Purpose. The article aims to provide practical recommendations for calculating natural frequencies in axisymmetric shells using finite element methods. It focuses on the need to develop a simplified model that can be used in any modern finite element software package. The study analyzes the impact of the simplified homogeneous model on the deviation and error of natural frequencies compared to real structures. Design / Method / Approach. The research is based on creating a simplified shell (...) geometry by determining parameters such as shell thickness and density. These parameters are derived under the condition of equivalence in the moment of inertia and mass of the cross-sectional element. These parameters can vary along the height of the shell. Findings. The natural frequencies of the experimental shell with complex geometry were calculated and compared with those of the simplified model. The deviations and errors in the calculated frequencies were determined. It was demonstrated that the simplified model allows the calculation of natural frequencies with a deviation of no more than 1% from the experimental model, while significantly reducing computation time and the required computer resources. Theoretical Implications. The research expands the understanding of challenges in calculating the natural frequencies of complex objects using finite element methods under limited computational resources. Practical Implications. Practical recommendations are provided for engineers and designers when performing modeling tasks in the mechanics of deformable solid bodies. Originality / Value. The article presents an original analysis of a real case where a simplified model was implemented to determine the natural harmonics of a liquid rocket engine nozzle, making it a valuable tool for studying complex structures. Research Limitations / Future Research. The study is limited to the analysis of determining the natural frequencies of axisymmetric shells and does not cover all possible geometric features. Future research may focus on developing simplified models based on the equivalence of stiffness and mass parameters. Article Type. Case study, practical article. (shrink)

Today, the space industry is undergoing a period of significant technological advancement. Continuous progress in additive manufacturing technologies and the adoption of modern materials for 3D printing are driving this transformation. This trend has intensified competition among various space companies—both state-owned and private—each striving to introduce innovative and unique solutions. FlightControl Propulsion, a private space company in Ukraine, is one such example. This study focuses on the design of the power frame for a low-thrust liquid rocket engine. Power frames in (...) rocket engines must withstand significant mechanical loads. The application of topology optimization and high-strength steels enables the development of compact and efficient power frames that are substantially lighter than traditional designs. Additive manufacturing not only significantly reduces the production time of various parts and assemblies but also offers nearly unlimited possibilities for creating complex geometric shapes. What was previously challenging or even impossible to manufacture using conventional methods has now become feasible. This work examines a component fabricated using Selective Laser Melting (SLM) technology. A structured algorithm for topology optimization is described, along with the fundamental principle of the SIMP (Solid Isotropic Material with Penalization) topology optimization method. Numerical modeling of the stress-strain state for the initial design variant is performed using the finite element method (FEM) in a computer-aided engineering (CAE) environment. A computational finite element mesh is generated, and the safety margins of the design are evaluated. Following topology optimization, the final design variant is determined, and numerical modeling of the stress-strain state is repeated for the optimized design. The final design is then prepared for manufacturing and subsequent experimental testing. (shrink)

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

Vibration, especially basic vibration, may cause loose contacts, open circuits, or other contact problems, which account for a large proportion of system failure causes. Due to the complexity of the chassis structure used in the biomedical motors, the vibration analysis of a single component cannot solve the vibration problems encountered in the work of the system. Therefore, it is necessary to use system simulation and experiments to monitor and enhance the health of the structure. Finite element method (...) is used to carry out the dynamic analysis from the component to the system, and calculate the natural frequency, modal shape and harmonic response. Then, the effectiveness and accuracy of the analysis results are verified by experiments through simulation and experiments. The results show that the measures taken have effectively reduced the vibration of the chassis equipment and improved its safety for better health safety of patients. There is just a 2% variation between the natural frequencies acquired from the experiment and the simulation computation. In terms of natural frequency, the first 6-order natural frequencies all have errors of less than 10%, and the natural frequency error is comparable to that of fireproof board. (shrink)

The automotive door system's weather-strip seals play a crucial role in determining the degree of door closure, sealing the passenger cabin from water, and reducing wind noise inside the vehicle. Wrinkles often occur when installing weather-strips on door surfaces with bent or twisted profiles, affecting both the closure tightness and the noise insulation properties of the car door system. This study characterizes the wrinkling of Ethylene Propylene Diene Monomer (EPDM) automotive weather-strip seals during bending and identifies critical conditions for wrinkle (...) formation. The hyper elastic behaviour of the seal's EPDM sponge and dense EPDM rubber was modeled using the Foam and Mooney-Rivlin models, respectively. A Finite Element Analysis (FEA) model of the automotive weather strip seal was then developed and analysed using the linear FEA software Abaqus to determine the deformation and thickness reduction in areas prone to wrinkling. Finally, the critical criteria for wrinkle formation were determined through reaction force analysis in these areas. The proposed analytical method significantly reduces the product design cycle and cuts down on design and prototype costs. (shrink)

The automotive door system's weather-strip seals play a crucial role in determining the degree of door closure, sealing the passenger cabin from water, and reducing wind noise inside the vehicle. Wrinkles often occur when installing weather-strips on door surfaces with bent or twisted profiles, affecting both the closure tightness and the noise insulation properties of the car door system. This study characterizes the wrinkling of Ethylene Propylene Diene Monomer (EPDM) automotive weather-strip seals during bending and identifies critical conditions for wrinkle (...) formation. The hyper elastic behaviour of the seal's EPDM sponge and dense EPDM rubber was modeled using the Foam and Mooney-Rivlin models, respectively. A Finite Element Analysis (FEA) model of the automotive weather strip seal was then developed and analysed using the linear FEA software Abaqus to determine the deformation and thickness reduction in areas prone to wrinkling. Finally, the critical criteria for wrinkle formation were determined through reaction force analysis in these areas. The proposed analytical method significantly reduces the product design cycle and cuts down on design and prototype costs. (shrink)

