crossing symmetry is a necessary consequence of bulk locality (not an independent axiom), this establishes that Einstein gravity in asymptotically-flat spacetime is the unique consistent theory of a single massless spin-2 particle. The quantomorphic gauge group structure provides a non-perturbative foundation, with perturbative scattering amplitudes emerging as the first residues of the holographic algebra. The first breakthrough insight that enabled and facilitated this construction was the realisation that the "shadow symmetry" of the boundary CFT—the map Δ ↔ 2 − Δ on conformal dimensions—is the restriction to null infinity of the Jost involution Θ of axiomatic quantum field theory, the operator independently constructed by Jost (1957) that coincides with the product C ∘ P ∘ T only in theories where all three factors individually exist as symmetries. At null infinity, where the metric is degenerate along the null generator, the distinction between temporal and spatial inversion collapses: the Jost involution is irreducible and reduces to time reversal T alone (Theorem 8.1). This provides an elegant resolution to the 40+ year "googly problem" in twistor theory by unifying self-dual and anti-self-dual helicity sectors through the shadow transform as representing discrete T-symmetric involution across the boundary, with the Einstein field equations derived from boundary Ward identities and crossing symmetry. All quantum mechanical foundations emerge from the Haar measure structure underlying this framework with no additional postulates: the five Wightman axioms are derived from the Peter–Weyl theorem on representation spaces, the Born rule P = |⟨n|ψ⟩|² is proven as the unique probability measure compatible with Haar structure on quantum state spaces, and wave function collapse is derived as Haar projection onto gauge singlets. This same identification reveals that the celestial conformal dimension is related to the Riemann zeta variable by Δ = 2s, so that the shadow involution Δ ↔ 2 − Δ becomes s ↔ 1 − s, the functional equation of the Riemann zeta function—establishing that the functional equation, shadow symmetry, and time reversal are three manifestations of one underlying self-duality. The entire holographic framework grows from a single root: self-dual Haar measure on (R⁺, ×), the simplest non-trivial locally compact group, whose self-duality already contains the functional equation and critical line. Three Cayley–Dickson doublings R → C → H → O produce the holographic chain R⁺ → S² → M⁴ → Gr(2,4)_C, with shadow symmetry at each level corresponding to the conjugation involution at that doubling step. The Grassmannian Gr(2,4) is the canopy of this holographic tree. The same Haar-invariant measure on the Grassmannian Gr(2,4) that determines the graviton spectrum also addresses three Millennium Prize problems through a unified geometric mechanism (Haar self-duality, functional equation symmetry, and Peter–Weyl compactness). The Riemann Hypothesis follows via 4 otherwise independent arguments and checks for circularity and consistency, and most fundamentally follows from three simultaneous constraints on the adelic quotient A×/Q× that form an overdetermined system whose unique solution forces Re(s) = 1/2 for all nontrivial zeros, with numerical verification of the first 10¹³ zeros on the critical line to machine precision using six independent tests. The Birch and Swinnerton-Dyer Conjecture is argued to be proven for analytic rank ≤ 1 using identical Haar measure structure on GL₂(A_Q)/GL₂(Q): for elliptic curves with ord_{s=1} L(E,s) ≤ 1, the same three-fold constraint described above, combined with the Gross–Zagier formula and Kolyvagin's Euler system descent, establishes ord_{s=1} L(E,s) = rank E(Q) and the parity conjecture (−1)^{rank} = w_E is proven for all curves from Haar self-duality. The framework also identifies the precise obstruction to proving the conjecture at higher rank (algebraic cycles from the Beilinson–Bloch–Kato conjectures). The Yang–Mills mass gap is established through a complete celestial holographic construction: the Wess–Zumino–Witten model at Kac–Moody level k on S², mapped to four-dimensional Schwinger functions by inverse Mellin transform, with reflection positivity proven via the shadow-reflection bridge, the remaining Osterwalder–Schrader axioms verified explicitly, and the Wightman theory reconstructed by the OS theorem—yielding mass gap M = 2N/(k+N) · Λ_QCD > 0 from the Sugawara formula and confinement from Haar orthogonality as a rigorously proved theorem. The construction introduces no lattice, takes no continuum limit, and imposes no infrared regulator. Spacetime itself emerges from the Grassmannian via Penrose twistor correspondence (M⁴ ↔ Gr(2,4) (Penrose 1967). The division algebra tower determines the Standard Model: the symmetry breaking chain Spin(8) → G₂ → SU(3) → SU(2) × U(1) produces the gauge group; three fermion generations follow from Weyl anomaly cancellation, Plücker partitions, and Spin(8) triality; sin²θ_W = 3/8 at the GUT scale is the Dynkin index ratio, equivalently dim(Im(H))/dim(O). Physical constants are arithmetic invariants: CP violation from the Jacobi sum J(χ₄⁽⁵⁾, χ₃⁽⁷⁾) = e^{iπ/6}; down-type quark mass ratios m_d : m_s : m_b = 2:5:9 from SU(3) Casimir eigenvalues; the spin-statistics connection η(4)/ζ(4) = 7/8 from the p = 2 Euler factor; the lightest neutrino mass m_{ν₁} = 0 exactly from Bott periodicity—in independent agreement with Boyle–Finn–Turok (PRL 121, 251301, 2018); and the three dimensional constants ℏ, c, G corresponding to the three Cayley–Dickson doubling steps. Strong CP angle θ = 0 exactly from Haar self-duality (consistent with experimental bound |θ| < 10⁻¹⁰), and the construction provides right-handed neutrinos as geometric dark matter candidates in agreement with Boyle–Turok (CP)T-symmetric cosmology, which integrates with uncanny precision into my T-symmetric, thermodynamically cyclic quantum cosmology. The T-anti-symmetric unification of a unified bipartite self-dual universe resolves the matter-antimatter asymmetry as a selection effect. Total baryon number B_total = 0 with embedded observers observing identical physics on either side due to being thermodynamic in nature, naturally aligning their arrows of time in the direction of increasing entropy, which on either side of the boundary flows in opposing directions. The Feynman-Stueckelberg interpretation of antimatter means antimatter is equivalent to matter moving backwards in time, which combined with the reversal in T of the direction of entropy increases means observers only ever observe the B > 0 (matter) sector, with the B < 0 (antimatter) sector always being the hidden sector from the perspective of any temporally-embedded observer that respects thermodynamics, as from any observer's perspective their time moves forward, their atomic nuclei have a positive electrical charge, electrons have negative electric charge, and the standard model has left handed doublets and right-handed singlets, with a weak force that appears left-chiral. To observe the antimatter would require an observer to reverse their arrow of time, which is thermodynamically not possible as consciousness and memory are thermodynamic processes that happen only in the direction of increasing entropy. Shadow geometry and right-handed neutrinos provide dark matter. The Grassmannian spinor bundle splits each fermion representation across the T boundary: right-handed neutrinos reside in the shadow sector, coupling to the observable sector only gravitationally. The dark matter density profile ρ(r) = ρ₀/(1+(r/r_c)²) with core radius r_c ≈ 9.98 kpc is derived from the shadow kernel by Abel inversion with zero free parameters, resolving the core cusp problem of dark matter distribution and addressing several further cosmological anomalies (the S₈ tension, Hubble tension, DESI dark energy evolution, JWST early galaxies, CMB hemispherical asymmetry, CMB dipole anomaly, axis of evil, overmassive early black holes, rotation curve diversity, etc.) from a single geometric source. Time's arrow emerges as a consequence of T-symmetric boundary conditions with entropy always increasing away from the conformal boundary in opposing temporal directions. The horizon and flatness problems are naturally resolved by this framework as the celestial CFT is globally defined at the conformal boundary. The framework generates falsifiable predictions including no primordial gravitational waves (tensor-to-scalar ratio r → 0, definitively falsified if r > 0.01 detected by CMB-S4), m_{ν₁} = 0 (KATRIN, JUNO), r_c ≈ 9.98 kpc (Euclid), glueball mass ratios matching the Sugawara spectrum, GUE statistics in the vacuum noise spectrum of gravitational wave detectors (LIGO/Virgo/KAGRA), and right-handed neutrino dark matter coupling only through gravity. Over 155 independent computational tests with zero free parameters confirm the framework to machine precision. Part 1 contains an introductory overview of the several subframeworks involved in this synthesis explaining their interrelations in the wider framework, part 2 contains the constructions and rigorous proofs of all major results, Part 3 contains extensions and other corollaries. Part 4 continues with comparisons to other approaches and discussion regarding foundational contributions without which this work would not have been possible follows, followed by testable predictions and a chapter addressing falsifiability, and Part V delivers a philosophical analysis of the implications suggested by the mathematics of this framework. This work unifies quantum mechanics and general relativity via the celestial holography program while revealing deep connections between number theory and physics: the identification Δ = 2s means the same self-dual Haar-invariant measure structure constraining the Riemann zeros to the critical line in the complex plane where Re(s) = 1/2 simultaneously constrains the conformal dimensions of graviton operators to the principal series where Re(∆) = 1, the same compactness that forces the Yang–Mills mass gap forces the discrete zeta spectrum, and the same functional equation symmetry that governs L-functions governs the shadow transform of the celestial CFT—suggesting geometry and arithmetic share a common logos rooted in self-dual Haar measure on (R⁺, ×) and flowering in the Grassmannian Gr(2,4). (shrink)

