We develop a Priestley-style duality theory for different classes of algebras having a bilattice reduct. A similar investigation has already been realized by B. Mobasher, D. Pigozzi, G. Slutzki and G. Voutsadakis, but only from an abstract category-theoretic point of view. In the present work we are instead interested in a concrete study of the topological spaces that correspond to bilattices and some related algebras that are obtained through expansions of the algebraic language.

A ‘duality’ is a formal mapping between the spaces of solutions of two empirically equivalent theories. In recent times, dualities have been found to be pervasive in string theory and quantum field theory. Naïvely interpreted, duality-related theories appear to make very different ontological claims about the world—differing in e.g. space-time structure, fundamental ontology, and mereological structure. In light of this, duality-related theories raise questions familiar from discussions of underdetermination in the philosophy of science: in the (...) presence of dual theories, what is one to say about the ontology of the world? In this paper, we undertake a comprehensive and non-technical survey of the landscape of possible ontological interpretations of duality-related theories. We provide a significantly enriched and clarified taxonomy of options—several of which are novel to the literature. (shrink)

Článek se snaží přiblížit přístup Josepha Priestleyho ke zkoumání lidské mysli. Postupně jsou ukázány dva kroky, ve kterých Priestley mění svůj pohled na hmotu a ducha a dochází k materialismu. V prvním kroku redefinuje pojem hmoty a přisuzuje hmotě zcela nové vlastnosti – síly přitahování a odpuzování. V druhém kroku pomocí těchto nových vlastností vysvětluje schopnost vnímání a myšlení. V těchto krocích navíc využívá poznatky tehdejší přírodní filosofie, zejména mechaniky. Člověk a jeho mysl jsou podle Priestleyho součástí přírody. To (...) znamená, že člověk a lidská mysl jsou určitým mechanismem, který pracuje podle přírodních zákonů a lze jej pomocí těchto zákonů také vysvětlit. (shrink)

The mature materialism of Joseph Priestley's Disquisitions relating to Matter and Spirit of 1777 is based on three main arguments: that Newton's widely-accepted scientific methodology requires the rejection of the 'hypothesis' of the soul; that a dynamic theory of matter breaks down the active/passive dichotomy assumed by many dualists; and that interaction between matter and spirit is impossible. In Matter and Spirit it is the first two arguments which are given greatest prominence; but it is the third argument (...) which first brought Priestley to take materialism seriously. It was an argument which had persistently troubled him in his dualist years, but it was not until 1774 in the Examination that he 'first entertained a serious doubt of the truth of the vulgar hypothesis'. Underlying this fact is an episode of some complexity which this article examines. (shrink)

Joseph Priestley was a man of many and varied intellectual interests. This thesis surveys his philosophical thought, with a central focus on his philosophical theology. The subject can be divided into two parts, natural theology and moral theology. Priestley's natural theology is a perhaps unique attempt to combine and harmonize materialism, determinism and theism, under the auspices of Newtonian methodology. His materialism is based on three arguments: that interaction between matter and spirit is impossible; that a dynamic (...) class='Hi'>theory of matter breaks down the active/passive dichotomy assumed by many dualists; and that Newton's "Rules of Reasoning in Philosophy" require the rejection of the "hypothesis" of the soul. His determinism arises from his theory of causation. He attempts to show that the only acceptable account of causation is one in which every cause is invariably followed by the same effect, and that libertarianism violates this central assumption of scientific thought. His theism rests on the Argument from Design. He defends the Argument by trying to show that none of the alternatives to Design advanced in Hume's Dialogues concerning Natural Religion constitute a plausible scientific hypothesis. His critics accused his synthesis of materialism, determinism and theism of leading to atheism or pantheism. His defence against these charges is that his system is essentially theistic, and that its ontology is determined by the Argument from Design. Priestley's moral theology is also in part a response to Hume's Dialogues. He offers a number of replies to the "problem of evil". Evil and adversity heighten our appreciation of good; they are a consequence of the finitude of the creation; they follow from the desirability of having a world governed by general laws; and they make possible the achievement of moral character. Character-formation is his main defence, and his methodology requires him to show that adversity leads more often than not to positive results. This requirement is embodied in his progressivist philosophy of history. History, he holds, exhibits temporal purpose and Design, just as nature exhibits atemporal purpose and Design. Priestley's political thought can be seen as arising from his moral theology, mediated by the notions of "luxury", which he regards as morally harmless, and "idleness", which is the main source of moral evil. His combination of liberalism and radicalism is examined both for internal consistency and as a response to the events of his day, ending with the French Revolution. Priestley is interesting partly for his unorthodoxy, partly for the inter-connectedness of his diverse concerns, and partly because he debated with distinguished contemporaries. Throughout the thesis his views are juxtaposed with those of Hume, Reid, Price, Boscovich, Burke and a number of other thinkers. (shrink)

There is a fundamental subsets–partitions duality that runs through the exact sciences. In more concrete terms, it is the duality between elements of a subset and the distinctions of a partition. In more abstract terms, it is the reverse-the-arrows of category theory that provides a major architectonic of mathematics. The paper first develops the duality between the Boolean logic of subsets and the logic of partitions. Then, probability theory and information theory (as based on (...) logical entropy) are shown to start with the quantitative versions of subsets and partitions. Some basic universal mapping properties in the category of Sets are developed that precede the abstract duality of category theory. But by far the main application is to the clarification and interpretation of quantum mechanics. Since classical mechanics illustrates the Boolean worldview of full distinctness, it is natural that quantum mechanics would be based on the indefiniteness of its characteristic superposition states, which is modeled at the set level by partitions (or equivalence relations). This approach to interpreting quantum mechanics is not a jury-rigged or ad hoc attempt at the interpretation of quantum mechanics but is a natural application of the fundamental duality running throughout the exact sciences. (shrink)