The automotive door system's weather-strip seals play a crucial role in determining the degree of door closure, sealing the passenger cabin from water, and reducing wind noise inside the vehicle. Wrinkles often occur when installing weather-strips on door surfaces with bent or twisted profiles, affecting both the closure tightness and the noise insulation properties of the car door system. This study characterizes the wrinkling of Ethylene Propylene Diene Monomer (EPDM) automotive weather-strip seals during bending and identifies critical conditions for wrinkle (...) formation. The hyper elastic behaviour of the seal's EPDM sponge and dense EPDM rubber was modeled using the Foam and Mooney-Rivlin models, respectively. A Finite Element Analysis (FEA) model of the automotive weather strip seal was then developed and analysed using the linear FEA software Abaqus to determine the deformation and thickness reduction in areas prone to wrinkling. Finally, the critical criteria for wrinkle formation were determined through reaction force analysis in these areas. The proposed analytical method significantly reduces the product design cycle and cuts down on design and prototype costs. (shrink)

Vibration, especially basic vibration, may cause loose contacts, open circuits, or other contact problems, which account for a large proportion of system failure causes. Due to the complexity of the chassis structure used in the biomedical motors, the vibration analysis of a single component cannot solve the vibration problems encountered in the work of the system. Therefore, it is necessary to use system simulation and experiments to monitor and enhance the health of the structure. Finite element method (...) is used to carry out the dynamic analysis from the component to the system, and calculate the natural frequency, modal shape and harmonic response. Then, the effectiveness and accuracy of the analysis results are verified by experiments through simulation and experiments. The results show that the measures taken have effectively reduced the vibration of the chassis equipment and improved its safety for better health safety of patients. There is just a 2% variation between the natural frequencies acquired from the experiment and the simulation computation. In terms of natural frequency, the first 6-order natural frequencies all have errors of less than 10%, and the natural frequency error is comparable to that of fireproof board. (shrink)

We present a novel approach to defining the mathematical constant π through the infinite den- sification of a sweeping net, which approximates a circle as the net becomes infinitely dense. By developing and enhancing notation related to sweeping nets and saddle maps, we establish a rigor- ous framework for expressing π in terms of the densification process using reverse integration. This method, inspired by the concept that numbers ”come from infinity,” leverages a reverse integral approach to model the transition (...) from infinite densification to the finite circle. Our work not only offers a new perspective on the geometric interpretation of π but also provides insights into reverse integration techniques and their applications in mathematical analysis. (shrink)

Hyperboolean algebras are Boolean algebras with operators, constructed as algebras of complexes (or, power structures) of Boolean algebras. They provide an algebraic semantics for a modal logic (called here a {\em hyperboolean modal logic}) with a Kripke semantics accordingly based on frames in which the worlds are elements of Boolean algebras and the relations correspond to the Boolean operations. We introduce the hyperboolean modal logic, give a complete axiomatization of it, and show that it lacks the finite model property. (...) The method of axiomatization hinges upon the fact that a "difference" operator is definable in hyperboolean algebras, and makes use of additional non-Hilbert-style rules. Finally, we discuss a number of open questions and directions for further research. (shrink)

The Cartesian concept of nature, which has determined modern thinking until the present time, has become obsolete. It shall be shown that Hegel's objective-idealistic conception of nature discloses, in comparison to that of Descartes, new perspectives for the comprehension of nature and that this, in turn, results in possibilities of actualizing Hegel's philosophy of nature. If the argumentation concerning philosophy of nature is intended to catch up with the concrete Being-of-nature and to meet it in its concretion, then this is (...) impossible for the finite spirit in a strictly a priori sense – this is the thesis supported here which is not at all close to Hegel. As the argumentation rather has to consider the conditions of realization concerning the Being-of-nature, too, it is compelled to take up empirical elements – concerning the organism, for instance, system-theoretical aspects, physical and chemical features of the nervous system, etc. With that, on the one hand, empirical-scientific premises are assumed (e.g. the lawlikeness of nature), which on the other hand become (now close to Hegel) possibly able to be founded in the frame of a Hegelian-idealistic conception. In this sense, a double strategy of empirical-scientific concretization and objective-idealistic foundation is followed up, which represents the methodical basic principle of the developed considerations. In the course of the undertaking, the main aspects of the whole Hegelian design concerning the philosophy of nature are considered – space and time, mass and motion, force and law of nature, the organism, the pro-blem of evolution, psychic being – as well as Hegel's basic thesis concerning the philosophy of nature, that therein a tendency toward coherence and idealization manifests itself in the sense of a (categorically) gradually rising succession of nature: from the separateness of space to the ideality of sensation. In the sense of the double strategy of concretization and foundation it is shown that on the one hand possibilities of philosophical penetration concerning actual empirical-scientific results are opened, and on the other hand – in turn – a re-interpretation of Hegel's theorem on the basis of physical, evolution-theoretical and system-theoretical argumentation also becomes possible. In this mutual crossing-over and elucidation of empirical and Hegelian argumentation not only do perspectives of a new comprehension of nature become visible, but also, at the same time – as an essential consequence of this methodical principle – thoughts on the possibilities of actualizing Hegel's philosophy of nature. (shrink)