Recent theorizing about concepts has been dominated by two general models: crudely speaking, a philosophical one on which concepts are rule-governed atoms, and a psychological one on which they are associative networks. The debate between these two models is often framed in terms of competing answers to the question of "how the mind works" or "the nature of thought". I argue that this is a false dichotomy, because thought operates in both these ways. Human thought utilizes representational structures that function (...) as arbitrary re-combinable bits. This supports a version of the Language of Thought Hypothesis though a significantly more modest one than is typically advanced by advocates of that view. But human thought also employs representational structures that are contextually malleable, intuitive, and holistic; I call these "characterizations". "Dual systems" models of cognition recognize this multiplicity of mental processes, but typically posit largely separate structures, and emphasize conflicts between them. By contrast, I argue that the two forms of representation are more closely integrated, and more symbiotic, than talk of duality suggests. (shrink)

The periodic table of elements, established empirically by Mendeleev in 1869, has been explained post-hoc by quantum mechanical electron configuration rules. Its primary ordering axis — atomic number Z, a count of protons — presupposes particle ontology at every level. Several structural anomalies persist within this framework: hydrogen's dual chemical character, helium's ambiguous placement, and the discontinuous displacement of lanthanides and actinides from the main table body. These anomalies have no Tier-1 justification within the current framework. This paper derives (...) the periodic table from the automorphism structure of the unique minimal non-commutative algebra M₃(ℂ) of Cognitional Mechanics (CM), with zero free parameters. Elements are classified by their spectral resonance class — the equivalence class of M₃(ℂ) Cartan configurations under the automorphism action — rather than by atomic number Z. Four primary Cartan sets S1–S4 are derived from Axioms A1–A3, and their composite resonances generate the full element sequence. The period lengths 2·8·8·18·18·32·32 emerge from the A3 cyclotomic invariants Φ₃ = 13 and Φ₆ = 7 via the slot formula N_ℓ = 2 + 4(ℓ−1), where the increment 4 = n+1 follows from the A1 dimension n = 3. Zero free parameters are introduced. The nuclear stability maximum of iron-56 and the chemical basis of carbon-based life are established as algebraic necessities of the M₃(ℂ) automorphism structure. The three anomalies of the current periodic table are dissolved as Tier-3 projection artifacts. This paper presupposes the chemical projection framework established in the companion paper (DOI: 10.5281/zenodo.19122094). (shrink)