In this essay, we consider the formal and ontological implications of one specific and intensely contested dialectical context from which Deleuze’s thinking about structural ideal genesis visibly arises. This is the formal/ontological dualism between the principles, ἀρχαί, of the One (ἕν) and the Indefinite/Unlimited Dyad (ἀόριστος δυάς), which is arguably the culminating achievement of the later Plato’s development of a mathematical dialectic.3 Following commentators including Lautman, Oskar Becker, and Kenneth M. Sayre, we argue that the duality of the One (...) and the Indefinite Dyad provides, in the later Plato, a unitary theoretical formalism accounting, by means of an iterated mixing without synthesis, for the structural origin and genesis of both supersensible Ideas and the sensible particulars which participate in them. As these commentators also argue, this duality furthermore provides a maximally general answer to the problem of temporal becoming that runs through Plato’s corpus: that of the relationship of the flux of sensory experiences to the fixity and order of what is thinkable in itself. Additionally, it provides a basis for understanding some of the famously puzzling claims about forms, numbers, and the principled genesis of both attributed to Plato by Aristotle in the Metaphysics, and plausibly underlies the late Plato’s deep considerations of the structural paradoxes of temporal change and becoming in the Parmenides, the Sophist, and the Philebus. After extracting this structure of duality and developing some of its formal, ontological, and metalogical features, we consider some of its specific implications for a thinking of time and ideality that follows Deleuze in a formally unitary genetic understanding of structural difference. These implications of Plato’s duality include not only those of the constitution of specific theoretical domains and problematics, but also implicate the reflexive problematic of the ideal determinants of the form of a unitary theory as such. We argue that the consequences of the underlying duality on the level of content are ultimately such as to raise, on the level of form, the broader reflexive problem of the basis for its own formal or meta-theoretical employment. We conclude by arguing for the decisive and substantive presence of a proper “Platonism” of the Idea in Deleuze, and weighing the potential for a substantive recuperation of Plato’s duality in the context of a dialectical affirmation of what Deleuze recognizes as the “only” ontological proposition that has ever been uttered. This is the proposition of the univocity of Being, whereby “being is said in the same sense, everywhere and always,” but is said (both problematically and decisively) of difference itself. (shrink)

Recent developments in pure mathematics and in mathematical logic have uncovered a fundamental duality between "existence" and "information." In logic, the duality is between the Boolean logic of subsets and the logic of quotient sets, equivalence relations, or partitions. The analogue to an element of a subset is the notion of a distinction of a partition, and that leads to a whole stream of dualities or analogies--including the development of new logical foundations for information theory parallel to (...) Boole's development of logical finite probability theory. After outlining these dual concepts in mathematical terms, we turn to a more metaphysical speculation about two dual notions of reality, a fully definite notion using Boolean logic and appropriate for classical physics, and the other objectively indefinite notion using partition logic which turns out to be appropriate for quantum mechanics. The existence-information duality is used to intuitively illustrate these two dual notions of reality. The elucidation of the objectively indefinite notion of reality leads to the "killer application" of the existence-information duality, namely the interpretation of quantum mechanics. (shrink)

Many results in logic and mathematics rely on techniques that allow for concrete, often visual, representations of abstract concepts. A primary example of this phenomenon in logic is the distinction between syntax and semantics, itself an example of the more general duality in mathematics between algebra and geometry. Such representations, however, often rely on the existence of certain maximal objects having particular properties such as points, possible worlds or Tarskian first-order structures. -/- This dissertation explores an alternative to such (...) representations known as possibility semantics. Its core idea is to replace maximal objects with ordered systems of partial approximations. Although it originates in the semantics of modal logic and the representation of abstract ordered structures, I argue that it has far-reaching mathematical, foundational and philosophical significance, especially in the context of semiconstructive mathematics, a foundational framework that does not assume any fragment of the Axiom of Choice beyond the Axiom of Dependent Choices. -/- The dissertation is divided in two main parts. The first part explores various applications of the mathematical framework underlying possibility semantics to lattice theory and non-classical propositional logics. A major theme is the development of constructive dualities for various categories of lattices, which are related to standard non-constructive dualities via Vietoris constructions. -/- The second part of the dissertation explores the alternative foundational setting of semi-constructive mathematics, focusing on three applications of possibility semantics for classical first-order logic to the philosophy of the mathematical infinite. In particular, we introduce generic powers, a semi-constructive analogue of ultrapowers in classical model theory, and we explore the merits of these structures from a foundational, conceptual and historical viewpoint. (shrink)

This paper introduces the category of b-frames as a new tool in the study of complete lattices. B-frames can be seen as a generalization of posets, which play an important role in the representation theory of Heyting algebras, but also in the study of complete Boolean algebras in forcing. This paper combines ideas from the two traditions in order to generalize some techniques and results to the wider context of complete lattices. In particular, we lift a representation theorem of (...) Allwein and MacCaull to a duality between complete lattices and b-frames, and we derive alternative characterizations of several classes of complete lattices from this duality. This framework is then used to obtain new results in the theory of complete Heyting algebras and the semantics of intuitionistic propositional logic. (shrink)

This theory is an attempt to describe the universal phenomena like space, time, matter and energy as an inter-relationship bound by a newly discovered force named as the universal force. The universal force is shown to be the force of gravitation, electricity, magnetism, strong nuclear and weak nuclear forces. I believe any other force, hitherto fore not discovered; also, can be explained in terms of this universal force. Liberal use of wave-particle duality, relativity, quantum concepts is made to (...) achieve a harmonious and comprehensive synthesis of all the existing beliefs in physics into a new theory with some new concepts added here and there. While adding new concepts, enormous care has been taken to ensure that the existing beliefs are not contradicted. Moreover, the new concepts are proved to be correct theoretically by deriving the constants like G, σ, etc. (shrink)

One of the most important theories in linear programming is the dualistic theory and its basic idea is that for every linear model has dual linear model, so that solving the original linear model gives a solution to the dual model. Therefore, when we solving the linear programming model, we actually obtain solutions for two linear models. In this research, we present a study of the models. The neutrosophic dual and the binary simplex algorithm, which works to find the (...) optimal solution for the original and dual models at the same time. The importance of this algorithm is evident in that it is relied upon in several operations research topics, such as integer programming algorithms, some nonlinear programming algorithms, and sensitivity analysis in linear programming. (shrink)

