Sir Sayyid Ahmad Khan was a prominent South Asian reformer of Islam who focused on the reconciliation of science and Islam in his most influential texts. This article aims to analyze the implications of science becoming the dominant discourse in nineteenth-century South Asia for the conception of Islam and religion in general. Sayyid Ahmad is an intriguing example because he actively participated in religious as well as scientific discourses since as early as the 1830s. After a concise outline of his (...) early writings, his stances toward science and reason shall be compared with his later writings, primarily those written after 1870, to uncover the impact of the increasing influence of science in South Asia during the latter half of the nineteenth century. In his later writings, Sayyid Ahmad accomplishes a complex effort of translation, claiming mutual compatibility of science and Islam. The question of how this influences his conception of Islam and religion will be addressed, exploring whether this process should be described as a mere adoption of foreign discourse? Or does it trigger transformative effects? (shrink)

Dieser Buchtitel ist Teil des Digitalisierungsprojekts Springer Book Archives mit Publikationen, die seit den Anfängen des Verlags von 1842 erschienen sind. Der Verlag stellt mit diesem Archiv Quellen für die historische wie auch die disziplingeschichtliche Forschung zur Verfügung, die jeweils im historischen Kontext betrachtet werden müssen. Dieser Titel erschien in der Zeit vor 1945 und wird daher in seiner zeittypischen politisch-ideologischen Ausrichtung vom Verlag nicht beworben.

This article attempts to clarify and critically to discuss some variants of the sociological Interpretation of regularities in social action. The widely held view that the concept of norm yields the decisive approach to a specifically sociological understanding of behavioural regularities is placed in opposition to Weber’s reflections on the basic concepts of sociology. Weber from the start reserves room for an utility - and interestoriented component of explanation, apart from the concept of norm and in principle not less important. (...) In this connection the article also works out and criticises Parsons' attempt to ‘integrate’ Weber's sociology into a normativistic conception of the discipline. As o consequence of this criticism the author stresses the value of using the concept of norm - and also tho of rule - in o more differentiated fashion. In particular we should distinguish clearly between on the one hand norms, or rules with obligatory components, and on the other utility- or means -ends-oriented rules, followed in the process of furthering one’s own interests. If we neglect this distinction and, like Parsons, subsume o conflation of these concepts under the notion of norm, we run the risk of perceiving any moderately polished and strategically prudent pursuit of an agent’s own interests as a case of norm-governed action. (shrink)

Das zentrale »Spätwerk« von Wilfred Bion, die fiktionale Trilogie »A Memoir of the Future« (1975–1979), wurde im deutschsprachigen psychoanalytischen Diskurs bisher wenig beachtet. Die Rezeption wird zweifellos durch die fehlende Übersetzung, aber auch durch die Sperrigkeit und überbordende Komplexität des Werks erschwert. In seiner Trilogie geht es Bion nicht um die Präsentation neuer psychoanalytischer Theorien oder klinischer Fakten, vielmehr ist er darum bemüht, eine Sprache und Form zu finden, die unmittelbare emotionale Erfahrung evoziert. In diesem Erfahrungsbericht sollen in diesem Sinne (...) weniger Inhalte referiert als vielmehr der Versuch einer Untersuchung der Wirkungen, die das Werk im Leser hervorruft, unternommen werden. Das Buch erweist sich als harte Prüfung für die Fähigkeit, Nichtwissen und Nichtverstehen auszuhalten und somit der Verführung zu widerstehen, sich in Altbekanntes zu flüchten und damit das Aufkommen einer tatsächlich neuen Erfahrung zu verhindern. Anhand der detaillierten Analyse eines Kapitels aus dem ersten Band der Trilogie werden die Möglichkeiten der Auseinandersetzung mit dem Werk exemplarisch dargestellt und diskutiert. (shrink)

The independence of research is a key strategic issue of modern societies. Dealing with it appropriately poses legal, economic, political, social and cultural problems for society, which have been studied by the corresponding disciplines and are increasingly the subject of reflexive discourses of scientific communities. Unfortunately, problems of independence are usually framed in disciplinary contexts without due consideration of other perspectives’ relevance or possible contributions. To overcome these limitations, we review disciplinary perspectives and findings on the independence of research and (...) identify interdisciplinary prospects that could inform a research programme. (shrink)