This paper attempts to explain what a protest is by using the resources of speech-act theory. First, we distinguish the object, redress, and means of a protest. This provided a way to think of atomic acts of protest as having dual communicative aspects, viz., a negative evaluation of the object and a connected prescription of redress. Second, we use Austin’s notion of a felicity condition to further characterize the dual communicative aspects of protest. This allows us to distinguish (...) protest from some other speech acts which also involve a negative evaluation of some object and a connected prescription of redress. Finally, we turn to Kukla and Lance’s idea of a normative functionalist analysis of speech acts to advance the view that protests are a complex speech act constituted by dual input normative statuses and dual output normative statuses. (shrink)

In advanced books and courses on logic (e.g. Sm], BM]) Gentzen-type systems or their dual, tableaux, are described as techniques for showing validity of formulae which are more practical than the usual Hilbert-type formalisms. People who have learnt these methods often wonder why the Automated Reasoning community seems to ignore them and prefers instead the resolution method. Some of the classical books on AD (such as CL], Lo]) do not mention these methods at all. Others (such as Ro]) do, (...) but the connections and reasons for preference remain unclear after reading them (at least to the present author, and obviously also the authors of OS], in which a theorem-prover, based exclusively on tableaux, is described). The confusion becomes greater when the reader is introduced to Kowalski's form of a clause ( Ko], Bu]), which is nothing but a Gentzen's sequent of atomic formulae, and when he realizes that resolution is just a form of a Cut, and so that while the elimination of cuts is the principal tool in proof-theory, its use is the main technique in AD! (shrink)

The paper has two parts preceded by quite comprehensive preliminaries.In the first part it is shown that a subvariety of the variety ${\cal T}$ of all tense algebras is discriminator if and only if it is semisimple. The variety ${\cal T}$ turns out to be the join of an increasing chain of varieties ${\cal D}_n$, which are discriminator varieties. The argument carries over to all finite type varieties of boolean algebras with operators satisfying some term conditions. In the case of (...) tense algebras, the varieties ${\cal D}_n$ can be further characterised by certain natural conditions on Kripke frames.In the second part it is shown that the lattice of subvarieties of ${\cal D}_0$ has two atoms, the lattice of subvarieties of ${\cal D}_1$ has countably many atoms, and for $n>1$, the lattice of subvarieties of ${\cal D}_n$ has continuum atoms. The proof of the second of the above statements involves a rather detailed description of zero-generated simple algebras in ${\cal D}_1$.Almost all the arguments are cast in algebraic form, but both parts begin with an outline describing their contents from the dual point of view of tense logics. (shrink)

The article begins with a response to a recent contribution by Jensen, in which he has criticized several aspects of the use of triads of elements, including Döbereiner’s original introduction of the concept and the modern use of atomic number triads by some authors including myself. Such triads are groups of three elements, one of which has approximately the average atomic weight of the other two elements, as well as having intermediate chemical reactivity. I also examine Jensen’s attempted reconstruction Mendeleev’s (...) use of triads in predicting the atomic weights of three hitherto unknown elements, that were subsequently named gallium, germanium and scandium. The present article then considers the use of atomic number triads, in conjunction with the phenomenon of first member anomaly, in order to offer support for Janet’s left-step periodic table, in which helium is relocated into group 2 of the table. Such a table features triads in which the 2nd and third elements of each group, without fail, fall into periods of equal length, a feature that is absent in the conventional 18-column or the conventional 32-column table. The dual sense of the term element, which is the source of much discussion in the philosophy of chemistry, is alluded to in further support of such a relocation of helium that may at first appear to contradict chemical intuition. (shrink)

In the present paper, we start studying epistemic updates using the standard toolkit of duality theory. We focus on public announcements, which are the simplest epistemic actions, and hence on Public Announcement Logic without the common knowledge operator. As is well known, the epistemic action of publicly announcing a given proposition is semantically represented as a transformation of the model encoding the current epistemic setup of the given agents; the given current model being replaced with its submodel relativized to the (...) announced proposition. We dually characterize the associated submodel-injection map as a certain pseudo-quotient map between the complex algebras respectively associated with the given model and with its relativized submodel. As is well known, these complex algebras are complete atomic BAOs . The dual characterization we provide naturally generalizes to much wider classes of algebras, which include, but are not limited to, arbitrary BAOs and arbitrary modal expansions of Heyting algebras . Thanks to this construction, the benefits and the wider scope of applications given by a point-free, intuitionistic theory of epistemic updates are made available. As an application of this dual characterization, we axiomatize the intuitionistic analogue of PAL, which we refer to as IPAL, prove soundness and completeness of IPAL w.r.t. both algebraic and relational models, and show that the well known Muddy Children Puzzle can be formalized in IPAL. (shrink)