Both for Kant and for Nietzsche, aesthetics must not be considered as a systematic science based merely on logical premises but rather as a set of intuitively attained artistic ideas that constitute or reconstitute the sensible perceptions and supersensible representations into a new whole. Kantian and Nietzschean aesthetics are both aiming to see beyond the forms of objects to provide explanations for the nobility and sublimity of human art and life. We can safely say that Kant and Nietzsche used the (...) dualities of the beautiful/sublime and Apollonian/Dionysian to advocate their general philosophical worldview, and that the initial formation (in Observations and The Birth of Tragedy) and final dissolution (in the Critique of Judgment and Zarathustra and other later works) of these dualities are determined by the gradually established telos of their philosophical endeavor. Therefore, by observing the evolution of these so-called dualities, Kaplama gathers important clues as to how Kant’s and Nietzsche’s aesthetics transformed into different ways to affirm human art and life. On the one hand, Kaplama argues, the Dionysian came to be the heart and soul of Nietzschean aesthetics and ethics, and the Apollonian (or the formal drive of individuation) was reduced into a mere aesthetic criterion. On the other, Kant treats the sublime (which is originally an idea-producing feeling and/or judgment) as a mere appendix to his Critique of Judgment and aesthetic theory teleologically reducing it into its possible moral consequences. This is why Schopenhauer calls the sublime “by far the most excellent thing in the Critique of Judgment” which touches on the real problem of aesthetics very closely but does not provide a real solution for it. Kant’s forced teleological move is to make his theory of aesthetic judgment stand as a ‘reaffirmation’ of the earlier ethical justification he believed to have accomplished in the first two Critiques and the Groundwork where he defends an affirmation of human life through a teleological morality centered on the principle of free-will. In contrast, Nietzsche’s aesthetics (particularly the Dionysian) guides his ethics and metaphysics again through defining an ideal human nature without which ethos would be static and meaningless, lacking the ability to move and change and represent the tragic pathos of human life. (shrink)

This paper presents a unified theory of reality, which integrates two interdependent frameworks: Cellular Primary Consciousness Theory (CPCT) and Open and Closed Systems Theory (OCST). Although CPCT and OCST can each stand as individual theories, they are, in this work, combined to form a cohesive explanation of both the mechanics and purpose of the universe. CPCT posits that consciousness is a fundamental aspect of all life, extending to even the simplest cells, rather than being an emergent property (...) exclusive to complex neural systems. Drawing upon evidence from quantum mechanics, cell biology, and systems theory, CPCT challenges traditional views on the origins of consciousness by suggesting that awareness is a universal property present from the cellular level. OCST, which forms the second component of this unified theory, examines the nature of the universe as a closed system subject to the laws of entropy. This theory explores how the universe is moving toward maximum entropy, where meaning and contrasts dissolve. However, beyond this closed system lies the realm of an open system—a domain of infinite potential that transcends the dualities and limitations of the physical universe. This open system offers a philosophical explanation for existence and the possibility of eternal meaning. Together, these two theories provide a novel and cohesive framework that addresses both the mechanics of consciousness and the ultimate purpose of the universe. The integration of CPCT and OCST bridges scientific evidence from quantum biology and systems theory with philosophical explorations of existence, presenting a comprehensive vision of reality as both a closed physical system and an open metaphysical one. This unified theory encourages a reexamination of our place in the cosmos, suggesting that beyond the observable universe lies an infinite realm of potential where consciousness and meaning endure. (shrink)

The naive idea of a mimesis between theory and experiments, a concept still lasing in many epistemologies, is here substituted by a more sophisticated mathematical methexis where theoretical physics is a system of production of formal structures under strong mathematical constraints, such as global and local symmetries. Instead of an ultimate “everything theory”, the image of physical theories here proposed is a totality of interconnected structures establishing the very conditions of its “thinkability” and the relations with the experimental (...) domain. (shrink)

Nous proposons dans cet article une caractérisation, à notre connaissance, nouvelle, d’une distorsion cognitive : la requalification dans le même pôle. Une telle caractérisation prend place au sein du modèle général des distorsions cognitives (Franceschi, 2007). Nous commençons par définir un modèle étendu des distorsions cognitives, intégrant les éléments du cadre conceptuel des matrices de concepts (Franceschi, 2002), afin de permettre une définition élargie du système de taxons. Nous nous attachons ensuite à définir la requalification dans le même pôle et (...) à la distinguer d’une distorsion cognitive voisine : la requalification dans l’autre pôle. (shrink)

In a previous paper (Compléments pour une théorie des distorsions cognitives, Journal de Thérapie Comportementale et Cognitive, 2007), we introduced some elements aimed at contributing to a general theory of cognitive distortions. Based on the reference class, the duality and the system of taxa, these elements allow to define the general cognitive distortions as well as the specific cognitive distortions. This model is extended here to the description of two other classical cognitive distortions: over-generalization and mislabeling. The definition (...) of the two latter cognitive distortions is based on preliminary distinction between three levels of reasoning: primary, secondary and ternary pathogenic arguments. The latter analysis also leads to define two other cognitive distortions which insert themselves into this framework: ill-grounded inductive projection and confirmation bias. (shrink)

In a previous paper (Compléments pour une théorie des distorsions cognitives, Journal de Thérapie Comportementale et Cognitive, 2007), we did present some elements aimed at contributing to a general theory of cognitive distortions. Based on the reference class, the duality and the system of taxa, these elements led to distinguish between the general cognitive distortions (dichotomous reasoning, disqualification of one pole, minimization, maximization) and the specific cognitive distortions (disqualifying the positive, selective abstraction, catastrophism). By also distinguishing between three (...) levels of reasoning – the instantiation stage, the interpretation stage and the generalization stage – we did also define two other cognitive distortions: over-generalization and mislabeling (Théorie des distorsions cognitives : la sur-généralisation et l'étiquetage, Journal de Thérapie Comportementale et Cognitive, 2009). We currently extend this model to another classical cognitive distortion: personalization. (shrink)

In a previous paper (Compléments pour une théorie des distorsions cognitives, Journal de Thérapie Comportementale et Cognitive, 2007), we did present some elements aimed at contributing to a general theory of cognitive distortions. The latter elements, based on the reference class, the duality and the system of taxa, are applied here to generalised anxiety disorder. This allows to describe, on the one hand, the specific distortions related to generalised anxiety disorder, consistently with recent work emphasising the role played (...) by uncertain situations with regard to future events. On the second hand, these elements allow to define one type of structured reasoning, of inductive nature, which contributes to the formation and maintenance of anxious ideas. (shrink)

Can the theory that reality is a simulation be tested? We investigate this question based on the assumption that if the system performing the simulation is nite (i.e. has limited resources), then to achieve low computational complexity, such a system would, as in a video game, render content (reality) only at the moment that information becomes available for observation by a player and not at the moment of detection by a machine (that would be part of the simulation and (...) whose detection would also be part of the internal computation performed by the Virtual Reality server before rendering content to the player). Guided by this principle we describe conceptual wave/particle duality experiments aimed at testing the simulation theory. (shrink)

