Axiomatic Notion Research Articles

What is Light, Really? A Quantum Dialectical View

Radiant energy in the form of visible light has been and still remains the most mysterious and venerated object in human history. Gradual understanding of the nature of light now in its very wide range of energy, both above and below the visible range; has led to the proliferation of technologies, especially after the recognition of its quantum nature. Although impressive knowledge about the nature of light, its properties, its source, and its interaction with other existing matter, etc., have been gained and profitably utilized in technologies; its fundamental unit as a discrete point particle or an extended continuous wavelet, as well as its mass, still remains a subject of intense debate among the physicists. Understanding the enigmatic properties and the nature of light as difficult as it proved to be; understanding the velocity of its propagation proved to be the most misunderstood aspect of light. As has been shown through some recent publications by this author, the false axiomatic notion of Albert Einstein at the turn of the 20th century, about the universal and absolute constancy (in vacuum) of the velocity c of light; caused the century-long confusion, paradoxes, myths and ironically, the darkest period of modern physics and cosmology! Another wrong centuries-old axiomatic notion of Isaac Newton about the one-sided universal gravitational attraction of matter, acted in a synergistic way with Einstein’s false axiomatic notion about light; to create the modern and sophisticated ruling mythology of the “Big Bang” creation of the universe, undermining scientific progress both in theoretical physics and in cosmology, since Copernicus and Johannes Kepler. It can now be demonstrated that this new mythology has absolutely no basis in objective reality and is the product of brain-cooked and abstract mathematical fabrications based on an axiomatic truth and apparently willful deceptions by official science. A quantum dialectical approach reveals that light is composed of point particles (photons) with a wide range of energy, velocity, and mass; over the whole electromagnetic spectrum, from the microwave to the highest energy gamma-ray photons. The only difference from other matter particles is that photons exist only in their free elementary state and are created instantly (until absorbed) from their virtual existence in matter atoms or in the quantum vacuum; in this infinite, eternal, and ever-changing universe; thereby resolving all mysteries about light.

Why is economics the only discipline with so many curves going up and down? There is an alternative

Even the most rudimentary training from Economics 101 starts with demand curves going down and supply curves going up. They are so ‘natural’ that they sound even more obvious than the Euclidian postulates in mathematics. But are they? What do they actually mean? Start with “demand curves”. Are they hypothetical ‘psychological constructs’ on individual preferences? Propositions on aggregation over them? Reduced forms of actual dynamic proposition of time profiles of prices and demanded quantities? Similar considerations apply to “supply curves” The point here, drawing upon the chapter by Kirman and Dosi, in Dosi (Dosi, Foundations of Complex Evolving Economies Innovation, Organization and Industrial Dynamics, Oxford University Press, 2023), is that the forest of demand and supply curves is basically there to populate the analysis with double axiomatic notions of equilibria, both ‘in the head’ of individual agents, and in environments in which they operate. Supply and demand “curves”, I am arguing, are one of the three major methodological stumbling blocks on the way of progress in economics, the other related ones being ‘utility functions’ and ‘production functions’. There is an alternative: represent markets and industries how they actually works, and model them both via fully fledged Agent Based Models and via lower dimensional dynamical systems.

Data‐driven collusion and competition in a pricing duopoly with multinomial logit demand

We consider dynamic pricing and demand learning in a duopoly with multinomial logit demand, both from the perspective where firms compete against each other and from the perspective where firms aim to collude to increase revenues. We show that joint‐revenue maximization is not always beneficial to both firms compared to the Nash equilibrium, and show that several other axiomatic notions of collusion can be constructed that are always beneficial to both firms and a threat to consumer welfare. Next, we construct a price algorithm and prove that it learns to charge supra‐competitive prices if deployed by both firms, and learns to respond optimally against a class of competitive algorithms. Our algorithm includes a mechanism to infer demand observations from the competitor's price path, so that our algorithm can operate in a setting where prices are public but demand is private information. Our work contributes to the understanding of well‐performing price policies in a competitive multi‐agent setting, and shows that collusion by algorithms is possible and deserves the attention of lawmakers and competition policy regulators.