This work is a attempt to describe various braches of mathematics and the analogies betwee them. Namely: 1) Symbolic Analogic 2) Lateral Algebraic Expressions 3) Calculus of Infin- ity Tensors Energy Number Synthesis 4) Perturbations in Waves of Calculus Structures (Group Theory of Calculus) 5) Algorithmic Formation of Symbols (Encoding Algorithms) The analogies between each of the branches (and most certainly other branches) of mathematics form, ”logic vectors.” Forming vector statements of logical analogies and semantic connections between the di↵erentiated branches (...) of math- ematics is useful. It’s useful, because it gives us a linguistic notation from which we can derive other insights. These combined insights from the logical vector space connections yield a combination of Numeric Energy and the logic space. Thus, I have derived and notated many of the most useful tangent ideas from which even more correlations and connections ca be drawn. Using AI, these branches can be used to form even more connections through training of lan- guage engines on the derived models. Through the vector logic space and the discovery of new sheaf (Limbertwig), vast combinations of novel, mathematical statements are derived. This paves the way for an AGI that is not rigid, but flex- ible, like a Limbertwig. The Limbertwig sheaf is open, meaning it can receive other mathematical logic vectors with di↵erent designated meanings (of infi- nite or finite indicated elements). Furthermore, the articulation of these syntax forms evolves language away from imperative statements into a mathematically emotive space. Indeed, shown within, we see how the supramanifold of logic is shared with the supramanifold of space-time mathematically. Developing clean mathematical spaces can help meditation, thought pro- cess, acknowledgment of ideas spoken into that cognitive-spacetime and in turn, methods by which paradoxes can be resolved linguistically. This toolkit should be useful to all in the sciences as well as those bridging the humantities to mathematics. Using our memories as a toolkit to aggregate these ideas breaks down bound- aries between them in a new, exciting way. Merging philosophy and Quantum Mechanics together through the lens of symbolic analogies gives the tools to unravel this mystery of all mysteries. Mathematics thus exists as a bridge al- beit a complex one between the two disciplines, giving life to a composite art of problem-solving. Furthermore, mathematics yields to millions of other applications that are potentially limited only by our imagination. From massive data sets used for predictive analytics to emerging fields in medicine, mathematics is an energy and force at the center of possibilities. The power of mathematics to help manage life exists in its ability to shape and model the world in which we live and interact with one another. In conclusion, mathematics is a powerful tool that creates bridges and con- nections between many disciplines and serves as a powerful form of analytical data consumption. It provides language-rich bridges from which to assemble vast fields of theoretical investigations and create groundbreaking innovations. As we approach new horizons in the technology timeline, mathematics will con- tinue to be a powerful driver of creativity and progress. (shrink)

The present article is a primary introduction to the semi-structured interviewing method SMILE_PH, an acronym for Sense-Making Interviews Looking at Elements of Philosophical Health. Beyond grounding this new methodology theoretically (a work that is started here but will in the future necessitate several developments), the main motivation here is pragmatic: to provide the recent philosophical health movement with a testable method and show that philosophically-oriented interviews are possible in a manner that can be reproduced, compared, tested and used (...) systematically with a population that has received no training in philosophy. The SMILE_PH approach was conceived by the author during an ethically approved pilot study focused on the philosophy of life of persons living with spinal cord injury (SCI), with the intention of rectifying the epistemic obstacles generated by rationalist, Socratic or unstructured ways of in-depth interviewing. The six-step structure of the method is also inspired by hundreds of individual dialogue sessions with philosophical counselees, led by the author between 2018 and 2022: the SMILE_PH method progressively gathers phenomenological data about 1 – our bodily sense, 2 – our sense of self, 3 – our sense of belonging, 4 – our sense of the possible, 5 – our sense of purpose and 6 – our philosophical sense. (shrink)

When are we, in fact, arguing? Even one and the same author may offer more than one definition of what he understands by argumentation: this is partly because the problem of argumentation is not confined to a single area of knowledge or of practical life. Definitions of argumentation are as varied as the different positions taken on the question of what exactly we do when we argue. Be that as it may, we are struck by the fact that the problem (...) of argumentation (above all in its application to hypothetic-inductive methods) has not been analysed as a problem linked to interpretation. (shrink)

Among historians of philosophy it is often taken for granted that the “Brentano school” was one of the influential philosophical movements at the end of the nineteenth and the beginning of the twentieth century – but Brentano’s own contributions are often eclipsed by that of his direct students. This invites to reflect on the nature of and the unity within the school. Since Brentano’s conception of a rigorous, scientific philosophy had a strong impact on his students, it has been argued (...) that this conception constitutes a unifying element in an otherwise heterogeneous group. The scope of this article is to shed light on this thesis and to show its limits. I argue for a differentiated view: the Brentano school is best seen not as a compact movement, but as a heterogeneous group of scholars who approached, in a given historical and geographical period, similar topics in very similar ways. (shrink)

Methods have been a controversial element in theories of knowledge for the last 40 years. Recent developments in theories of justification, concerning the identification and individuation of belief-forming processes, can shed new light on methods, solving some longstanding problems in the theory of knowledge. We needn’t and shouldn’t shy away from methods; rather, methods, construed as psychological processes of belief-formation, need to play a central role in any credible theory of knowledge.

This article introduces the notion of duplex elements of the finite rings and corresponding neutrosophic rings. The authors establish duplex ring Dup(R) and neutrosophic duplex ring Dup(R)I)) by way of various illustrations. The tables of different duplicities are constructed to reveal the comparison between rings Dup(Zn), Dup(Dup(Zn)) and Dup(Dup(Dup(Zn ))) for the cyclic ring Zn . The proposed duplicity structures have several algebraic systems with dissimilar consequences. Author’s characterize finite rings with R + R is different from the (...) duplex ring Dup(R). However, this characterization supports that R + R = Dup(R) for some well known rings, namely zero rings and finite fields. (shrink)

The method of reflective equilibrium (MRE) is a method of justification popularized by John Rawls and further developed by Norman Daniels, Michael DePaul, Folke Tersman, and Catherine Z. Elgin, among others. The basic idea is that epistemic agents have justified beliefs if they have succeeded in forming their beliefs into a harmonious system of beliefs which they reflectively judge to be the most plausible. Despite the common reference to MRE as a method, its mechanisms or rules are (...) typically expressed in a metaphorical or simplified manner and are therefore criticized as too vague. Recent efforts to counter this criticism have been directed towards the attempt to provide formal explications of MRE. This paper aims to supplement these efforts by providing an informal working definition of MRE. This approach challenges the view that MRE can adequately be characterized only in the negative as a set of anti-essentialisms. I argue that epistemic agents follow MRE iff they follow four interconnected rules, which are concerned with a minimalistic form of foundationalism, a minimalistic form of fallibilism, a moderate form of holism, and a minimalistic form of rationality. In the critical spirit of MRE, the corresponding working definition is, of course, provisional and revisable. In general, the aim is to contribute to a reflective equilibrium (RE) concerning MRE. If it is successful, this working definition provides a better grasp of the most basic elements of the method and thereby enhances our understanding of it. (shrink)