A new advanced systems theory concerning the emergent nature of the Social, Consciousness, and Life based on Mathematics and Physical Analogies is presented. This meta-theory concerns the distance between the emergent levels of these phenomena and their ultra-efficacious nature. The theory is based on the distinction between Systems and Meta-systems (organized Openscape environments). We first realize that we can understand the difference between the System and the Meta-system in terms of the relationship between a ‘Whole greater than the sum of (...) the parts’ and a ‘Whole less than the sum of its parts’, i.e., a whole full of holes (like a sponge) that provide niches for systems in the environment. Once we understand this distinction and clarify the nature of the unusual organization of the Meta-system, then it is possible to understand that there is a third possibility which is a whole exactly equal to the sum of its parts that is only supervenient like perfect numbers. In fact, there are three kinds of Special System corresponding to the perfect, amicable, and sociable aliquot numbers. These are all equal to the sum of their parts but with different degrees of differing and deferring in what Jacques Derrida calls “differance”. All other numbers are either excessive (systemic) or deficient (metasystemic) in this regard. The Special Systems are based on various mathematical analogies and some physical analogies. But the most important of the mathematical analogies are the hypercomplex algebras, which include the Complex Numbers, Quaternions, and Octonions, with the Sedenions corresponding to the Emergent Meta-system. However, other analogies are the Hopf fibrations between hyperspheres of various dimensions, nonorientable surfaces, soliton solutions, etc. These Special Systems have a long history within the tradition since they can be traced back to the imaginary cities of Plato. The Emergent Meta-system is a higher order global structure that includes the System with the three Special Systems as a cycle. An example of this from our tradition is in the Monadology of Gottfried Wilhelm von Leibniz. There is a conjunctive relationship between the System schema and the Special Systems that produce the Meta-system schema cycle. The Special Systems are a meta-model for the relationship between the emergent levels of Consciousness (Dissipative Ordering based on the theory of negative entropy of Prigogine), Living (Autopoietic Symbiotic based on the theory of Maturana and Varela), and Social (Reflexive based on the theory of John O’Malley and Barry Sandywell). These different special systems are related to the various existenitals identified by Martin Heidegger in Being and Time and various temporal reference frames identified by Richard M. Pico. We also relate the special systems to morphodynamic and teleodynamic systems of Terrence Deacon in Incomplete Nature to which we add sociodynamic systems to complete the series of Special Systems. (shrink)

It is shown that a wave vector representing a light pulse in an adiabatically evolving expanding space should develop, after a round trip a geometric phase for helicity states at a given fixed position coordinate of this expanding space. In a section of the Hopf fibration of the Poincaré sphere S2 that identifies a projection to the physically allowed states, the evolution defines a parallel transported state that can be joined continuously with the initial state by means of (...) the associated Berry–Pancharatnam connection. The connection allows to compute an anomaly in the frequency for the vector modes in terms of the scale factor of the space–time background being identical to the reported Pioneer Anomaly. (shrink)

In this paper, a finance system with delay is considered. By analyzing the corresponding characteristic equations, the local stability of equilibrium is established. The existence of Hopf bifurcations at the equilibrium is also discussed. Furthermore, formulas for determining the direction of Hopf bifurcation and the stability of the bifurcating periodic solutions are derived by applying the normal form method and center manifold theorem. Finally, numerical simulation results are presented to validate the theoretical analysis. Numerical simulation results show that (...) delay can lead a stable system into a chaotic state. (shrink)

As far as we know, no notion of concrete fibration is available. We provide one such notion in adherence to the foundational attitude that characterizes the adoption of the fibrational perspective in approaching fundamental subjects in category theory and discuss it in connection with the notion of concrete category and the notions of locally small and small fibrations. We also discuss the appropriateness of our notion of concrete fibration for fibrations of small maps, which is relevant to algebraic (...) set theory. (shrink)