A robust MADM-approach to recruitment-based pattern recognition by using similarity measures of interval-valued fuzzy hypersoft set

<abstract><p>Interval-valued fuzzy hypersoft set ($ \mathbb{IVFHSS} $) is considered a pertinent fuzzy set-like model that is the combination of an interval-valued fuzzy set and a hypersoft set. It is more flexible and trustworthy for dealing with information-based uncertainties due to the consideration of interval-based hypersoft settings. This kind of setting enables the decision makers to approximate the alternatives in terms of interval-type opinions by considering multiple arguments concurrently. These features make it a fitting model for dealing with uncertain decision-making scenarios like the recruitment process. The vagueness arises in the recruitment process when the data obtained is hesitant. The analogous educational norms among the candidates may increase its complexity. Evaluation techniques focus on leveling hypersoft sets for grading several alternatives based on multi-arguments. When several alternatives have an identical status, such grading systems frequently encounter problems, making it challenging for decision-makers to select the preeminent alternative. This settlement of such an issue is the basis of this article. Thus, in this study, first the axiomatic notions of similarity measures between $ \mathbb{IVFHSS}s $ are characterized, and then their relevant theorem is proved. In order to provide a consistent decision-support framework for the recruitment process, a robust algorithm is proposed. Finally, the effectiveness, feasibility, and efficiency of the proposed model are demonstrated through the depiction of recruitment-based pattern recognition.</p></abstract>

Properties of Statistical Depth with Respect to Compact Convex Random Sets: The Tukey Depth

We study a statistical data depth with respect to compact convex random sets, which is consistent with the multivariate Tukey depth and the Tukey depth for fuzzy sets. In addition, it provides a different perspective to the existing halfspace depth with respect to compact convex random sets. In studying this depth function, we provide a series of properties for the statistical data depth with respect to compact convex random sets. These properties are an adaptation of properties that constitute the axiomatic notions of multivariate, functional, and fuzzy depth-functions and other well-known properties of depth.

A metalanguage for guarded iteration

Notions of guardedness serve to delineate admissible recursive definitions in various settings in a compositional manner. In recent work, we have introduced an axiomatic notion of guardedness in symmetric monoidal categories, which serves as a unifying framework for various examples from program semantics, process algebra, and beyond. In the present paper, we propose a generic metalanguage for guarded iteration based on combining this notion with the fine-grain call-by-value paradigm, which we intend as a unifying programming language for guarded and unguarded iteration in the presence of computational effects. We give a generic (categorical) semantics of this language over a suitable class of strong monads supporting guarded iteration, and show it to be in touch with the standard operational behaviour of iteration by giving a concrete big-step operational semantics for a certain specific instance of the metalanguage and establishing soundness and (computational) adequacy for this case.

Towards a critique on intellectual property

Abstract In order to understand the essence of digital and virtual world relations and their outcomes, as they gain more social relevance in contemporary society, this paper investigates the category of intellectual property not from the prism of the law but rather on philosophical terms. Such philosophical analysis is based on immanent critique. The starting point is the axiomatic notion of modern capitalism, where the categories of property and intellectual property are regarded as two separated entities. Hegel’s philosophy of law enables an important reflection on these two categories since, already in its method, it apprehends the contradictions of bourgeoisie society. Accordingly, contrasting reality and Hegel’s understanding, a conflict arises within the notion of intellectual property and its praxis under the rule of law. The state appears as a necessity to guarantee and mediate an immanent conflict that arises from the privatization of intellectual property. As an insoluble problem that emerges within such praxis, the present analysis offers an alternative to the paradigm of a split between property and intellectual property. Based on Lukács’ non-essentialist-ontology of the social-being, intellectual property is explained through the prisms of labour and cultural development of human thought.