The immense outpouring of archaeological discoveries this past century has shed new light on ancient East Asia, and China in particular. Yet in concert with this development another, more troubling, trend has likewise gained momentum: the looting of cultural heritage and the sale of unprovenienced antiquities. Scholars face difficult questions, from the ethics of working with objects of unknown provenance, to the methodological problems inherent in their research. The goal of this Element is to encourage scholars to critically examine (...) their relationships to their sources and reflect upon the impact of their research. The three essays in this Element present a range of disciplinary perspectives, focusing on systemic issues and the nuances of method versus ethics, with a case study of the so-called 'Han board' MSS given as a specific illustration. This title is also available as open access on Cambridge Core. (shrink)

Propositional logics in general, considered as a set of sentences, can be undecidable even if they have “nice” representations, e.g., are given by a calculus. Even decidable propositional logics can be computationally complex (e.g., already intuitionistic logic is PSPACE-complete). On the other hand, finite-valued logics are computationally relatively simple—at worst NP. Moreover, finite-valued semantics are simple, and general methods for theorem proving exist. This raises the question to what extent and under what circumstances propositional logics represented in various (...) ways can be approximated by finite-valued logics. It is shown that the minimal m-valued logic for which a given calculus is strongly sound can be calculated. It is also investigated under which conditions propositional logics can be characterized as the intersection of (effectively given) sequences of finite-valued logics. (shrink)

The proof theory of many-valued systems has not been investigated to an extent comparable to the work done on axiomatizatbility of many-valued logics. Proof theory requires appropriate formalisms, such as sequent calculus, natural deduction, and tableaux for classical (and intuitionistic) logic. One particular method for systematically obtaining calculi for all finite-valued logics was invented independently by several researchers, with slight variations in design and presentation. The main aim of this report is to develop the proof theory of (...) class='Hi'>finite-valued first order logics in a general way, and to present some of the more important results in this area. In Systems covered are the resolution calculus, sequent calculus, tableaux, and natural deduction. This report is actually a template, from which all results can be specialized to particular logics. (shrink)

In this article I offer an opinionated overview of the central elements of Kant’s philosophical methodology during the critical period. I begin with a brief characterization of how Kant conceives of the aims of human inquiry – focusing on the idea that inquiry ideally aims at not just cognition (Erkenntnis), but also the more demanding cognitive achievements that Kant labels insight (Einsehen) and comprehension (Begreifen). Then I explore the implications of this picture for philosophy — emphasizing Kant’s distinction between critical (...) and doctrinal phases of philosophical inquiry, with the first of these playing both a negative and a positive role with respect to the second. Then, I will argue that this positive role is possible, according to Kant, only insofar as philosophy follows what I call a “capacities-first” methodology – that is, one that treats basic cognitive capacities (such as reason) and their self-conscious activities as fundamental (in both a cognitive sense and in an explanatory sense) for the sort of philosophy human beings are capable of. It is this methodology, I will argue, that allows Kant to introduce the first principles that philosophy in its doctrinal phase requires in a manner that is neither arbitrary nor (at least obviously) incompatible with Kant’s own critical restrictions on cognition. I conclude by discussing some of the implications of this methodological picture – including the methodological significance of self-consciousness and regressive or “transcendental” arguments, Kant’s distinction between analytic and synthetic methods in philosophy, and Kant’s conception of reason as autonomous. (shrink)

What is the relation between method and truth? Are we justified in accepting a theory that satisfies the rules of scientific method as true? Such questions divide realism from anti-realism in the philosophy of science. Scientific realists take the methods of science to promote the realist aim of correspondence truth. Anti-realists either claim that the methods of science promote lesser epistemic goals than realist truth, or else they reject the realist conception of truth altogether. In this paper, I (...) propose a realist theory of the relation between method and truth. The theory consists of three basic elements: (a) a naturalistic treatment of epistemic normativity, (b) an instrumentalist conception of the nature of methodological rules, and (c) an abductive argument for the truth-conduciveness of the rules of scientific method. (shrink)

This paper examines the performance elements in Asu Ekiye’s musical video entitled Back to Base. The study cuts across the use of costume and other theatrical elements to portray various ethnic nationalities as represented in the production. This style of music video production has not been given adequate scholarly attention by researchers. Thus, the paper examines the performance elements in Asu Ekiye’s music video, Back to Base. It is against this backdrop that the content analysis method of investigation is (...) deployed. It adopts comparative analysis investigative approach which appropriates primary and secondary sources. The primary sources are musical video CD of Asu Ekiye. The secondary sources are scholarly materials related to musical performance and theatre. This paper observes that Asu Ekiye’s musical video performance dialogue with performers ranging from lead singers to back-up singers, actors and dancers also involves audience participation and other performance elements. Asu Ekiye’s musical video entitled Back to Base is performed on two different performing areas: the arena stage and the aquatic stage. This paper holds that costumes, dances, and dramatic performances, props and locations are the main strengths and attractions of the music video. It recommends that for music to thrive in Nigeria, a multicultural society, musicians should ensure that their musical productions should be cross cultural and they should deploy variety of performances elements. (shrink)

New algorithms for the numerical solution of Ordinary Differential Equations (ODEs) with initial condition are proposed. They are designed for work on a new kind of a supercomputer – the Infinity Computer, – that is able to deal numerically with finite, infinite and infinitesimal numbers. Due to this fact, the Infinity Computer allows one to calculate the exact derivatives of functions using infinitesimal values of the stepsize. As a consequence, the new methods described in this paper are able to (...) work with the exact values of the derivatives, instead of their approximations. (shrink)

This study is the first comprehensive analysis of the physical theory of the Islamic philosopher Avicenna (d. 1037). It seeks to understand his contribution against the developments within the preceding Greek and Arabic intellectual milieus, and to appreciate his philosophy as such by emphasising his independence as a critical and systematic thinker. Exploring Avicenna’s method of "teaching and learning," it investigates the implications of his account of the natural body as a three-dimensionally extended composite of matter and form, and (...) examines his views on nature as a principle of motion and his analysis of its relation to soul. Moreover, it demonstrates how Avicenna defends the Aristotelian conception of place against the strident criticism of his predecessors, among other things, by disproving the existence of void and space. Finally, it sheds new light on Avicenna’s account of the essence and the existence of time. For the first time taking into account the entire range of Avicenna’s major writings, this study fills a gap in our understanding both of the history of natural philosophy in general and of the philosophy of Avicenna in particular. (shrink)