The complex chaotic dynamics and multistability of financial system are some important problems in micro- and macroeconomic fields. In this paper, we study the influence of two-delay feedback on the nonlinear dynamics behavior of financial system, considering the linear stability of equilibrium point under the condition of single delay and two delays. The system undergoes Hopf bifurcation near the equilibrium point. The stability and bifurcation directions of Hopf bifurcation are studied by using the normal form method and central (...) manifold theory. The theoretical results are verified by numerical simulation. Furthermore, one feature of the proposed financial chaotic system is that its multistability depends extremely on the memristor initial condition and the system parameters. It is shown that the nonlinear dynamics of financial chaotic system can be significantly changed by changing the values of time delays. (shrink)

This paper addresses the existence of Hopf bifurcations in a directed acyclic network of neurons, each of them being modeled by a Hindmarsh–Rose neuronal model. The bifurcation parameter is the small parameter corresponding to the ratio of time scales between the fast and the slow dynamics. We first prove that, under certain hypotheses, the single uncoupled neuron can undergo a Hopf bifurcation. Hopf bifurcation occurrences in a directed acyclic network of HR neurons are then discussed. Numerical simulations (...) are carried out to observe these bifurcations and to illustrate the theoretical results. (shrink)

A reaction diffusion system is used to study the interaction between species in a population dynamic system. It is not only used in a population dynamic system with the diffusion phenomenon but also used in physical chemistry, medicine, and animal and plant protection. It has been studied by more and more scholars in recent years. The FitzHugh–Nagumo model is one of the most famous reaction-diffusion models. This article takes a deeper look at a FitzHugh–Nagumo model in a network with time (...) delay. Firstly, we studied the linear stability of the equilibrium, then the existence of Hopf bifurcation is given, and finally, the stability of the Hopf bifurcation is introduced. (shrink)

Limit cycles, because they are constituted of a periodic succession of states (discrete or continuous) constitute a good manner to store information. From any points of the state space reached after a perturbation or stimulation of the cognitive system storing this information, one can aim to join through a more or less long return trajectory a precise neighbourhood of the asymptotic trajectory at a specific moment (or a specific place) on the limit cycle, i.e. where the information of interest stands. (...) We propose that the isochronal fibration, initially imagined and described by A. T. Winfree may be an excellent way to connect directly those two locations. Each isochron is indeed the set of points in temporal phase with one single point of the attractor. The characterisation of the isochronal fibration of various dynamical systems is not easy and until now has principally only been done numerically but not analytically. By integrating the homogeneous solutions of the dynamical system we can solve this fibration in the case of the well known anharmonic pendulum. Other isochronal fibration on classical examples such as the van der Pol system and the non-symmetrical PFK limit cycle are obtained numerically and we also provide the first numerical study on 3-dimentional systems like the anharmonic pendulum with a linear relaxation on its third variable and the Lorenz attractor. The empirical approach seems us useful for dealing with the isochronal fibration which could constitute a powerful tool for understanding and controlling the dynamics of biological or biological-inspired systems. (shrink)

We present a full completeness theorem for the multiplicative fragment of a variant of noncommutative linear logic, Yetter's cyclic linear logic (CyLL). The semantics is obtained by interpreting proofs as dinatural transformations on a category of topological vector spaces, these transformations being equivariant under certain actions of a noncocommutative Hopf algebra called the shuffie algebra. Multiplicative sequents are assigned a vector space of such dinaturals, and we show that this space has as a basis the denotations of cut-free proofs (...) in CyLL + MIX. This can be viewed as a fully faithful representation of a free *-autonomous category, canonically enriched over vector spaces. This paper is a natural extension of the authors' previous work, "Linear Lauchli Semantics", where a similar theorem is obtained for the commutative logic MLL + MIX. In that paper, we interpret proofs as dinaturals which are invariant under certain actions of the additive group of integers. Here we also present a simplification of that work by showing that the invariance criterion is actually a consequence of dinaturality. The passage from groups to Hopf algebras in this paper corresponds to the passage from commutative to noncommutative logic. However, in our noncommutative setting, one must still keep the invariance condition on dinaturals. (shrink)