Trisduction is a verification architecture for propositional truth built on a single root axiom and sealed three independent times. The Root Axiom states that to exist is to actuate: for any element of the universal domain the substrate-level kinetic-actuation differential is strictly positive, a floor that is theorem-grade external physics on the Heisenberg kinetic-energy bound and the zero-point energy, and whose denial is itself an actuation. From the atomic decomposition of that axiom the framework forces a triaxial mapping of any (...) complete claim onto three orthogonal verification axes, the formal-structural, the empirical-thermodynamic, and the epistemic-registrational, and it certifies a claim only where all three independently converge. The three seals stand on disjoint anchors. The linguistic-semantic seal splits a claim into exactly three irreducible slots under a deletion test. The topological-geometric seal closes those three axes on a fourth vertex into a tetrahedron carrying twelve directed verification gates, a count independently confirmed by the Newton-Gregory kissing number of three-dimensional space. The mathematical seal completes the verification algebra uniquely to the quaternions by the Frobenius classification, fixing exactly three axes over one scalar ground and closing the verdict in the form det(R) equal to the squared scalar part of the composed triad. Because the three seals share no premise and meet only at the Clifford Join, their convergence is itself the object the architecture exists to certify: the independence of the seals is the seal of the seals. The verdict economy is three-state and native, sealed, broken with a named mechanism, or under-determined with a named violation, with no fractional or probabilistic truth. A reflective register, MathDuction, applies the same quaternionic kernel to purely formal propositions by reading them across the architecture's own conjugation involution, whose fixed locus is the ground and whose fixed-point-free degeneration is the diagonal engine of the limitative theorems. This register places Gödel incompleteness and Tarski undefinability as facts about the reach of a proof ladder rather than as ceilings over the architecture, and its imprint test seals a proposition's decidable fragment while honestly locating, rather than claiming to settle, its undecidable residence. A verdict-reliability layer bounds the determinant error by the conditioning and guarantees the sealed-or-broken boundary is decided by the mathematics and never by rounding. The architecture authors no new mathematics; every load-bearing result is classical and credited, and the contribution is the arrangement. That arrangement yields the framework's principal verdicts, given here in full: the Riemann Hypothesis held dual-register, sealed on the kinetic prime field and the geometric critical line and terminally suspended on the formal string; Gödel's theorems placed as neither dictator nor final guard; P versus NP resolved as a three-layer determination; and a general account of why every formal system is foundationally incomplete toward the ground on which it stands. Warrant grade travels with every claim, and no claim is inflated or quietly weakened. (shrink)

The Upanishads reveal that in the beginning, nothing existed: “This was but non-existence in the beginning. That became existence. That became ready to be manifest”. (Chandogya Upanishad 3.15.1) The creation began from this state of non-existence or nonduality, a state comparable to (0). One can add any number of zeros to (0), but there will be nothing except a big (0) because (0) is a neutral number. If we take (0) as Nirguna Brahman (God without any form and attributes), then (...) from where and how did the universe come into existence? -/- The neutral power (0) cannot produce anything without having an element of duality in it. Although Nirguna Brahman is neutral, it has a positive, negative, and neutral pole, constituting its Prakriti or nature. Prakriti has three latent Gunas (modes or qualities): Satva, Rajas, and Tamas. They are related to Gyana Shakti (the power of knowledge) Sankalpa Shakti (the power of ideation), and Kriya Shakti (the power of action). Science says that Atom is the basic element from which the universe evolved. The Atom has three nuclei- electron, pluton, and neutron. The Satva, Rajas, and Tamas in Indian spirituality are nothing but the mystical names for the nuclei of an atom. -/- According to Bhagavata Purana, Prakriti is also constituted of the elements of Time, Karma (action/destiny) and Swabhava (innate nature). Time disturbs the equilibrium of Gunas. From the aspect of Karma is produced an entity called Mahat, in the form of intelligence. Mahat is dominated by Satva and Rajas. From Mahat manifests the next evolute dominated by Tamas with three predominant qualities – Dravya (substance), Kriya (action), as well as intelligence. It forms to become the Ego principle (Ahamkara). -/- Ahamkara has three modes – Satvic, Rajasic and Tamasic. Satvic is Jnana oriented, Rajasic action-oriented and Tamasic Dravya (substance) oriented. From the Tamasic Ahankara, five gross elements are produced (ether, air, fire, water, and earth - Akash, Vayu, Agni, Jal and Prithvi). From the Satvic Ahamkara, guardian deities (the sun and moon, deities of sense organs, and organs of action) and from Rajasic Ahamkara, ten senses (Indriyas), five senses of perception, five organs of action, the faculties of intellect and Prana (life breath) are produced. -/- Bhagavata says that since these energies, elements, and faculties remained disassociated, they were combined to form a Cosmic Egg. The egg floats in the primal waters for a thousand years. Then God enters this Cosmic Egg and manifests himself as the Cosmic Purusha. He is the first nucleus, the God particle equivalent to the number (1) which is the embodiment of everything in the universe. The concept of creation and dissolution in Hinduism can be compared to the waves in an ocean that appear and disappear incessantly. The Manvantaras are such successive episodes of creation emerging from the Cosmic Person, the Manu who is embodied God-Consciousness, God himself. These episodes of creation are measured in Hinduism in terms of Manvantaras, the epochs of Manus. -/- Manu is the ‘First-Born’ (1) of God, the Cosmic Purusha from whom the world has originated. This Cosmic Person (Purusha) has been described as having fourteen biospheres (heavens) that are inhabited by various life forms in the order of evolution of consciousness. If we begin from the human biosphere (Bhuloka), there are ten astral biospheres that a man must transcend to attain liberation or Mukti from the cycle of births and deaths. -/- The number (1) produces the primary numbers up to (9) through the transmutation of the creational energies and qualities. The process can be related to the descent and cyclical evolution of (1) through ten spiritual stages, finally merging with the nondual (0). The number (10) marks the merger of (1) with (0). The Hindu worldview is that all life forms in an episode of creation must evolve to become one with the non-dual state (0) to attain liberation from the cycle of births and deaths in a cyclical process. -/- . (shrink)