Any formalized system can be conceptualized as a geometric shape that operates according to the laws of logic and existing theorems. This method allows for the easy analysis of formal logic by representing systems geometrically, providing a visual framework to understand their logical structure. For example, when we formalize a system, it can be described as a closed circle, "closed" because the system has been finalized. Inside this circle, the content consists of axioms, statements, and everything that constitutes the (...) system. This circle can also be viewed as a set, where the elements of the set represent the axioms, rules, and statements defining the system. When we attempt to modify a system, we do not change the system itself but instead create a new system, S2, which includes system S1 as a part of it. If the system has already been created, after modification, we do not remove or expand system S1; instead, we create a new system, as both the original and the modified systems will coexist in their formalized forms. This can be visualized as a new circle being created on top of the original one, with the new circle representing the modified system and the original circle being a subset of it. This method applies universally to all logical systems and can be used to analyze any system. For example, consider two religions, R1 and R2, both claiming their absolute truth. If only one religion existed asserting its absolute truth, it would indeed be considered absolutely true, as there would be no opposing system. However, by formalizing these religions, we can represent R1 and R2 as separate circles. When we enclose them within a larger circle, we see that R1 and R2 are merely parts of a broader system that includes both. In this context, R1 and R2 are contradictory, as they cannot both be absolutely true within the same larger system. This example underscores that while truth may exist, it can only be understood as subjective truth within a specific system. The continuous creation of larger circles points to the idea that truth is always relative to the system it belongs to. When claiming absolute truth, it contradicts other definitions of truth, as it fails to account for the multiplicity of systems that may assert their own truths. Thus, absolute truth becomes a relative concept, defined only within the boundaries of a given system, and contradicts others when considered outside that context. This is the foundation of the method. With it, formal systems can be visualized, making it easier to work with and analyze them. (shrink)

In this paper we consider the logics L(i,n) obtained from the (n+1)-valued Lukasiewicz logics L(n+1) by taking the order filter generated by i/n as the set of designated elements. In particular, the conditions of maximality and strong maximality among them are analyzed. We present a very general theorem that provides sufficient conditions for maximality between logics. As a consequence of this theorem, it is shown that L(i,n) is maximal w.r.t. CPL whenever n is prime. Concerning strong maximality (i.e. maximality w.r.t. (...) rules instead of only axioms), we provide algebraic arguments in order to show that the logics L(i,n) are not strongly maximal w.r.t. CPL, even for n prime. Indeed, in such case, we show that there is just one extension between L(i,n) and CPL obtained by adding to L(i,n) a kind of graded explosion rule. Finally, using these results, we show that the logics L(i,n) with n prime and i/n < 1/2 are ideal paraconsistent logics. (shrink)

We give a new and elementary construction of primitive positive decomposition of higher arity relations into binary relations on finite domains. Such decompositions come up in applications to constraint satisfaction problems, clone theory and relational databases. The construction exploits functional completeness of 2-input functions in many-valued logic by interpreting relations as graphs of partially defined multivalued ‘functions’. The ‘functions’ are then composed from ordinary functions in the usual sense. The construction is computationally effective and relies on well-developed methods of (...) functional decomposition, but reduces relations only to ternary relations. An additional construction then decomposes ternary into binary relations, also effectively, by converting certain disjunctions into existential quantifications. The result gives a uniform proof of Peirce’s reduction thesis on finite domains, and shows that the graph of any Sheffer function composes all relations there. (shrink)

In this chapter, I defend the program of conceptual analysis, broadly construed, and the method of thought experiments in epistemology, as a first-person enterprise, that is, as one which draws on the investigator's own competence in the relevant concepts. I do not suggest that epistemology is limited to conceptual analysis, that it does not have important a posteriori elements, that it should not draw on empirical work wherever relevant (and non-question begging), or that it is not a communal enterprise. (...) Although discussion in the space available will necessarily be brief, and many points must be elided altogether, I aim to sketch salient features of the landscape, clarify issues, set aside some confusions, and outline responses to some recent challenges. In §2, I sketch a traditional account of concepts and conceptual truths. In §3, I review a broad conception of analysis as encompassing not just reduction but also articulation of conceptual connections. In §4, I address the charge that in studying epistemic concepts we turn away from our proper target of study, the actual phenomena of knowledge, justification, and so on. In §5, I give a brief overview of the method of thought experiments. In §6, I address objections to thought experiments that have their source in "experimental philosophy." In §7, I address the charge that pursuing conceptual analysis in epistemology is misplaced because 'knowledge', 'justification', 'evidence' and so on, are natural kind terms, and hence that we must engage in empirical research to discover the real essences of the kinds they pick out (if any). (shrink)

This paper will provide information about the concrete brand produced in the factory for the prefabricated elements and the comparison of the results given by the test of resistance to compression and the results of the test of the hammer impact of the sclerometer. The idea and the need to conduct this study arose for 2 main reasons: first, from the poor results often obtained from sclerometer impact to the elements in the field, despite the compression resistance test with cubic (...) samples taken in the concrete cast and the carrot test directly on the element assembled in the building provides good results. Secondly, to have a connection between the values of the concrete brand resulting from the pressure resistance test with a press performed in the laboratory and the impact test with the sclerometer hammer which is often performed in the field under different conditions. The sclerometer impact tests will be performed on each cube sample before it is broken, in the press, and the sclerometer impact tests will be performed on the concrete elements from which the cube sample was taken on the day that this sample will be destroyed. The predicted results are relatively close values related to the age between14th day and the 28th day of the concrete maturity, as determined by the manual of the sclerometer that the study is going to use, and other values for the other days (1, 3,7,14,28). But in fact, just like in the field tests done before, it is noticed that the results obtained from the blows with the sclerometer hammer are weak. The aim of the paper is to find a logical connection between the results of these 2 types of tests. This study will contain information on the composition of the concrete produced in the IXHEM SHPK factory (ltd) located in Durres-Albania, the brands of concrete on different days for different elements, and the comparison of the results between the 2 methods mentioned above. (shrink)