A novel conservative chaotic system with no equilibrium is investigated in this study. Various dynamics such as the conservativeness, coexistence, symmetry, and invariance are presented. Furthermore, a partial-state feedback control scheme is proposed, and the stable domain of control parameters is analyzed based on the degenerate Hopf bifurcation. In order to verify the numerical simulation analysis, an analog circuit is designed. The simulation results show that the output of the analog circuit system can reproduce the numerical simulation results and (...) verify the correctness of the theoretical analysis. (shrink)

We present a full completeness theorem for the multiplicative fragment of a variant of noncommutative linear logic, Yetter's cyclic linear logic. The semantics is obtained by interpreting proofs as dinatural transformations on a category of topological vector spaces, these transformations being equivariant under certain actions of a noncocommutative Hopf algebra called the shuffie algebra. Multiplicative sequents are assigned a vector space of such dinaturals, and we show that this space has as a basis the denotations of cut-free proofs in (...) CyLL + MIX. This can be viewed as a fully faithful representation of a free *-autonomous category, canonically enriched over vector spaces. This paper is a natural extension of the authors' previous work, "Linear Lauchli Semantics", where a similar theorem is obtained for the commutative logic MLL + MIX. In that paper, we interpret proofs as dinaturals which are invariant under certain actions of the additive group of integers. Here we also present a simplification of that work by showing that the invariance criterion is actually a consequence of dinaturality. The passage from groups to Hopf algebras in this paper corresponds to the passage from commutative to noncommutative logic. However, in our noncommutative setting, one must still keep the invariance condition on dinaturals. (shrink)

We present a short review of the action and coaction of Hopf algebras on Clifford algebras as an introduction to physically meaningful examples. Some q-deformed Clifford algebras are studied from this context and conclusions are derived.

The past two decades have seen an explosion in the methods and directions of neuroscience research. Along with many others, complexity research has rapidly gained traction as both an independent research field and a valuable subdiscipline in computational neuroscience. In the past decade alone, several studies have suggested that psychiatric disorders affect the spatiotemporal complexity of both global and region-specific brain activity (Liu et al., 2013; Adhikari et al., 2017; Li et al., 2018). However, many of these studies have not (...) accounted for the distributed nature of cognition in either the global or regional complexity estimates, which may lead to erroneous interpretations of both global and region-specific entropy estimates. To alleviate this concern, we propose a novel method for estimating complexity. This method relies upon projecting dynamic functional connectivity into a low-dimensional space which captures the distributed nature of brain activity. Dimension-specific entropy may be estimated within this space, which in turn allows for a rapid estimate of global signal complexity. Testing this method on a recently acquired obsessive-compulsive disorder dataset reveals substantial increases in the complexity of both global and dimension-specific activity versus healthy controls, suggesting that obsessive-compulsive patients may experience increased disorder in cognition. To probe the potential causes of this alteration, we estimate subject-level effective connectivity via a Hopf oscillator-based model dynamic model, the results of which suggest that obsessive-compulsive patients may experience abnormally high connectivity across a broad network in the cortex. These findings are broadly in line with results from previous studies, suggesting that this method is both robust and sensitive to group-level complexity alterations. (shrink)

We introduce a homotopy-theoretic interpretation of intuitionistic first-order logic based on ideas from Homotopy Type Theory. We provide a categorical formulation of this interpretation using the framework of Grothendieck fibrations. We then use this formulation to prove the central property of this interpretation, namely homotopy invariance. To do this, we use the result from [8] that any Grothendieck fibration of the kind being considered can automatically be upgraded to a two-dimensional fibration, after which the invariance property is reduced (...) to an abstract theorem concerning pseudonatural transformations of morphisms into two-dimensional fibrations. (shrink)

We present a neuro-geometrical model for generating the shape of Kanizsa's modal subjective contours which is based on the functional architecture of the primary areas of the visual cortex. We focus on V1 and its pinwheel structure and model it as a discrete approximation of a continuous fibration π: R × P → P with base space the space of the retina R and fiber the projective line P of the orientations of the plane. The horizontal cortico-cortical connections of (...) V1 implement what the geometers call the contact structure of the fibration π, and defines therefore an integrability condition which can be shown to correspond to Field's, Hayes', and Hess' psychophysical concept of association field. We present then a variational model of curved modal illusory contours based on the idea that virtual contours are “geodetic” integral curves of the contact structure. (shrink)