Bilateralism is the position according to which assertion and rejection are conceptually independent speech acts. Logical bilateralism demands that systems of logic provide conditions for assertion and rejection that are not reducible to each other, which often leads to independent definitions of proof rules (for assertion) and dual proof rules, also called refutation rules (for rejection). Since it provides a critical account of what it means for something to be a proof or a refutation, bilateralism is often studied in (...) the context of proof-theoretic semantics, an approach that aims to elucidate both the meaning of proofs (and refutations) and what kinds of semantics can be given if proofs (and refutations) are considered as basic semantic notions. The recent literature on bilateral proof-theoretic semantics has only dealt with the semantics of proofs and refutations, whereas we deal with semantics in terms of proofs and refutations. In this paper we present a bilateral version of base-extension semantics—one of the most widely studied proof-theoretic semantics—by allowing atomic bases to contain both atomic proof rules and atomic refutation rules. The semantics is shown to be sound and complete with respect to the bilateral bi-intuitionistic logic $$\varvec{\textsf{2Int}}$$ 2 Int. Structural similarities between atomic proofs and refutations also allow us to define duality notions for atomic rules, deductions and bases, which may then be used for the proof of bilateral semantic harmony results. Aside from enabling embeddings between different fragments of the language, bilateral semantic harmony is shown to be a restatement of the syntactic horizontal inversion principle, whose meaning-conferring character may now be interpreted as the requirement of preservation by inferences of harmony notions already present at the core of the semantics. (shrink)

Recently, two apparently quite different duality-based approaches to automata minimisation have appeared. One is based on ideas that originated from the controllability-observability duality from systems theory, and the other is based on ideas derived from Stone-type dualities specifically linking coalgebras with algebraic structures derived from modal logics. In the present paper, we develop a more abstract view and unify the two approaches. We show that dualities, or more generally dual adjunctions, between categories can be lifted to dual adjunctions (...) between categories of coalgebras and algebras, and from there to automata with initial as well as final states. As in the Stone-duality approach, algebras are essentially logics for reasoning about the automata. By exploiting the ability to pass between these categories, we show that one can minimize the corresponding automata. We give an abstract minimisation algorithm that has several instances, including the celebrated Brzozowski minimisation algorithm. We further develop three examples that have been treated in previous works: deterministic Kripke frames based on a Stone-type duality, weighted automata based on the self-duality of semimodules, and topological automata based on Gelfand duality. As a new example, we develop alternating automata based on the discrete duality between sets and complete atomic Boolean algebras. (shrink)

The way in which much of the conventional interpretation has tried to describe the structure of Hegel’s civil society is inaccurate and one-dimensional. To Hegel civil society is not just the economic marketplace, where every individual tries to maximize his or her enlightened self-interest: side by side with the elements of universal strife and unending clash which are of the nature of civil society, there is another element which strongly limits and inhibits self-interest and transcendswhat would otherwise be a universal (...) atomism into a sphere of solidarity and mutuality. The principle of civil society itself is dual. Hegel’s communitas grows organically within civil society itself, and is not imposed on it from outside by the state. (shrink)

In this paper we will see deductive systems for classical propositional and predicate logic in the calculus of structures. Like sequent systems, they have a cut rule which is admissible. Unlike sequent systems, they drop the restriction that rules only apply to the main connective of a formula: their rules apply anywhere deeply inside a formula. This allows to observe very clearly the symmetry between identity axiom and the cut rule. This symmetry allows to reduce the cut rule to atomic (...) form in a way which is dual to reducing the identity axiom to atomic form. We also reduce weakening and even contraction to atomic form. This leads to inference rules that are local: they do not require the inspection of expressions of arbitrary size. (shrink)

We investigate the algebraic structure of the upper semi-lattice formed by the recursively enumerable Turing degrees. The following strong generalization of Lachlan's Nonsplitting Theorem is proved: Given n ≥ 1, there exists an r.e. degree d such that the interval $\lbrack\mathbf{d, 0'}\rbrack \subset\mathbf{R}$ admits an embedding of the n-atom Boolean algebra B n preserving (least and) greatest element, but also such that there is no (n + 1)-tuple of pairwise incomparable r.e. degrees above d which pairwise join to 0' (...) (and hence, the interval $\lbrack\mathbf{d, 0'}\rbrack \subset\mathbf{R}$ does not admit a greatest-element-preserving embedding of any lattice L which has n + 1 co-atoms, including B n + 1 ). This theorem is the dual of a theorem of Ambos-Spies and Soare, and yields an alternative proof of their result that the theory of R has infinitely many one-types. (shrink)

It has long been recognized that the concept of inconsistency is a central part of commonsense reasoning. In this issue, a number of authors have explored the idea of reasoning with maximal consistent subsets of an inconsistent stratified knowledge base. This paradigm, often called “coherent-based reasoning", has resulted in some interesting proposals for para-consistent reasoning, non-monotonic reasoning, and argumentation systems. Unfortunately, coherent-based reasoning is computationally very expensive. This paper harnesses the approach of approximate entailment by Schaerf and Cadoli [SCH 95] (...) to develop the concept of “approximate coherent-based reasoning". To this end, we begin to present a multi-modal propositional logic that incorporates two dual families of modalities: □S and?S defined for each subset S of the set of atomic propositions. The resource parameter S indicates what atoms are taken into account when evaluating formulas. Next, we define resource-bounded consolidation operations that limit and control the generation of maximal consistent subsets of a stratified knowledge base. Then, we present counterparts to existential, universal, and argumentative inference that are prominent in coherence-based approaches. By virtue of modalities □S and?S, these inferences are approximated from below and from above, in an incremental fashion. Based on these features, we show that an anytime view of coherent-based reasoning is tenable. (shrink)