This article proposes a way of doing type theory informally, assuming a cubical style of reasoning. It can thus be viewed as a first step toward a cubical alternative to the program of informalization of type theory carried out in the homotopy type theory book for dependent type theory augmented with axioms for univalence and higher inductive types. We adopt a cartesian cubical type theory proposed by Angiuli, Brunerie, Coquand, Favonia, Harper, and Licata as the (...) implicit foundation, confining our presentation to elementary results such as function extensionality, the derivation of weak connections and path induction, the groupoid structure of types, and the Eckmman–Hilton duality. (shrink)

The early history of string theory is marked by a shift from strong interaction physics to quantum gravity. The first string models and associated theoretical framework were formulated in the late 1960s and early 1970s in the context of the S-matrix program for the strong interactions. In the mid-1970s, the models were reinterpreted as a potential theory unifying the four fundamental forces. This paper provides a historical analysis of how string theory was developed out of S-matrix physics, (...) aiming to clarify how modern string theory, as a theory detached from experimental data, grew out of an S-matrix program that was strongly dependent upon observable quantities. Surprisingly, the theoretical practice of physicists already turned away from experiment before string theory was recast as a potential unified quantum gravity theory. With the formulation of dual resonance models (the “hadronic string theory”), physicists were able to determine almost all of the models' parameters on the basis of theoretical reasoning. It was this commitment to “non-arbitrariness”, i.e., a lack of free parameters in the theory, that initially drove string theorists away from experimental input, and not the practical inaccessibility of experimental data in the context of quantum gravity physics. This is an important observation when assessing the role of experimental data in string theory. (shrink)

The purpose of this paper is to show that the dual notions of elements & distinctions are the basic analytical concepts needed to unpack and analyze morphisms, duality, and universal constructions in the Sets, the category of sets and functions. The analysis extends directly to other concrete categories (groups, rings, vector spaces, etc.) where the objects are sets with a certain type of structure and the morphisms are functions that preserve that structure. Then the elements & distinctions-based definitions can (...) be abstracted in purely arrow-theoretic way for abstract category theory. In short, the language of elements & distinctions is the conceptual language in which the category of sets is written, and abstract category theory gives the abstract arrows version of those definitions. (shrink)

Now we live in the age of professionalism, and the public office in any nation is some reservoir of intelligent competition in their specific field. They are the leaders and paragon of community as a loyal and professional fiduciary. A hybrid nature of officers creates the rules and exercises their professional knowledge to serve a public good. The not unusual word,“scholar practitioner” may reflect the tendency of learning community within the business and government officers. They wish to overcome a bum (...) rap, say, most unproductive group or bureaucrats in maze, attributed to the bureaucrats generally. They now are required to be not only a manager but also professional researcher for his or her specific field of expertise. Beyond this duality, they may face with the challenge from a serious question about the tenet or theory within either a managerial responsibility or any research responsibility in the discipline of public policy. This paper begins with the classic loci for the theories and tenets, which have interacted with the research and professional circle. Then the author illustrates one hypothetical ego, who now works for the Korean government. In pursuit of his work role,he is situated to ramble encompassing the tenet, theories, and assumption of public policy discipline. The paper suggests three theories considered most foundational in the context of Korean politics and history at modern times, which would possibly be applicable to many other similar nations in the post colonial period. The author argues that it could be exemplary for the policy makers or administrators, who have to learn and research. (shrink)

Quantum mechanics is a fundamental theory in physics that describes the behavior of subatomic particles and systems at very small scales. Unlike classical theories, quantum mechanics introduces elements of indeterminism in the description of physical phenomena. There are fundamental limits to the precision with which certain physical properties, such as the position and momentum of a particle, can be measured simultaneously. This implies that, even if all the initial conditions of a quantum system are known, its future behavior cannot (...) be predicted with absolute certainty. -/- This quantum indeterminacy raises philosophical questions about determinism and free will, as well as their relationship to morality. Determinism holds that all actions and events are predetermined by prior causes, which challenges the traditional notion of moral responsibility based on control and predictability. In contrast, indeterminism posits that there are elements of randomness and variability in the workings of the universe. -/- From a moral and philosophical point of view, the presence of indeterminism in quantum mechanics poses challenges to the attribution of moral responsibility. If our actions are influenced by random events, how can we be morally responsible for them? (shrink)

From the comparison of the Grundrisse (1857-58) manuscripts with Marx's subsequent writings, it is clear that the so-called « deduction » of fundamental economic categories follows two distinctive patterns, one of which is close to ordinary logical analysis, the other being inspired by Hegel's dialectics of essence. This duality is reflected in the double meaning of the concept of « presupposition » (Voraussetzung) and, finally, in the simultaneous endorsement by the Grundrisse of two labour-value theories, one of which is (...) Smithian-like, the other is Ricardian. Marx's reinterpretation of economic value as an « immanent measure », i.e., his claim that commodities are measured by each other when exchange takes place, should help to bridge the gap between the two theories. However, such reinterpretation is shown to be inadequate ; as a result, Marx's account of value should be seen as internally inconsistent. (shrink)

The mistake of quantum physics relying on classical physics with its concept of reality confined to mas and space. The mistake of viewing the photon as a particle. The mistake of ignoring the latent identities of entities.

In his book “Galileo’s Error”, Philip Goff lays out what he calls “foundations for a new science of consciousness”, which are decidedly anti-physicalist (panpsychist), motivated by a critique of Galileo’s distinction into knowable objective and unknowable subjective properties and Arthur Eddington’s argument for the limitation of purely structural (physical) knowledge. Here we outline an alternative theory, premised on the Interface Theory of Perception, that too subscribes to a “post-Galilean” research programme. However, interface theorists disagree along several lines. 1. (...) They note that Galileo’s distinction should be replaced by a truly non-dual account, referring to a difference of degree only. 2. They highly appreciate the role of mathematics, in particular when it comes to actually engage scientifically with consciousness. Some notable features of the interface theory are its skepticism towards our epistemic capacities and its rejection of the existence of a public, mind-independent reality. In addition, some interface theorists further employ a thin concept of “conscious agency” to ground their theory. The interface theory leaves open many of the problems of consciousness science (e.g. what is a “self”?) as questions for further (scientific, mathematical) research. (shrink)