In this paper I revisit nineteenth-century debates over historical objectivity and the political functions of historiography. I focus on two central contributors to these debates: Leopold von Ranke and Johann Gustav Droysen. In their takes on objectivity and subjectivity, impartiality and political engagement I reveal diametrically opposed solutions to shared concerns: how can historians reveal history to be meaningful without taking recourse to speculative philosophy? And how can they produce a knowledge that is relevant to the present when the project (...) of “exemplary” history has been abandoned? I put a special focus on the relativist themes in Ranke’s and Droysen’s answers to these questions. Ranke’s demand for impartiality leads him to think of all historical epochs as equally valid, while Droysen’s emphasis on the historian’s subjectivity relativizes historical truth. In order to explain why Ranke and Droysen nevertheless remained unfazed by the problem of historical relativism, I analyze their normative conceptions of the historian’s disciplinary ethos. I show that Ranke and Droysen think of objective impartiality and subjective partiality not only in methodological terms, but also in terms of justice and ethic duty. This normative element secures the professional study of history an ethical-political relevance for the present. (shrink)

Avner Baz argues that the philosophical method of cases presupposes a problematic view of language and linguistic competence, namely what he calls "the atomistic-compositional view". Combining key elements of social pragmatism and contextualism, Baz presents a view of language and linguistic competence, which he takes to be more sensitive to the open-endedness of human language. On this view, there are conditions for the "normal" and "felicitous" use of human words, conditions that Baz thinks are lacking in the context of (...) the philosophical method of cases, and which make the question that philosophers are prone to ask in that context and the answers they give to that question to be pointless. However, in this paper, I argue as follows. First, Baz's conditions for the "normal" and "felicitous" use of human words are in tension with the open-endedness of human language and the use of human words. Second, it is not even clear that those conditions are really missing in the context of the philosophical method of cases. And third, even if we grant that those conditions are missing in that context, this does not licence his damning conclusion on the philosophical method of cases since we are not forced to embrace the view of language and linguistic competence on which that damning conclusion is plausible. This last move is secured by advancing and defending a skill or virtue-based view of language and linguistic competence inspired by the later work of Donald Davidson. (shrink)

A well known and referenced global result is the nilpotent characterisation of the finite p-groups. This un doubtedly transends into neutrosophy. Hence, this fact of the neutrosophic nilpotent p-groups is worth critical studying and comprehensive analysis. The nilpotent characterisation depicts that there exists a derived series (Lower Central) which must terminate at {ϵ} (an identity), after a finite number of steps. Now, Suppose that G(I) is a neutrosophic p-group of class at least m ≥ 3. We show in (...) this paper that Lm−1(G(I)) is abelian and hence G(I) possesses a characteristic abelian neutrosophic subgroup which is not supposed to be contained in Z(G(I)). Furthermore, If L3(G(I)) = 1 such that pm is the highest order of an element of G(I)/L2(G(I)) (where G(I) is any neutrosophic p-group) then no element of L2(G(I)) has an order higher than pm. (shrink)

The exploration of chemical periodicity over the past 250 years led to the development of the Periodic System of Elements and demonstrates the value of vague ideas that ignored early scientific anomalies and instead allowed for extended periods of normal science where new methodologies and concepts are developed. The basic chemical element provides this exploration with direction and explanation and has shown to be a central and historically adaptable concept for a theory of matter far from the reductionist frontier. (...) This is explored in the histories of Prout’s hypothesis, Döbereiner Triads, element inversions necessary when ordering chemical elements by atomic weights, and van den Broeck’s ad-hoc proposal to switch to nuclear charges instead. The development of more accurate methods to determine atomic weights, Rayleigh and Ramsey’s gas separation and analytical techniques, Moseley’s X-ray spectroscopy to identify chemical elements, and more recent accelerator-based cold fusion methods to create new elements at the end of the Periodic Table point to the importance of methodological development complementing conceptual advances. I propose to frame the crossover from physics to chemistry not as a loss of accuracy and precision but as an increased application of vague concepts such as similarity which permit classification. This approach provides epistemic flexibility to adapt to scientific anomalies and the continued growth of chemical compound space and rejects the Procrustean philosophy of reductionist physics. Furthermore, it establishes chemistry with its explanatory and operational autonomy epitomized by the periodic system of elements as a gateway to other experimental sciences. (shrink)

How to participate proactively in a process of change and transformation, to shape our path within an uncertain future? With this publication, the State Of The Art Network marks a waypost on a journey which started in 2018, when like-minded Nordic and Baltic art organisations and professionals initiated this network as a multidisciplinary collaboration facing the Anthropocene. Over five years, ten organisations and around 80 practitioners from different disciplines, like the arts, natural sciences and humanities came together, online and in (...) person, for workshops, seminars and discussions. The aim was to find ways to create resilience and concrete actions on how to live through the change in culture, economy and the environment and to find concrete, hands-on methods to deal with the Anthropocene and the environmental crisis. As an outcome of this process, this publication takes a closer look at how we as practising artists, researchers and cultural actors can create elements for critical thinking and doing which can assist us in navigating the complexities of the present. -/- Edited for the State Of The Art Network by Erich Berger, Mari Keski-Korsu, Marietta Radomska and Line Thastum. -/- Produced and published by Bioart Society 2023. (shrink)