A note on “Similarity and dissimilarity measures between fuzzy sets: A formal relational study” and “Additive similarity and dissimilarity measures”

We revisit the relational study between different axiomatic definitions of similarity and dissimilarity of fuzzy sets developed in two previous articles. We observe that every axiomatic definition admits two variants, depending on whether we assume that the measure fulfills the corresponding properties when we restrict ourselves to a fixed finite cardinal universe, or that it complies with them in a general universe. The results and counterexamples presented in those articles concern the implication relations between different axiomatic notions, and they implicitly consider a general finite universe (whose cardinality is not fixed in advance). Most of them fit both variants, but some others need to be adapted, in order to meet the first option. In this short note, we offer the adapted versions of the corresponding results and counterexamples.

A note on phonological similarity in Tesar’s (2014) theory of output-drivenness

Tesar’s (Output-Driven Phonology: Theory and Learning, Cambridge Studies in Linguistics, 2014) notion of output-drivenness is an attempt at characterizing non-opaque phonological mappings in terms of a notion of phonological similarity between underlying and surface levels. Tesar defines phonological similarity concretely in terms of segment strings and correspondence relations. Magri (2017, Journal of Logic, Language, and Information) instead defines similarity axiomatically through an inequality on faithfulness constraint violations. This paper studies the formal properties of the latter axiomatic notion of similarity. In particular, it shows that Tesar’s concrete definition of similarity satisfies Magri’s axiomatization in terms of faithfulness constraints. The theory of output-drivenness reconstructed in Magri (2017, Journal of Logic, Language, and Information) thus subsumes Tesar’s (Output-Driven Phonology: Theory and Learning, Cambridge Studies in Linguistics, 2014) original theory as a special case.

Convex Spaces, Affine Spaces, and Commutants for Algebraic Theories

Certain axiomatic notions of affine space over a ring and convex space over a preordered ring are examples of the notion of $$\mathscr {T}$$ -algebra for an algebraic theory $$\mathscr {T}$$ in the sense of Lawvere. Herein we study the notion of commutant for Lawvere theories that was defined by Wraith and generalizes the notion of centralizer clone. We focus on the Lawvere theory of left R -affine spaces for a ring or rig R, proving that this theory can be described as a commutant of the theory of pointed right R-modules. Further, we show that for a wide class of rigs R that includes all rings, these theories are commutants of one another in the full finitary theory of R in the category of sets. We define left R -convex spaces for a preordered ring R as left affine spaces over the positive part $$R_+$$ of R. We show that for any firmly archimedean preordered algebra R over the dyadic rationals, the theories of left R-convex spaces and pointed right $$R_+$$ -modules are commutants of one another within the full finitary theory of $$R_+$$ in the category of sets. Applied to the ring of real numbers $$\mathbb {R}$$ , this result shows that the connection between convex spaces and pointed $$\mathbb {R}_+$$ -modules that is implicit in the integral representation of probability measures is a perfect ‘duality’ of algebraic theories.

Homotopy Path Spaces for Families of Admissible Paths

Motivated by the search for universal orbits in geometric control theory and universal topological semigroups over local semigroups in topological groups, particularly Lie groups, we introduce a very general axiomatic notion of "trajectory," namely a topological space equipped with a family of paths satisfying certain properties that make it what we call an "admissible family." Considering one-parameter families of these paths as a homotopy allows us to construct a homotopy path space, our main object of consideration. We identify a distinguished subfamily of admissible paths via what we call a selection or partial selection and show how this insures collapses in the homotopy path space structure. We establish sufficient conditions to identify the homotopy path space as the simply connected covering or as residing in the simply connected covering and point out certain of its universal properties in this setting. We close by applying and illustrating our results in the setting of Lie groups and semigroups.