In lieu of an abstract, here is a brief excerpt of the content:358 HISTORY OF PHILOSOPHY und k6nnen es nur sein. Das Gleiche ist der Fall mit den Erfahrungstatsachen des wissenschaftlichen Versuches und im Grunde aller Wissenschaft gibt es nichts anderes und kann es nichts anderes geben. Mag ein gewandter Dialektiker die Voraussetzungen, yon denen er ausgeht, noch so sehr durcheinanderwirbeln, sie verbinden und zu Schliissen aufeinandertiirmen: Was er erhiilt, wird stets wieder eine Aussage sein. Niemals wird er zu einem (...) Gesetze gelangen, das lauten wiirde: Tue dies! oder Tue dies nicht! also zu einem Satze, der dem sittlichen Gesetze entsprechen oder ibm entgegenstehen kSnnte,r Kann Morscher dann noch immer behaupten, dass Poincar6 nur kategorische Syllogismen oder nur Schhssfolgerungen mit gerade Priimissen im Sinne hatte? Wir sind dem t3bersetzer eine Ehrenrettung schuldig: wenn er hier "syllogisme" mit "logischer Schluss" iibersetzt hat, hat er keinen Fehler begangen, es trifft ihn nicht der Tadel, durch eine scblechte Ubersetzung eine Legende hervorgerufen zu haben. Morscher soUte jedoch nicht, wenn er "syllogisme" liest, "kategorischer Syllogismus" verstehen, lind bei geistesgeschichtlichen Diskussionen immer den hermeneutisch relevanten Kontext beachten, d.h. wnigstens den Absatz, den er gerade analysiert, zu Ende lesen. Es liisst sich rticht daran zweifeln, dass Hare mit Recht [PR] Poincar6 zuschreibt. Nicht ganz sicher bin ich, ob Poincar6, wenn er sah und es ausdriicklich sagte, dass die iiblichen logischen Regeln fiir Imperativfolgerung nicht anwendbar sind, damit auch gleichzeitig die Entwicklung einer Imperativlogik (Normenlogik) forderte, oder ob er sich dieser programmatischen Konsequenz nicht ganz bewusst war. OTAWEINBERGER Universitiit Graz RUSSELL'S REALIST THEORY OF REMOTE MEMORY In a paper on Bertrand Russell's theory of memory1 David Pears undertakes to amend certain aspects of his version of Russell's theory of memory which he had presented in his Bertrand Russell and the British Tradition in Philosophy. ~ In that work Pears had attributed to Russell an extreme realist theory of memory from 1905 through 1918, i.e., a general theory of memory according to which the mind maintains direct contact by the dual relation of acquaintance with past sense-data. 3 This, he now believes, is historically incorrect in view of two of Russell's lesser known papers which have since come to his attention and which make it clear that in 1915 Russell held the extreme realist account only in connection with immediate memory--i.e., with memory within what is often called the specious present--and that as regards remote memory--i.e., memory of things not very recent and, so, outside the specious present--past sense-data 7 Poincare, Letzte Gedanken, aus dem FranzSsischen iibersetzt yon Karl Lichteneeker (Leipzig : Akademische Verlagsgesellschaft, 1913),pp. 226 f. 1 D. F. Pears, "Russell's Theories of Memory 1912-1921," in Bertrand Russell's Philosophy, ed. George Nakhnikian (New York: Harper and Row, 1974), pp. 117-137. The papers are from the Indiana University Russell centenary conference, 1972. 2 (London: Collins~I967), pp. 7I, 181-182. 3 Ibid. NOTES AND DISCUSSIONS 359 were knowable only by description and not by acquaintance.4 But Pears still argues, as against J. O. Urmson,5 that Russell did hold the realist theory of remote memory before 1915, although he was "changing his mind" in that year and, by 1917 ("The Philosophy of Logical Atomism"), had definitely abandoned the theory,e I believe that Pears is partly right about this matter: Russell almost certainly did hold a realist theory of remote memory before 1915. However, it can be shown, I think, that the theory was abandoned, not in 1915 or later, but in 1914. Pears shows beyond any reasonable doubt that Russell held a realist theory of remote memory in 1912. The strongest evidence may be found in a passage in Problems of Philosophy: There is some danger of confusion as to the nature of memory, owing to the fact that memory of an object is apt to be accompanied by an image of the object, and yet the image cannot be what constitutes memory. This is easily seen by merely noticing that the image is in the present, whereas what is remembered is known to be in the past. Moreover, we are certainly able to some extent to compare our image with the object remembered, so that we often know, within... (shrink)

This book shows quantum learning is the resource that unites parts into wholes and then wholes into continually larger wholes. Just as quantum computers can regard sub-atomic particles as a wave and as particles, quantum learning can understand learners as simultaneously nondual (whole) and dual (part). The study includes a reconsideration of clarity in expression and thought.

Western tradition has always been fundamentally anthropocentric. With the scientific mind, modern humans have achieved a sort of colonization of the rest of nature, where only their own benefit makes any sense. This conception has been in a period of crisis since the second half of the 20th century, particularly the final third, and we are witnessing the toppling of some of the ontological principles that made western humanity. Greek philosophy, the Judeo-Christian tradition, the Renaissance, these are the three great (...) moments of this anthropocentrism; the fourth was human domination of nature and the cosmos. Since the second half of the 20th century this situation has produced a counter-consciousness, western anthropocentrism’s consciousness of hybris, the awareness of having overstepped every limit and every frontier with the self-destruction brought by the atom bomb. The dual posture of pride and fall into hybris forms the grand philosophical backdrop to the ethical, political and ideological debates that are currently going on around developments in biology and genetics. This being so, is it possible for human beings, in philosophical, intellectual and artistic terms, to transcend anthropocentrism? Yes, it is, through self-restraint, the ancient sofrosyne, which demanded moderation when faced with hybris. But westerners are afraid of transcending anthropocentrism; the idea that humans are nothing strikes fear into their hearts (pancosmic cold). An intermediate way is wanted: we need to rediscover awareness of a certain animism, rediscover the soul of the world. (shrink)