Hegel's Science of Logic makes the just not low claim to be an absolute, ultimate-grounded knowledge. This project, which could not be more ambitious, has no good press in our post-metaphysical age. However: That absolute knowledge absolutely cannot exist, cannot be claimed without self-contradiction. On the other hand, there can be no doubt about the fundamental finiteness of knowledge. But can absolute knowledge be finite knowledge? This leads to the problem of a self-explication of logic (in the sense of (...) Hegel) and further, as will be shown, to a new definition of the dialectical procedure. The stringency of which results from the fact that always exactly that implicit content is explicated that was generated by the preceding explication step itself and is thus concretely comprehensible. At the same time, a new implicit content is generated by this act of explication, which requires a new explication step, and so forth. In the dialectical procedure reinterpreted in this way, dialectical arguments are not beheld, guessed at or even surreptitiously obtained, but are methodically accountable. Thereby dialectics is understood as a self-explication of logic by logical means and thus as a proof of the possibility of ultimate-grounding in the form of absolute and nevertheless finite – and thus also fallible – knowledge. (shrink)

Notwithstanding diverse opinions and debates about mixing methods, mixed methods research (MMR) is increasingly being used in sport and exercise psychology. In this paper, we describe MMR trends within leading sport and exercise psychology journals and explore critical realism as a possible underpinning framework for conducting MMR. Our meta-study of recent empirical mixed methods studies published in 2017–2019 indicates that eight (36%) of the 22 MMR studies explicitly stated a paradigmatic position (five drew on pragmatism, two switched paradigms between qualitative (...) and quantitative elements of the study, and one was situated in relativist-interpretivism). The remaining 14 (64%) studies did not report their underpinning research philosophical assumptions. Evaluating the merits and limitations of these positions against critical realist assumptions suggests that several paradigmatic disagreements are potentially reconcilable. These include (a) maintaining that ontological and epistemological concerns are important for methodological integrity of a mixed methods study; (b) switching between paradigms in the same study is problematic; and (c) refuting the qualitative-quantitative incommensurability thesis, therefore allowing mixed methods research without compromising philosophical coherence. From a critical realist position, we suggest that both quantitative and qualitative designs are justifiable in a mixed methods study because (1) they help corroborate, refine, or refute plausible explanations of phenomena (epistemological), but (2) with different methodologies utilised to perform different tasks in the same research design related to different psycho-social system features (ontological). We call for a collaborative engagement by researchers across paradigmatic positions to work towards the advancement of methodological pluralism in our research community. (shrink)

Xenophon’s conception of the dialectical method shares many similarities with Antisthenes’ point of view regarding the relation between language and reality. The key element supporting this reading is the parallel between Xenophon’s method of dialegein kata genē and Antisthenes’ method of episkepsis tōn onomatōn. In this paper, I claim that a correct understanding of both methods yields a clear structural proximity between the two Socratics on the issue of dialectics. Although they present some significant differences, which (...) I will also explore, I will argue that both variants express a single Socratic motive with regard to dialectics. That is that dialectics, in its basic structure, consists of organizing reality through discourse in order to make it comprehensible. In particular, this is done through establishing unified instances capable of comprehending a multiplicity. This nuclear position could also be extended to include middle Plato’s concept of dialectics. This concurrence takes up different forms in Plato, Xenophon and Antisthenes. Nevertheless, they share the same structure, which indicates quite plausibly a major characteristic of Socratic philosophies, as opposed to previous attempts by the Presocratics and the Sophists. (shrink)

As the lyrics to the traditional nineteenth century gospel hymn state, one of the goals of many magical and religious practices is to experience ‘a closer walk with Thee,’ coming into the presence of the holy in both figurative and arguably literal terms. One of the many ways to improve this likelihood of achieving the deep and immersive presence of the holy—described by the scholar of comparative religion Rudolf Otto as the “gentle tide, [the] pervading [of] the mind with a (...) tranquil mood” numinous experience—is through the careful use of various sonic elements. To this point, an exploration of physical worship spaces themselves, a review of the means of creating sounds within worship, and a study of the related uses of sonic technology during worship rituals can help to elucidate just how these sonic elements compare in their utilization between ancient magic and more contemporary magical and religious applications. It is my contention that the overall goal of creating an immersive environment for worship and ritual practice has remained a constant from Ancient Greek and Roman times through to the present, while the technology available to achieve this goal (both in the creation of an immersive physical space and in the use of engaging and relatable musical instruments and instrumental styles) has continually progressed. Put another way, the methods in which we might best utilize various sonic elements to achieve the most numinous experience—the ‘how’— have certainly changed over time, but the underlying ‘why’ and the core goal of using sound to increase this sense of a presence with the holy has remained largely unchanged. (shrink)

The aim of this paper is to make a proposal for a new extension of the MULTIMOORA method extended to deal with bipolar fuzzy sets. Bipolar fuzzy sets are proposed as an extension of classical fuzzy sets in order to enable solving a particular class of decision-making problems. Unlike other extensions of the fuzzy set of theory, bipolar fuzzy sets introduce a positive membership function, which denotes the satisfaction degree of the element x to the property corresponding to (...) the bipolar-valued fuzzy set, and the negative membership function, which denotes the degree of the satisfaction of the element x to some implicit counter-property corresponding to the bipolar-valued fuzzy set. By using single-valued bipolar fuzzy numbers, the MULTIMOORA method can be more efficient for solving some specific problems whose solving requires assessment and prediction. The suitability of the proposed approach is presented through an example. (shrink)

In Aristotle's cosmology, the nature of the elements is defined by their place in the Totality. Their cosmic motions keep the whole in motion, and this is their nature. Thus, the cosmos is an organized whole, a single substance directed to the good; this body constitutes together with its Prime Mover a composite substance that can be regarded as a self-mover.