Martyrdom: An Investigation into Issues of Religious Violence in North Africa

Aims: The paper aims to clarify the relationship of martyrdom between two religious organizational structures, the Donatists and the Catholic Church. It proposes modeling a social transformation process by stressing a homogeneity of martyrdom between these two realms. Study Design: It is a theoretical construct based on historical data. Place and Duration of Study: Although this paper is a modern day text (constructed from December 2012 till November 2014), its literature sources is historical by nature. Religious violence in North Africa dated back to 340 BCE and found its culmination in 429 CE. Methodology: The research is based on a theoretical (desk top) and exploratory study. The data required are complemented by documentary analysis. This study poses a clear database which the author generated and on which he draws. This article is a serious inquiry based on original data and the writings are universal. Results: This paper purports to enervate the polemical views of Catholic sentiments against the Donatists. Two prominent Catholic scholars, Optatus and Augustine have divulged that martyrdom status is only to be afforded to Catholics who have suffered and died for their faith. The outcome Original Research Article Swartz; JSRR, 6(4): 267-275, 2015; Article no.JSRR.2015.152 268 and implications of this paper is that there should be no indication of prejudice and enmity in a literary work and that the researcher should not be afraid to transcend cultural boundaries in search for the truth or to present the view of the “other” objectively. These ideas, in the context of North Africa, where almost all of the historical writings on martyrdom accounts have been produced by Catholic writers, have been challenged. Conclusion: This study stresses the axiomatic notion that to be a martyr one has to suffer and eventually dies for your faith. It is true that both the Donatists and the Catholic Christians were subjected to martyrdom in North Africa and both of them have also conformed to the Gospel requirements for such a status. As such both religious groups can be afforded martyrdom status as per this study. Certain claims, for example by one of these religious sections that they are the “true” Church and the bringing about by the other section the method of exclusion that the other is not Christian, must be regarded as not important. The research wants to dwarf the polemical atmosphere that surrounds these two important groups and wants to elevate the concept of martyrdom they have forged in North Africa.

Hilbert's 6th Problem and Axiomatic Quantum Field Theory

��� 1. The Main Claims This paper has two parts, a historical and a systematic. In the historical part it is argued that the two major axiomatic approaches to relativistic quantum aeld theory, the Wightman and Haag-Kastler axiomatizations, are realizations of the program of axiomatization of physical theories announced by Hilbert in his 6th of the 23 problems discussed in his famous 1900 Paris lecture on open problems in mathematics, if axiomatizing physical theories is interpreted in a soft and opportunistic sense suggested in 1927 by Hilbert, Nordheim, and von Neumann. To show this, Section 2 recalls arst some of Hilbert’s views about the axiomatic approach to physical theories as these were formulated in his 6th problem. It will be seen that Hilbert did not specify in his Paris lecture what precisely the axiomatic approach in physics is supposed to be. It will be seen in Section 3 that he was more explicit in 1927 however: The joint paper (Hilbert et al. 1927) addresses the issue of the axiomatic approach in physics explicitly and embraces a soft notion of axiomatization, which is assumed to be carried out in an opportunistic way only in physics. Axiomatic aeld theories are axiomatizations in this sense. The systematic part of the paper isolates and comments on some characteristic features of the axiomatic quantum aeld theories, elements of which are recalled brieoy in Section 4. The features will be of two types: general-methodological and speciac-physical. The arst category includes what we call here ‘intended non-categoricity” and “large internal room,” discussed in Section 5; the speciac-physical we discuss (in Section 6) are “ontological silence” and “causal completeness.” “Intended Research supported in part by the Hungarian Scientiac Research Found (OTKA). Contract number: 100715

Everyday Politics of (In)formal Marital Dissolution in Cambodia and Indonesia

ABSTRACTPlacing contemporary marriage and its dissolution at its heart, this paper explores rural women's experiences of customary and legal unions in Cambodia and Indonesia. We contend that women's navigation in-between ‘informal’ ethics and morals versus ‘formal’ state-sponsored legal doctrine constitute a form of ‘everyday politics’ that has been unduly neglected. Critiquing the taken-for-granted nature of marriage in academic scholarship, we show how the axiomatic notion that marriage registration is inherently beneficial to women is complicated by the nonlinear and mobile trajectories of conjugality in our two case study communities. In turn, we call for marriage and its breakdown to receive more sustained and nuanced analysis as the primary unit of Southeast Asian life.