There is a shortage of clergy, at least in the Roman Catholic Church. Protestant churches in general are experiencing more of a distribution or placement challenge than a shortage. The two greatest hindrances to addressing the Protestant clergy distribution challenge are a lack of adequate compensation for clergy and the undesirable geographical location of a number of churches, as perceived by clergy. Influences such as secularisation, duality of vocation, time management, change in type of ministry, family issues, congregational and (...) denominational conflict, burnout, sexual misconduct, divorce or marital problems, and suicide, affect clergy. Studies on the shortage of clergy have been conducted mostly in the USA and Europe and not in South Africa. This article focuses on the research gap by means of a practical theological grounded theory exploration of the exodus of clergy. Grounded theory methodology is used to identify the reasons why clergy trained at a Bible college of a Protestant charismatic mega church leave full-time pastoral ministry. Findings correspond to previous studies with two reasons appearing more frequently than others: responding to a call and leadership related issues. Firstly, respondents differed in their replies with respect to reconciling their exit from full-time pastoral ministry with their call. The replies included not being called, a dual call, or called but left anyway. Secondly, respondents indicated that leadership influence was mostly negative with regard to affirming their call. (shrink)

An endomorphism on an algebra \ is said to be strong if it is compatible with every congruence on \; and \ is said to have the strong endomorphism kernel property if every congruence on \, other than the universal congruence, is the kernel of a strong endomorphism on \. Here we characterise the structure of those double MS-algebras that have this property by the way of Priestley duality.

This dissertation concerns the active role of the organism in evolutionary theory. In particular, it concerns how our conception of the relationship between organism and environment, and the nature of natural selection, influences the causal and explanatory role of organismic activity and behavior in evolutionary explanations. The overarching aim is to argue that the behaviors and activities of organisms can serve both as the explananda (that which is explained) and the explanantia (that which explains) in evolutionary explanations. I attempt (...) to achieve this aim by offering three central arguments. First, that the organism-environment relation is the ontologically basic unit of biology. A common way of conceiving the relationship between organism and environment is as a duality—as two causally independent systems that overlap through interaction. I think this is a mistake. There cannot be organisms without environments and vice versa. They are codependent and codetermined. Second, that natural selection is an ecological process. By this I mean that natural selection acts primarily on organism-environment interactions. It is only in virtue of organisms interacting with their environments that there can be fitness differences amongst individual organisms in a population. The ecological approach to natural selection also entails that the nature of the system(s) of inheritance involved in the reoccurrence of favorable organism-environment interactions is, in principle, immaterial to the process of selection. It only matters for selection that organism-environment interactions actually do reoccur in subsequent generations. Third, that niche construction theory—the most well-developed theoretical and conceptual framework for studying how the activities of organisms influences evolutionary dynamics—can be seen as fully a compatible and integrated part of evolutionary theory. Together, these three arguments constitute an overarching argument. Namely that we both can, and should, take organismic activity and behavior to be crucial explanatory elements in evolutionary theory. Throughout the dissertation I also show how these three arguments have consequences for other debates in the philosophy of evolutionary theory, such as the nature of evolutionary processes, the structure of selection-based explanations, the validity and utility of the proximate-ultimate distinction, and the nature of teleology in evolutionary systems. (shrink)

Entanglement is one of the most striking features of quantum mechanics, and yet it is not specifically quantum. More specific to quantum mechanics is the connection between entanglement and thermodynamics, which leads to an identification between entropies and measures of pure state entanglement. Here we search for the roots of this connection, investigating the relation between entanglement and thermodynamics in the framework of general probabilistic theories. We first address the question whether an entangled state can be transformed into another by (...) means of local operations and classical communication. Under two operational requirements, we prove a general version of the Lo-Popescu theorem, which lies at the foundations of the theory of pure-state entanglement. We then consider a resource theory of purity where free operations are random reversible transformations, modelling the scenario where an agent has limited control over the dynamics of a closed system. Our key result is a duality between the resource theory of entanglement and the resource theory of purity, valid for every physical theory where all processes arise from pure states and reversible interactions at the fundamental level. As an application of the main result, we establish a one-to-one correspondence between entropies and measures of pure bipartite entanglement and exploit it to define entanglement measures in the general probabilistic framework. In addition, we show a duality between the task of information erasure and the task of entanglement generation, whereby the existence of entropy sinks (systems that can absorb arbitrary amounts of information) becomes equivalent to the existence of entanglement sources (correlated systems from which arbitrary amounts of entanglement can be extracted). (shrink)

What is the boundary between the animate and inanimate world? It is obvious that the animate world is under rules of inanimate world. Is the converse true? This paper is aimed at imposing the well-known Darwin's theory of evolution to inanimate world of atomic realm where bizarre behavior of electron challenges our everyday perception of inanimate world. This paper, suggests a weird, peculiar and highly elegant speculation of existing, leads suspicious about validity of the law of conservation of mass, (...) provides conceptual foundation for many odd explanations of quantum mechanics such wave-particle duality of elementary particles, the inherent randomness and probabilistic nature of world as quantum mechanics states, the Louis de Broglie proposition of wave-like behavior of moving particles, Schrödinger's wave function description of probability of finding electron at any location around the nucleus and even the roots of causality. It defines existence as follows: "All the elementary particles emerge spontaneously and randomly in space where the possibility of conforming the physical laws is higher and after appearing if they not conform the laws of physics, they vanish." It proposes, the emerging from nothing, as a natural process and in other word there is an inherent urge to existence not only for animate world but also for inanimate world. Assuming the correctness of the proposed speculation, leads to dramatic development of human perception of existing, reality and interaction with world. (shrink)

The purpose of this study is to describe a conceptual framework for cognitive distortions, which notably allows to specify more accurately their intrinsic relationships. This conceptual framework aims at inserting itself within the apparatus of cognitive therapy and of critical thinking. The present analysis is based on the following fundamental concepts: the reference class, the duality and the system of taxa. With the help of these three notions, each cognitive distortion can be defined. A distinction is also made between, (...) on the one hand, general cognitive distortions and on the other hand, specific cognitive distortions. The present model allows then to define within the same conceptual framework the general cognitive distortions such as dichotomous reasoning, disqualifying a given pole, minimisation and maximisation. It also allows to describe as specific cognitive distortions: disqualifying the positive, selective abstraction and catastrophism. Furthermore, the present model predicts the existence of two other general cognitive distortions: the omission of the neutral and requalifying in the other pole. (shrink)