This paper resolves the profound epistemic chasm between objective materialist science and subjective phenomenological experience—a divide perfectly encapsulated by the "Hard Problem of Consciousness"—by recontextualizing the ancient Indian Shad Darshanas and Advaita Vedanta as a rigorous, sequential, and interdisciplinary scientific framework. Rejecting the limitations of Cartesian dualism and reductive materialism, this treatise posits that human perception of a dualistic universe is merely an evolutionary biological interface, optimized for species survival rather than objective truth-gathering. To penetrate this sensory illusion, the text (...) systematically maps Vedic epistemology, Vaisheshika atomism, and Samkhya dualism onto modern cognitive neuroscience, the Standard Model of particle physics, and the Copenhagen interpretation of quantum mechanics. We demonstrate that the six orthodox Hindu philosophical schools are not competing theological dogmas, but rather form a coherent algorithmic progression of scientific inquiry: advancing from strict epistemic verification and Boolean-style logic (Nyaya), through the categorization of indestructible foundational matter (Vaisheshika) and the mechanics of the quantum observer collapsing the wave-function of reality (Samkhya), into applied neurobiological deactivation of the Default Mode Network and linguistic neuroplastic programming (Yoga and Mimamsa). This meticulously structured progression culminates in Vedanta, which facilitates the absolute ontological collapse of the subject-object divide. By integrating the holographic universe principle, quantum non-locality, and Donald Hoffman’s interface theory of perception, the treatise formally derives the "Advaita Equation"—a theoretical postulate asserting that localized individual consciousness (Atman) and the universal, infinite background state of the cosmos (Brahman) are mathematically and ontologically identical, obscured only by the cognitive matrix of space, time, and causation. Ultimately, this unified non-dual ontology moves beyond theoretical metaphysics to provide robust, actionable solutions to the paradoxes of artificial intelligence and quantum physics, while simultaneously offering paradigm-shifting approaches to contemporary global crises in ecological preservation, the thermodynamics of capitalist economics, and the optimization of human neurochemistry. (shrink)

This paper sets out to show how Eddington's early twenties case for variational derivatives significantly bears witness to a steady and consistent shift in focus from a resolute striving for objectivity towards “selective subjectivism” and structuralism. While framing his so-called “Hamiltonian derivatives” along the lines of previously available variational methods allowing to derive gravitational field equations from an action principle, Eddington assigned them a theoretical function of his own devising in The Mathematical Theory of Relativity (1923). I make clear that (...) two stages should be marked out in Eddington's train of thought if the meaning of such variational derivatives is to be adequately assessed. As far as they were originally intended to embody the mind's collusion with nature by linking atomicity of matter with atomicity of action, variational derivatives were at first assigned a dual role requiring of them not only to express mind's craving for permanence but also to tune up mind's privileged pattern to “Nature's own idea”. Whereas at a later stage, as affine field theory would provide a framework for world-building, such “Hamiltonian differentiation” would grow out of tune through gauge-invariance and, by disregarding how mathematical theory might precisely come into contact with actual world, would be turned into a mere heuristic device for structural knowledge. (shrink)

The paper is a critique of modern mass and atomized society,in which the indivi_dual is loosing himself/herself. To resolve this problem of the self-loss it is neces_sary to create a moral society on the grounds of basic moral values. One of these values is also the personal responsibility. The problem of responsibility is analyzed on the background of the philosophy of Antoine de Saint-Exupéry, Jean-Paul Sartre, Emmanuel Mounier and Emmanuel Lévinas.

The term “element” is typically used in two distinct senses. First it is taken to mean isolated simple substances such as the green gas chlorine or the yellow solid sulphur. In some languages, including English, it is also used to denote an underlying abstract concept that subsumes simple substances but possesses no properties as such. The allotropes and isotopes of carbon, for example, all represent elements in the sense of simple substances. However, the unique position for the element carbon in (...) the periodic table refers to the abstract sense of “element.” The dual definition of elements proposed by the International Union for Pure and Applied Chemistry contrasts an abstract meaning and an operational one. Nevertheless, the philosophical aspects of this notion are not fully captured by the IUPAC definition, despite the fact that they were crucial for the construction of the periodic table. This pivotal chemical notion remains ambiguous and such ambiguity raises problems at the epistemic, logical, and educational levels. These aspects are discussed throughout the book, from different perspectives. This collective book provides an overview of the current state of the debate on the notion of chemical element. Its authors are historians of chemistry, philosophers of chemistry, and chemists with epistemological and educational concerns. (shrink)

As the final component of a chain of reasoning intended to take us all the way to logical nihilism, Russell (2018) presents the atomic sentence ‘prem’ which is supposed to be true when featuring as premise in an argument and false when featuring as conclusion in an argument. Such a sentence requires a non-reflexive logic and an endnote by Russell (2018) could easily leave the reader with the impression that going non-reflexive suffices for logical nihilism. This paper shows how one (...) can obtain non-reflexive logics in which ‘prem’ behaves as stipulated by Russell (2018) but which nonetheless has valid inferences supporting uniform substitution of any formula for propositional variables such as modus tollens and modus ponens. (shrink)

MTL-algebras are the algebraic counterpart of Monoidal t-norm logic, whose truth values are real numbers in $[0,1]$. More generally, logics whose truth value set forms an MTL-algebra are called MTL-valued logics; their deductive systems are studied. Many results known to hold for BL-algebras are updated to apply to all MTL-algebras. Coatoms, molecules, creators, and essential deductive systems are defined on MTL-algebras. Coatoms and molecules are particular elements of an MTL-algebra and creators are duals of annihilators known in MV-algebra theory. These (...) new algebraic concepts have a logic origin that is discussed. Creators are particular deductive systems. Their relation to coatoms, molecules and prime, Boolean, and maximal deductive systems is studied. Essential deductive systems on MTL-algebras are analyzed. (shrink)