Après avoir consacré à Descartes de nombreuses études, parmi lesquelles les monumentales L’homme des passions (Albin Michel, 1995) et Les Méditations métaphysiques de Descartes (PUF, 2005), ainsi que, plus récemment, Le style de Descartes (Manucius, 2013), Denis Kambouchner nous offre Descartes n’a pas dit. Ce livre contient un errata des propos prêtés à Descartes dans l’enseignement, dans les représentations collectives, dans des publications généralistes ou même dans certains travaux spécialisés, et propose de corriger quelques-unes des erreurs les plus sérieuses. D’après (...) Kambouchner, la philosophie cartésienne, en réalité très nuancée et raffinée, est régulièrement victime de simplifications excessives. (shrink)

Throughout his career, Wundt recognized Völkerpsychologie (VP) as (at first) ancillary to experimental psychology or (later) as its required complement. New scholarship from around 1979 highlighted this fact while claiming to correct a picture of Wundt as a pure associationist, attributed to Boring’s History of Experimental Psychology, by instead emphasizing apperception in Wundt’s scheme (sec. 2). The criticisms of Boring, summarized by Blumenthal in 1980, overshot the mark. Boring’s Wundt was no pure associationist. Both Boring and the seventy-niner historians emphasized (...) psychic activity in Wundt. Section 3 considers Wundt’s endorsements of mental chemistry, elements, association, and psychological explanation via combinations of elements. Section 4 follows Wundt’s changing conceptions of VP; looks into the relations between VP and experiment, especially as regards “higher” mental processes; examines the (sometimes cooperative) interactions between individual (including experimental) psychology and VP; and considers how method, not type of mental process, distinguishes the two branches of psychology. Finally, section 5 acknowledges Wundt’s unification of VP and individual psychology and concludes that although he objected to the Würzburgers’ experimental methods in treating higher mental processes, he did not generally exclude the latter from experimental investigation, contrary to the seventy-niner narrative, which has been widely adopted. (shrink)

This study conducts a detailed friction-based performance analysis of stabilizer bar bush seals through numerical simulations. Utilizing state-of-the-art Finite Element Analysis (FEA) tools, the research aims to evaluate how varying levels of friction coefficients impact the mechanical integrity and functionality of bush seals within automotive stabilizer bars. By systematically altering the friction coefficients from 0.1 to 0.5, the investigation assesses the resulting changes in reaction forces and stress distribution across the seal components. The primary focus is on understanding (...) how different friction settings influence the operational performance of the seals, particularly in terms of wear patterns, durability, and the ability to maintain effective load transmission between the stabilizer bar and its adjoining components. Key performance metrics such as seal deformation, stress resistance, and longevity under cyclic loading conditions are analyzed to provide insights into the optimal frictional properties required for maximizing seal efficiency. The outcomes of this simulation study are expected to offer valuable guidelines for the design and material selection of bush seals, aiming to enhance the overall stability and noise, vibration, and harshness (NVH) characteristics of automotive suspension systems. Recommendations for future research will include exploring the impact of material heterogeneity and geometric modifications on the frictional behavior of stabilizer bar bush seals. This work sets a foundation for advancing the design standards of automotive bush seals by integrating friction considerations into the simulation protocols for component testing. (shrink)

The problem of approximating a propositional calculus is to find many-valued logics which are sound for the calculus (i.e., all theorems of the calculus are tautologies) with as few tautologies as possible. This has potential applications for representing (computationally complex) logics used in AI by (computationally easy) many-valued logics. It is investigated how far this method can be carried using (1) one or (2) an infinite sequence of many-valued logics. It is shown that the optimal candidate matrices for (1) (...) can be computed from the calculus. (shrink)

To obtain effective fusion results of multi source evidences with different importance, an evidence fusion method with importance discounting factors based on neutrosopic probability analysis in DSmT framework is proposed. First, the reasonable evidence sources are selected out based on the statistical analysis of the pignistic probability functions of single focal elements. Secondly, the neutrosophic probability analysis is conducted based on the similarities of the pignistic probability functions from the prior evidence knowledge of the reasonable evidence sources. Thirdly, the (...) importance discounting factors of the reasonable evidence sources are obtained based on the neutrosophic probability analysis and the reliability discounting factors of the real-time evidences are calculated based on probabilistic-based distances. Fourthly, the real-time evidences are discounted by the importance discounting factors and then the evidences with the mass assignments of neutrosophic empty sets are discounted by the reliability discounting factors. Finally, DSmT+PCR5 of importance discounted evidences is applied. Experimental examples show that the decision results based on the proposed fusion method are different from the results based on the existed fusion methods. Simulation experiments of recognition fusion are performed and the superiority of proposed method is testified well by the simulation results. (shrink)

This paper offers a new interpretation of the young Spinoza’s method of distinguishing the true ideas from the false, which shows that his answer to the sceptic is not a failure. This method combines analysis and synthesis as follows: if we can say of the object of an idea which simple things underlie it, how it can be constructed out of simple elements, and what properties it has after it has been produced, doubt concerning the object simply makes (...) no sense. The paper also suggests a way in which this methodology connects to the ontology of the Ethics. (shrink)

I propose a revision of ethical principles. Value-based ethics can be replaced with problem-based ethics. I suggest abandoning ethics that focus on absolute values. Instead, I propose starting with an understanding of the problem of death as the foundation for human development. Good and evil, in this context, are related to the problem of mortality. All issues facing humanity as a global socio-cultural system can be traced back to this central issue. Literally every aspect of our existence - civilizations, religions, (...) communities, nations, groups, families, individuals, and humanity itself - is affected by this fundamental challenge. We can think of Ethics as a universal problem-solving framework that guides humanity towards overcoming this obstacle. This approach to human development does not preclude different paths to achieving this goal. Different communities can pursue different methods to contribute to the collective effort. Diversity will be the hallmark of human progress. (shrink)

Jiangxi is a province in southeast China that is known for its pastoral scenery, which include rice fields, rivers, and mountains. It has traditionally been on important north-south trade routes, with its centre in the valley of the Gan River. The problem of students in learning historical subjects is a big problem. Historical subjects are tough for students to understand. So primary schools in Jiangxi, China are facing some problem to learn history subject. The purpose of this study is to (...) identify children’s preferences on graphic design. Generating design ideas of the preferences identified using participatory design method. As such, this study focuses on how graphic design and its important elements can become instrumental in improving the teaching of those subjects to students allowing the development of various materials which can help in developing that deeper understanding. In this research we will use qualitative research to identify children’s preferences on graphic design in Jiangxi, China. Keywords: Graphic Design, Chinese Historical Subject, Primary Students. (shrink)