This paper is a brief (and hopelessly incomplete) non-standard introduction to the philosophy of space and time. It is an introduction because I plan to give an overview of what I consider some of the main questions about space and time: Is space a substance over and above matter? How many dimensions does it have? Is space-time fundamental or emergent? Does time have a direction? Does time even exist? Nonetheless, this introduction is not standard because I conclude the discussion by (...) presenting the material with an original spin, guided by a particular understanding of fundamental physical theories, the so-called primitive ontology approach. (shrink)

As soon as you believe an imagination to be nonfictional, this imagination becomes your ontological theory of the reality. Your ontological theory (of the reality) can describe a system as the reality. However, actually this system is only a theory/conceptual-space/imagination/visual-imagery of yours, not the actual reality (i.e., the thing-in-itself). An ontological theory (of the reality) actually only describes your (subjective/mental) imagination/visual-imagery/conceptual-space. An ontological theory of the reality, is being described as a situation model (SM). There (...) is no way to prove/disprove that there is only one reality, or there are two realities (i.e., “subjective reality” and “objective reality”). So, every ontology talk/theory/imagination about the two realities is only a talk/theory/imagination – we will never know whether it is true or not. The conventionally-called “physical/objective reality/world” around my conventionally-called “physical/objective body” is actually a geometric mathematical model (being generated/mathematically-modeled by my brain) – it's actually a subset/component/part/element of my brain’s mind/consciousness/manifest-image. Our cosmos is an autonomous objective parallel computing automaton (aka state machine) which evolves by itself automatically/unintentionally – wave-particle duality and Heisenberg’s uncertainty principle can be explained under this SM of my brain. Each elementary particle (as a building block of our cosmos) is an autonomous mathematical entity itself (i.e., a thing in itself). Our cosmos has the same nature as a Game of Life system – both are autonomous objective parallel-computing automata. Cosmos (as a state machine) is indistinguishable from a digital simulation – my consciousness (as something nonphysical) is not cosmos (as a state machine). If we are happy to accept randomness/stochasticity, then it is obviously possible that all other worlds in the many-worlds interpretation (MWI) actually do not exist (objectively). As one metaphysical option, we can treat all other worlds as subjective only (even if they are actually objective). Under the context of this metaphysical option, we are only living in one world (i.e., the world we are currently living in; this world) – we are not living in many worlds at the same time parallelly. Under the context of this metaphysical option, there is only one possible future. The relationship among any number of elementary particles, is governed/described by Schrodinger equation. If (in theory) Schrodinger equation can’t be used to reliably forecast whether I will go to McDonald for dinner in this world (based on the current state of all elementary particles of the cosmos), then what can Schrodinger equation do? The conventionally-called “space” does not exist objectively. “Time” and “matter” are not physical. Consciousness is the subjective-form (aka quale) of the mathematical models (of the objective cosmos) which are intracorporeally/subjectively used by the control logic of a Turing machine’s program fatedly. A Turing machine’s mind/consciousness/manifest-image or deliberate decisions/choices should not be able to actually/objectively change/control/drive the (autonomous or fated) worldline of any elementary particle within this world (i.e., the world we are currently living in, under the context of MWI). Besides the Schrodinger equation (or another mathematical equation/function which is yet to be discovered) which is a valid/correct/factual causality of our cosmos/state-machine, every other causality (of our cosmos/state-machine) is either invalid/incorrect/counterfactual or can be proved by deductive inference based on the Schrodinger equation (or the aforementioned yet-to-be-discovered mathematical equation/function) only. Closed causality entails no causality. Consciousness plays no causal role (“epiphenomenalism”), or in other words, any cognitive/behavioural activity can in principle be carried out without consciousness (“conscious inessentialism”). If the “loop quantum gravity” theory is correct, then time/space does not actually/objectively exist in the objective-evolution of the objective cosmos, or in other words, we should not use the subjective/mental concept of “time”, “state” or “space” to describe/imagine the objective-evolution of our cosmos. (shrink)

A recent paper by Jakl, Jung and Pultr succeeded for the first time in establishing a very natural link between bilattice logic and the duality theory of d-frames and bitopological spaces. In this paper we further exploit, extend and investigate this link from an algebraic and a logical point of view. In particular, we introduce classes of algebras that extend bilattices, d-frames and N4-lattices to a setting in which the negation is not necessarily involutive, and we study corresponding (...) logics. We provide product representation theorems for these algebras, as well as completeness, algebraizability results for the corresponding logics. (shrink)

Substructural approaches to paradoxes have attracted much attention from the philosophical community in the last decade. In this paper we focus on two substructural logics, named ST and TS, along with two structural cousins, LP and K3. It is well known that LP and K3 are duals in the sense that an inference is valid in one logic just in case the contrapositive is valid in the other logic. As a consequence of this duality, theories based on either logic (...) are tightly connected since many of the arguments for and objections against one theory reappear in the other theory in dual form. The target of the paper is making explicit in exactly what way, if any, ST and TS are dual to one another. The connection will allow us to gain a more fine-grained understanding of these logics and of the theories based on them. In particular, we will obtain new insights on two questions concerning ST which are being intensively discussed in the current literature: whether ST preserves classical logic and whether it is LP in sheep’s clothing. Explaining in what way ST and TS are duals requires comparing these logics at a metainferential level. We provide to this end a uniform proof theory to decide on valid metainferences for each of the four logics. This proof procedure allows us to show in a very simple way how different properties of inferences (unsatisfiability, supersatisfiability and antivalidity) that behave in very different ways for each logic can be captured in terms of the validity of a metainference. (shrink)

I explore the logic of the conditional, using credence judgments to argue against Duality and in favor of Conditional Excluded Middle. I then explore how to give a theory of the conditional which validates the latter and not the former, developing a variant on Kratzer (1981)'s restrictor theory, as well as a proposal which combines Stalnaker (1968)'s theory of the conditional with the theory of epistemic modals I develop in Mandelkern 2019a. I argue that the (...) latter approach fits naturally with a conception of conditionals as referential devices which allow us to talk about particular worlds. (shrink)