Environment and classical channels in categorical quantum mechanics

We present a both simple and comprehensive graphical calculus for quantum computing. In particular, we axiomatize the notion of an environment, which together with the earlier introduced axiomatic notion of classical structure enables us to define classical channels, quantum measurements and classical control. If we moreover adjoin the earlier introduced axiomatic notion of complementarity, we obtain sufficient structural power for constructive representation and correctness derivation of typical quantum informatic protocols.

Queer Histories and the Global City

This essay reviews three books that center on the globalized city as a key site for unpacking disparate queer cultures. Two of the books discussed make an explicit effort to deterritorialize queer historiography outside the global North. They focus on the everyday experiences of postcolonial subjects in Cape Town and Hong Kong. In a moment of intensified counterterrorism, necropolitical nationalism, and resurgent yet covert forms of empire, both works have much to say about how the lives of sexual minorities are simultaneously affected by and resist Western imperialism. Thus they also enter into an already ongoing debate in contemporary queer studies that challenges the normalization of queer politics as a product of expanding capital both locally and abroad. All three books trace the shifting forms of the nation-state and how it affects the lived experiences of queer populations in the city. In the process, they collectively refuse the seemingly axiomatic notion that queer subjects are always being homogenized by transnational capital and neoliberal cosmopolitanism. Rather, as Andrew Tucker suggests, the hybrid queer cultures present in the city demand a more nuanced understanding of how these communities are shaped by historically, geographically, and politically specific national and cosmopolitan ideals.

Lax algebra meets topology

We combine two research directions of the past decade, namely the development of a lax-algebraic framework for categories of interest to topologists and analysts, and the exploration of key topological concepts, like separation and compactness, in an abstract category which comes equipped with an axiomatic notion of “closed” or “proper” map. Hence, we present various candidates for such notions in the context of the category of (T,V)-categories, with a Set-monad T=(T,e,m) laxly extended to the category of sets and V-valued relations, for a quantale V. Suitable categories of ordered sets, metric spaces, topological spaces, closure spaces, and approach spaces all fit into this framework and allow for applications of the the general theory.

What is the axiomatic method?

The modern notion of the axiomatic method developed as a part of the conceptualization of mathematics starting in the nineteenth century. The basic idea of the method is the capture of a class of structures as the models of an axiomatic system. The mathematical study of such classes of structures is not exhausted by the derivation of theorems from the axioms but includes normally the metatheory of the axiom system. This conception of axiomatization satisfies the crucial requirement that the derivation of theorems from axioms does not produce new information in the usual sense of the term called depth information. It can produce new information in a different sense of information called surface information. It is argued in this paper that the derivation should be based on a model-theoretical relation of logical consequence rather than derivability by means of mechanical (recursive) rules. Likewise completeness must be understood by reference to a model-theoretical consequence relation. A correctly understood notion of axiomatization does not apply to purely logical theories. In the latter the only relevant kind of axiomatization amounts to recursive enumeration of logical truths. First-order “axiomatic” set theories are not genuine axiomatizations. The main reason is that their models are structures of particulars, not of sets. Axiomatization cannot usually be motivated epistemologically, but it is related to the idea of explanation.