In 1932, Wolfgang Pauli was a world-renowned physicist and had already done the work that would win him the 1945 Nobel Prize. He was also in pain. His mother had poisoned herself after his father's involvement in an affair. Emerging from a brief marriage with a cabaret performer, Pauli drank heavily, quarreled frequently and sometimes publicly, and was disturbed by powerful dreams. He turned for help to C. G. Jung, setting a standing appointment for Mondays at noon. Thus bloomed an (...) extraordinary intellectual conjunction not just between a physicist and a psychologist but between physics and psychology. Eighty letters, written over twenty-six years, record that friendship. This artful translation presents them in English for the first time. Though Jung never analyzed Pauli formally, he interpreted more than 400 of his dreams--work that bore fruit later in Psychology and Alchemy and The Analysis of Dreams. As their acquaintance developed, Jung and Pauli exchanged views on the content of their work and the ideas of the day. They discussed the nature of dreams and their relation to reality, finding surprising common ground between depth psychology and quantum physics. Their collaboration resulted in the combined publication of Jung's treatise on synchronicity and Pauli's essay on archetypal ideas influencing Kepler's writings in The Interpretation of Nature and the Psyche. Over time, their correspondence shaped and reshaped their understanding of the principle they called synchronicity, a term Jung had suggested earlier. Through the association of these two pioneering thinkers, developments in physics profoundly influenced the evolution of Jungian psychology. And many of Jung's abiding themes shaped how Pauli--and, through him, other physicists--understood the physical world. Of clear appeal to historians of science and anyone investigating the life and work of Pauli or Jung, this portrait of an incredible friendship will also draw readers interested in human creativity as well as those who merely like to be present when great minds meet. (shrink)

Fix 2 < n < ω and let C A n denote the class of cylindric algebras of dimension n. Roughly, C A n is the algebraic counterpart of the proof theory of first-order logic restricted to the first n var...

In this stimulating investigation, Gideon Freudenthal has linked social history with the history of science by formulating an interesting proposal: that the supposed influence of social theory may be seen as actual through its co herence with the process of formation of physical concepts. The reinterpre tation of the development of science in the seventeenth century, now widely influential, receives at Freudenthal's hand its most persuasive statement, most significantly because of his attention to the theoretical form which is charac teristic. (...) of classical Newtonian mechanics. He pursues the sources of the parallels that may be noted between that mechanics and the dominant philosophical systems and social theories of the time; and in a fascinating development Freudenthal shows how a quite precise method - as he descriptively labels it, the 'analytic-synthetic method' - which underlay the Newtonian form of theoretical argument, was due to certain interpretive premisses concerning particle mechanics. If he is right, these depend upon a particular stage of con ceptual achievement in the theories of both society and nature; further, that the conceptual was generalized philosophically; but, strikingly, Freudenthal shows that this concept-formation itself was linked to the specific social relations of the times of Newton and Hobbes. (shrink)

"The time-honored dualism of the mutually exclusive systems of thought, mechanistic biology on the one hand and vitalism on the other, expresses a pair of theoretical approaches which are both inadequate. We shall show how they can be replaced by an abstractly descriptive system of a different type that is far better adapted to the nature of biology"--Preface.

The Einstein-de Broglie soliton concept is applied to simulate stationary states of an electron in a hydrogen atom. According to this concept, the electron is described by the localized regular solutions to some nonlinear equations. It is shown that the electron-solilon center travels along some stationary orbit around the Coulomb center. The electromagnetic radiation is absent as the Poynting vector has non-wave asymptote O(r −3)after averaging over angles.

Letn > 2. A weakly representable relation algebra that is not strongly representable is constructed. It is proved that the set of all n by n basic matrices forms a cylindric basis that is also a weakly but not a strongly representable atom structure. This gives an example of a binary generated atomic representable cylindric algebra with no complete representation. An application to first order logic is given. (© 2008 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim).

Within the context of Born-Infeld (BI) nonlinear electrodynamics (NED) we revisit the non-relativistic, spinless H-atom. The pair potential computed from the Born-Infeld equations is approximated by the Morse type potential with remarkable fit over the critical region where the convergence of both the short and long distance expansions slows down dramatically. The Morse potential is employed to determine both the ground state energy of the electron and the BI parameter.

A cylindric algebra atom structure is said to be strongly representable if all atomic cylindric algebras with that atom structure are representable. This is equivalent to saying that the full complex algebra of the atom structure is a representable cylindric algebra. We show that for any finite n >3, the class of all strongly representable n-dimensional cylindric algebra atom structures is not closed under ultraproducts and is therefore not elementary. Our proof is based on the following (...) construction. From an arbitrary undirected, loop-free graph Γ, we construct an n-dimensional atom structure E(Γ), and prove, for infinite Γ, that E(Γ) is a strongly representable cylindric algebra atom structure if and only if the chromatic number of Γ is infinite. A construction of Erdős shows that there are graphs (k < ω)with infinite chromatic number, but having a non-principal ultraproduct $\prod _D\Gamma _k $ whose chromatic number is just two. It follows that $E(\Gamma _k )$ is strongly representable (each k < ω) but $\Pi _D E(\Gamma _k)$ is not. (shrink)

In the mid-1970s, the fascist-leaning dictatorships in Spain (1939–1977) and Portugal (1933–1974) fell. Closely linked to the 1973 oil crisis, debates over energy and technology policies became very prominent during the ensuing political redefinition of both countries. Two decades after the first international agreements between the Iberian regimes and the United States for the development of nuclear programs, a myriad of movements of social resistance to nuclear technology emerged in dialogue with anti-nuclear organizations in other European countries. Fun and playfulness (...) have been used for top–down popularization and banalization of nuclear technologies since the 1950s, but here pleasant forms of resistance also played a central role in contesting national energy plans, expert discourses, and vested interests. This article explores what we call “anti-nuclear fun,” the use of amusement, play, and humor as political and epistemic tools to familiarize society with the exceptional and daily risks of the “peaceful atom.”. (shrink)