Classical logic is usually interpreted as the logic of propositions. But from Boole's original development up to modern categorical logic, there has always been the alternative interpretation of classical logic as the logic of subsets of any given (nonempty) universe set. Partitions on a universe set are dual to subsets of a universe set in the sense of the reverse-the-arrows category-theoretic duality--which is reflected in the duality between quotient objects and subobjects throughout algebra. Hence the idea arises of (...) a dual logic of partitions. That dual logic is described here. Partition logic is at the same mathematical level as subset logic since models for both are constructed from (partitions on or subsets of) arbitrary unstructured sets with no ordering relations, compatibility or accessibility relations, or topologies on the sets. Just as Boole developed logical finite probability theory as a quantitative treatment of subset logic, applying the analogous mathematical steps to partition logic yields a logical notion of entropy so that information theory can be refounded on partition logic. But the biggest application is that when partition logic and the accompanying logical information theory are "lifted" to complex vector spaces, then the mathematical framework of quantum mechanics is obtained. Partition logic models indefiniteness (i.e., numerical attributes on a set become more definite as the inverse-image partition becomes more refined) while subset logic models the definiteness of classical physics (an entity either definitely has a property or definitely does not). Hence partition logic provides the backstory so the old idea of "objective indefiniteness" in QM can be fleshed out to a full interpretation of quantum mechanics. (shrink)

In my 2013 article, “A New Theory of Free Will”, I argued that several serious hypotheses in philosophy and modern physics jointly entail that our reality is structurally identical to a peer-to-peer (P2P) networked computer simulation. The present paper outlines how quantum phenomena emerge naturally from the computational structure of a P2P simulation. §1 explains the P2P Hypothesis. §2 then sketches how the structure of any P2P simulation realizes quantum superposition and wave-function collapse (§2.1.), quantum indeterminacy (§2.2.), wave-particle (...) class='Hi'>duality (§2.3.), and quantum entanglement (§2.4.). Finally, §3 argues that although this is by no means a philosophical proof that our reality is a P2P simulation, it provides ample reasons to investigate the hypothesis further using the methods of computer science, physics, philosophy, and mathematics. (shrink)

This thesis is a sceptical investigation into the notion that the metaphorical wave-particle binary of Virginia Woolf's To the Lighthouse is related to quantum physics. Indeed, the field of literature and science has employed conceptual similarities as the main means of connecting quantum concepts to novels, however, this has led to a host of scholarly difficulties, prompting the need for a re-examination of analogical linkages. Woolf is the model candidate for such a re-examination, given her historical and philosophical proximity with (...) the developments of quantum mechanics. To the Lighthouse, in particular, was written between 1925 and 1927: precisely when quantum physicists were attempting to resolve the wave-particle duality, leading to Niels Bohr's complementarity. This parallel has been noted by researchers as relevant to the novel, as it too displays a general binary that can be read as wave-particle-like, which the author also attempts to resolve along similar philosophical lines. Nevertheless, other than proximity and similarity, there are no reasons to affirm that the science is related to the novel; hence, it is an ideal case study to examine in order to ascertain the value of conceptual similarities in literature and science. To do so, To the Lighthouse's binary and its resolution are interpreted in a thesis-long close reading, in order to compare aspects of it firstly to Woolf's personal thought, and secondly to various non-quantum intellectual contexts that preceded and surrounded her. In doing so, it becomes clear not only that invoking quantum physics serves no clear purpose in better understanding the novel, but also that the notion of resolving wave- particle-like binaries was a widespread philosophical procedure at the turn of the century, decades before Bohr's concept. This negative conclusion interrogates what the scholarly value of interpreting similarities is, though a hypothetical solution can be found in conceptual metaphor theory. (shrink)

Intelligent Design integrates the work of Ilexa Yardley and Stridjom van der Merwe to demonstrate and prove Conservation of the Circle is the Only Dynamic in Nature (The Circular Theory) (Quantum Mechanics) (Metaphysical Naturalism).

Metaphysical dualities divorce humankind from its natural environment, dualities that can precipitate environmental disaster. Loyal Rue in Religion Is Not About God seeks to resolve the abstract modalities of religion and naturalism in a unified monistic ecocentric metaphysic characterized as religious naturalism. Rue puts forward proposals for a general naturalistic theory of religion, a theory that lays bare the structural and functional features of religious phenomena as the critical first step on the road to badly needed religion- science (...) realignment. Only then will humanity be equipped to address the environmental imperative. (shrink)

This book concerns the foundations of epistemic modality and hyperintensionality and their applications to the philosophy of mathematics. David Elohim examines the nature of epistemic modality, when the modal operator is interpreted as concerning both apriority and conceivability, as well as states of knowledge and belief. The book demonstrates how epistemic modality and hyperintensionality relate to the computational theory of mind; metaphysical modality and hyperintensionality; the types of mathematical modality and hyperintensionality; to the epistemic status of large cardinal axioms, (...) undecidable propositions, and abstraction principles in the philosophy of mathematics; to the modal and hyperintensional profiles of the logic of rational intuition; and to the types of intention, when the latter is interpreted as a hyperintensional mental state. Chapter \textbf{2} argues for a novel type of expressivism based on the duality between the categories of coalgebras and algebras, and argues that the duality permits of the reconciliation between modal and hyperintensional cognitivism and modal and hyperintensional expressivism. Elohim develops a novel, topic-sensitive truthmaker semantics for dynamic epistemic logic, and develops a novel, dynamic two-dimensional semantics grounded in two-dimensional hyperintensional Turing machines. Chapter \textbf{3} provides an abstraction principle for two-dimensional (hyper-)intensions. Chapter \textbf{4} advances a topic-sensitive two-dimensional truthmaker semantics, and provides three novel interpretations of the framework along with the epistemic and metasemantic. Chapter \textbf{5} applies the fixed points of the modal $\mu$-calculus in order to account for the iteration of epistemic states in a single agent, by contrast to availing of modal axiom 4 (i.e. the KK principle). The fixed point operators in the modal $\mu$-calculus are rendered hyperintensional, which yields the first hyperintensional construal of the modal $\mu$-calculus in the literature and the first application of the calculus to the iteration of epistemic states in a single agent instead of the common knowledge of a group of agents. Chapter \textbf{6} advances a solution to the Julius Caesar problem based on Fine's `criterial' identity conditions which incorporate conditions on essentiality and grounding. Chapter \textbf{7} provides a ground-theoretic regimentation of the proposals in the metaphysics of consciousness and examines its bearing on the two-dimensional conceivability argument against physicalism. The topic-sensitive epistemic two-dimensional truthmaker semantics developed in chapters \textbf{2} and \textbf{4} is availed of in order for epistemic states to be a guide to metaphysical states in the hyperintensional setting. -/- Chapters \textbf{8-12} provide cases demonstrating how the two-dimensional hyperintensions of hyperintensional, i.e. topic-sensitive epistemic two-dimensional truthmaker, semantics, solve the access problem in the epistemology of mathematics. Chapter \textbf{8} examines the interaction between Elohim's hyperintensional semantics and the axioms of epistemic set theory, large cardinal axioms, the Epistemic Church-Turing Thesis, the modal axioms governing the modal profile of $\Omega$-logic, Orey sentences such as the Generalized Continuum Hypothesis, and absolute decidability. These results yield inter alia the first hyperintensional Epistemic Church-Turing Thesis and hyperintensional epistemic set theories in the literature. Chapter \textbf{9} examines the modal and hyperintensional commitments of abstractionism, in particular necessitism, and epistemic hyperintensionality, epistemic utility theory, and the epistemology of abstraction. Elohim countenances a hyperintensional semantics for novel epistemic abstractionist modalities. Elohim suggests, too, that higher observational type theory can be applied to first-order abstraction principles in order to make first-order abstraction principles recursively enumerable, i.e. Turing machine computable, and that the truth of the first-order abstraction principle for two-dimensional hyperintensions is grounded in its being possibly recursively enumerable and the machine being physically implementable. Chapter \textbf{10} examines the philosophical significance of hyperintensional $\Omega$-logic in set theory and discusses the hyperintensionality of metamathematics. Chapter \textbf{11} provides a modal logic for rational intuition and provides a hyperintensional semantics. Chapter \textbf{12} avails of modal coalgebras to interpret the defining properties of indefinite extensibility, and avails of hyperintensional epistemic two-dimensional semantics in order to account for the interaction between interpretational and objective modalities and the truthmakers thereof. This yields the first hyperintensional category theory in the literature. Elohim invents a new mathematical trick in which first-order structures are treated as categories, and Vopenka's principle can be satisfied because of the elementary embeddings between the categories and generate Vopenka cardinals in the category of Set in category theory. Chapter \textbf{13} examines modal responses to the alethic paradoxes. Elohim provides a counter-example to epistemic closure for logical deduction. Chapter \textbf{14} examines, finally, the modal and hyperintensional semantics for the different types of intention and the relation of the latter to evidential decision theory. (shrink)