We investigate the use of coalgebra to represent quantum systems, thus providing a basis for the use of coalgebraic methods in quantum information and computation. Coalgebras allow the dynamics of repeated measurement to be captured, and provide mathematical tools such as final coalgebras, bisimulation and coalgebraic logic. However, the standard coalgebraic framework does not accommodate contravariance, and is too rigid to allow physical symmetries to be represented. We introduce a fibrational structure on coalgebras in which contravariance is represented by indexing. (...) We use this structure to give a universal semantics for quantum systems based on a final coalgebra construction. We characterize equality in this semantics as projective equivalence. We also define an analogous indexed structure for Chu spaces, and use this to obtain a novel categorical description of the category of Chu spaces. We use the indexed structures of Chu spaces and coalgebras over a common base to define a truncation functor from coalgebras to Chu spaces. This truncation functor is used to lift the full and faithful representation of the groupoid of physical symmetries on Hilbert spaces into Chu spaces, obtained in our previous work, to the coalgebraic semantics. (shrink)

Objective interpretations of probability are usually discussed in two varieties: frequency and propensity accounts. But there is a third, neglected possibility, namely, probabilities as deriving from ranges in suitably structured initial state spaces. Roughly, the probability of an event is the proportion of initial states that lead to this event in the space of all possible initial states, provided that this proportion is approximately the same in any not too small interval of the initial state space. This idea can also (...) be expressed by saying that in the types of situations that give rise to probabilistic phenomena we may expect to find an initial state space such that any "reasonable" density function over this space leads to the same probabilities for the possible outcomes. This "method of arbitrary functions" was introduced by Poincaré, studied and extended by Hopf and more recently by Eduardo Engel, Jan von Plato and Michael Strevens. The natural-range, or method-of-arbitrary-functions approach to probabilities is usually treated as an explanation for the occurrence of probabilistic patterns, whereas I examine its prospects for an objective interpretation of probability, in the sense of providing truth conditions for probability statements that do not depend on our state of mind or information. The main objection to such a proposal is that it is circular, i.e. presupposes the concept of probability, because a measure on the initial state has to be introduced, and density functions over the space are considered. I try to argue that this objection can be successfully met. (shrink)

It is a well-known fact that although the poset of open sets of a topological space is a Heyting algebra, its Heyting implication is not necessarily stable under the inverse image of continuous functions and hence is not a geometric concept. This leaves us wondering if there is any stable family of implications that can be safely called geometric. In this paper, we will first recall the abstract notion of implication as a binary modality introduced in Akbar Tabatabai (Implication via (...) spacetime. In: Mathematics, logic, and their philosophies: essays in honour of Mohammad Ardeshir, pp 161–216, 2021). Then, we will use a weaker version of categorical fibrations to define the geometricity of a category of pairs of spaces and implications over a given category of spaces. We will identify the greatest geometric category over the subcategories of open-irreducible (closed-irreducible) maps as a generalization of the usual injective open (closed) maps. Using this identification, we will then characterize all geometric categories over a given category $${\mathcal {S}}$$ S, provided that $${\mathcal {S}}$$ S has some basic closure properties. Specially, we will show that there is no non-trivial geometric category over the full category of spaces. Finally, as the implications we identified are also interesting in their own right, we will spend some time to investigate their algebraic properties. We will first use a Yoneda-type argument to provide a representation theorem, making the implications a part of an adjunction-style pair. Then, we will use this result to provide a Kripke-style representation for any arbitrary implication. (shrink)