The International Criminal Court and the Foreign Policies of the United States

ON 6 MAY 2002, AMERICAN PRESIDENT George W. Bush withdrew the United States' signature from the Rome statute of the International Criminal Court (ICC). Three months later, Bush signed the American Servicemembers' Protection Act (ASPA) into law. The ASPA prohibits the United States from cooperating with the ICC and authorizes the president to use all means necessary to free American personnel imprisoned in by the ICC in The Hague. In addition, the ASPA withholds military aid to certain states party to the Rome statute and mandates that the United States negotiate impunity agreements with states party to ensure that American personnel do not fall under the jurisdiction of the ICC when operating on their territory.Given these and other measures, it has become commonplace for members of the international community to accuse the United States of intransigence towards the progress of international criminal law. Indeed, in light of the fact that it played a pivotal role in establishingPhilippe Lagasse is a doctoral student in the department of political science at Carleton University and the recipient of a Canada Graduate Scholarship. The author thanks Joel J. Sokolsky and Norman Hillmer for commenting on drafts of this article. the Nuremberg trials, the Helsinki Accords and the International Criminal Tribunal for the former Yugoslavia (ICTY), it appears that the US is reneging on the principles of international justice it previously championed. Were American foreign policy a consistent enterprise, such an estimation would have merit. What is often overlooked in commentaries on America's troubled relationship with the ICC is the ongoing internal debate within the American foreign policy elite about the worth and significance of the Rome statute. An examination of this debate shows that the United States is a nation of multiple foreign policy traditions, each competing to direct American statecraft. Seen from this vantage point, it is not simply an American debate about a particular treaty or even the pursuit of international justice. Rather, it is an example of fundamental differences within Washington about how the United States relates to the world.This article aims to place the American ICC debate in the context of these various foreign policy traditions. It begins with an overview of the foreign policy traditions identified by Walter McDougall in Promised Land, Crusader State.(1) It is argued that the American ICC debate is waged in the traditions of exceptionalism, unilateralism and Wilsonianism. Next, the article examines how each of these traditions views and has shaped American policy towards the Rome statute. The argument presented is that the United States' ambivalent relationship with international criminal law and the ICC results from not from hypocrisy or self-service, but from the essential philosophical divisions that exist in America's foreign policy traditions.MCDOUGALL'S TRADITIONSAmerica's first foreign policy tradition, exceptionalism, is defined by two principles. First and foremost is the axiomatic notion held by the American founders that their new country was destined to be different and better than others. Yet the uniqueness of the United States in no way implied that Americans were to be saviours. On the contrary, the creed of American exceptionalism is [l]iberty at home, period. Indeed, the aim of American exceptionalism is to protect the republic's foundational vision from alien infringements. Accordingly, the second principle of exceptionalism is an avoidance of the insidious wiles of foreign influence.A derivative of exceptionalism, the unilateralist tradition, compels the United States to act alone in defence of its liberties and national interests. Often confused with isolationism when it has manifested itself in American foreign policy, unilateralism is not equivalent to disinterest in international politics. Instead, unilateralism demands only that the United States be free of entangling alliances. …

Artaud's Jet de Sang: a Critical Post-Production Analysis

Artaud's Jet de Sang is a text of merely eight pages, published in 1925. This work has acquired a reputation of being ‘unperformable’, partly because of the ‘impossible’ scenic actions asked for in the stage directions (e.g. ‘two stars crash into each other, and we see a number of live pieces of human bodies falling down: hands, feet, scalps… with a maddening, vomit-inducing slowness’), partly because the only professional production, by Peter Brook in the London Season of Cruelty in 1964, was judged to have been a total flop (Hunt & Reeve 77). Over the past ten years, I have scrutinized this text time and time again, related it to the theatrical ideas Artaud was professing in the 1920s, and have never quite understood why the play should be considered unperformable. It is a challenging text, yes, but when not interpreted literally it could act as a springboard for an exploration of Artaud's mind and of our own responses to the topics addressed in the play. A group of students with whom I had worked before on a Dada project convinced me that a production of Jet de Sang, despite its reputation, could be contemplated. Nevertheless, at our first group meeting I expressed the view that the alliance between Surrealism and the theatre profession had been a failure in the past and that it was unlikely to succeed today without compromising either the fundamental intentions behind Surrealist art or the no less axiomatic notions of ‘quality’ in our contemporary theatre world. To explore Artaud's concept of Surrealist theatre would by necessity force us into taking a decision on whether to be faithful to Artaud's ideas or to produce ‘théâtre-bien-fait’.