This is the first book in a two-volume series. The present volume introduces the basics of the conceptual foundations of quantum physics. It appeared first as a series of video lectures on the online learning platform Udemy.]There is probably no science that is as confusing as quantum theory. There's so much misleading information on the subject that for most people it is very difficult to separate science facts from pseudoscience. The goal of this book is to make you able (...) to separate facts from fiction with a comprehensive introduction to the scientific principles of a complex topic in which meaning and interpretation never cease to puzzle and surprise. An A-Z guide which is neither too advanced nor oversimplified to the weirdness and paradoxes of quantum physics explained from the first principles to modern state-of-the-art experiments and which is complete with figures and graphs that illustrate the deeper meaning of the concepts you are unlikely to find elsewhere. A guide for the autodidact or philosopher of science who is looking for general knowledge about quantum physics at intermediate level furnishing the most rigorous account that an exposition can provide and which only occasionally, in few special chapters, resorts to a mathematical level that goes no further than that of high school. It will save you a ton of time that you would have spent searching elsewhere, trying to piece together a variety of information. The author tried to span an 'arch of knowledge' without giving in to the temptation of taking an excessively one-sided account of the subject. What is this strange thing called quantum physics? What is its impact on our understanding of the world? What is ‘reality’ according to quantum physics? This book addresses these and many other questions through a step-by-step journey. The central mystery of the double-slit experiment and the wave-particle duality, the fuzzy world of Heisenberg's uncertainty principle, the weird Schrödinger's cat paradox, the 'spooky action at a distance' of quantum entanglement, the EPR paradox and much more are explained, without neglecting such main contributors as Planck, Einstein, Bohr, Feynman and others who struggled themselves to come up with the mysterious quantum realm. We also take a look at the experiments conducted in recent decades, such as the surprising "which-way" and "quantum-erasure" experiments. Some considerations on why and how quantum physics suggests a worldview based on philosophical idealism conclude this first volume. This treatise goes, at times, into technical details that demand some effort and therefore requires some basics of high school math (calculus, algebra, trigonometry, elementary statistics). However, the final payoff will be invaluable: Your knowledge of, and grasp on, the subject of the conceptual foundations of quantum physics will be deep, wide, and outstanding. Additionally, because schools, colleges, and universities teach quantum physics using a dry, mostly technical approach which furnishes only superficial insight into its foundations, this manual is recommended for all those students, physicists or philosophers of science who would like to look beyond the mere formal aspect and delve deeper into the meaning and essence of quantum mechanics. The manual is a primer that the public deserves. (shrink)

The most habitual and common use of the term natural corresponds to that which is – or could be – property of our experience, irrespective of whether that experience is mental or physical, viz. whatever can be known, perceived, determined and categorized by human mind, after it has bumped into and passed through the channels of our senses. The cooperation between our intellectual and sensual capabilities in relation to the usurpation of what is considered to be “natural”, is extremely crucial (...) for us to presume something as such, even if we are not familiar with – or sympathetic to – the duality of the Kantian Theory of Knowledge. That is inasmuch as the human mind, to be specific, is characterized by the intrinsic ability to conceive and contemplate on beings or events, which anything but belong to the natural order of things, beings such as Pegasus or the Valkyries, for instance, and counterfactual realities like the Purgatory or the Valhalla. (shrink)

In a number of papers and in his recent book, Is Water H₂O? Evidence, Realism, Pluralism (2012), Hasok Chang has argued that the correct interpretation of the Chemical Revolution provides a strong case for the view that progress in science is served by maintaining several incommensurable “systems of practice” in the same discipline, and concerning the same region of nature. This paper is a critical discussion of Chang's reading of the Chemical Revolution. It seeks to establish, first, that Chang's assessment (...) of Lavoisier's and Priestley's work and character follows the phlogistonists' “actors' sociology”; second, that Chang simplifies late-eighteenth-century chemical debates by reducing them to an alleged conflict between two systems of practice; third, that Chang's evidence for a slow transition from phlogistonist theory to oxygen theory is not strong; and fourth, that he is wrong to assume that chemists at the time did not have overwhelming good reasons to favour Lavoisier's over the phlogistonists' views. (shrink)