In his postapocalyptic novel, Those Who Remain, G. Michael Hopf (2016) makes an important observation about the effect crises can have on human psychology by noting that "hard times create strong [humans]" (loc. 200). While the catastrophic effects of the recent COVID-19 outbreak are incontestable, there are arguments to be made that the situation itself could be materia prima of a more grounded, and authentic generation of humanity, at least in theory. In this article I draw on Heidegger's early, (...) implicit ethic of finitude as well as his later work surrounding the nature of technology, and place them into dialogue with a global milieu contextualized by worldwide pandemic. I approach this discussion from two different angles: in the first part, I explicate the ethic of finitude, and use it as a framework to describe the observable behavior of communities worldwide in order to better understand how global crises impact the psychical welfare of individual human beings. In the second part, I apply lessons given to us by the later Heidegger, specifically those oriented around the movement away from calculative thinking, in an effort to define a loose, albeit fundamentally ennobling prescriptive aimed at easing the existential strain of the situation we have found ourselves in. *This is a pre-print of an article published in Human Arenas. The final authenticated version is available at DOI: 10.1007/s42087-020-00142-6. (shrink)

This book explores the epistemology and the methodology of political knowledge and social inquiry. What can we know, and how do we know? Friedrich V. Kratochwil and Ted Hopf question all foundational claims of inquiry and envisage science as a self-reflective practice. Brian Pollins and Fred Chernoff accept their arguments to some degree and explore the implications for logical positivism. David A. Waldner, Jack Levy, and Andrew Lawrence address the purpose and methods of research. They debate the role of (...) explanation versus prediction, the relationship of theory to evidence, and their implications for the Democratic Peace research program. A concluding chapter by Mark Lichbach offers a pluralistic reformulation of neopositivism. An alternative conclusion by Steven Bernstein, Richard Ned Lebow, Janice Gross Stein and Steven Weber contends that social science should be modeled on medicine and reformulated as a set of case-based diagnostic tools. The distinguishing feature of the book is the inclusion of authors who represent different approaches to social science and their willingness to engage with one another in a constructive debate. (shrink)

We introduce type-theoretic algebraic weak factorisation systems and show how they give rise to homotopy-theoretic models of Martin-Löf type theory. This is done by showing that the comprehension category associated with a type-theoretic algebraic weak factorisation system satisfies the assumptions necessary to apply a right adjoint method for splitting comprehension categories. We then provide methods for constructing several examples of type-theoretic algebraic weak factorisation systems, encompassing the existing groupoid and cubical sets models, as well as new models based on normal (...) fibrations. (shrink)

This paper presents the nonlinear dynamic analysis of energy-based models arisen from the applied systems characterized by the energy transport in the presence of fractional order derivative and time delay. The studied model is the fractional version of Bianca-Ferrara-Dalgaard-Strulik model of economy which is viewed as a transport network for energy in which the law of motion of capital occurs. By considering the time delay as bifurcation parameter, a proof to investigate the existence of Hopf bifurcation and the phase (...) lock solutions using the Poincare-Linstedt and the harmonic balance methods is given. At definite values of time delay, period-doubling bifurcations followed up by the consequences of chaotic states are detected. Simulation results assure that the BFDS model can generate new chaotic attractors beyond half order derivatives through the effect of the time delay on that system. In accordance with the literatures related to the problem of chaos, the concluded results confirm the proposed theorem by El-Borhamy in which the time delay possesses the ability to change the dynamic state of nonlinear systems from regular to chaotic within the fractional order derivative domain. (shrink)

Logical universalism, a label that has been pinned on to Frege, involves the conflation of two features commonly ascribed to logic: universality and radicality. Logical universality consists in logic being about absolutely everything. Logical radicality, on the other hand, corresponds to there being the one and the same logic that any reasoning must comply with. The first part of this paper quickly remarks that Frege’s conception of logic makes logical universality prevail and does not preclude the admission of different contexts (...) of discourse. The paper then aims to make it clear how Frege’s universalism can make sense of contextuality. Drawing on a suggestion made by Frege in his discussion of Hilbert, it shows that a properly Fregean notion of model can be devised. Taking up a suggestion from Wilfrid Hodges and William Demopoulos that the non-logical constants of a formal language can be compared to indexicals, this paper shows,paceHodges and Demopoulos, that such an understanding of non-logical constants is not beyond Frege’s horizon. A formal framework, based on the modern tool of fibrations, is set out to explain and justify this point. This framework allows one to compare Frege and Tarski, by formalizing Frege’s suggestion and by presenting Tarski’s semantics in a generalized setting. (shrink)

Drawing on Russell's substitutional theory, this paper examines the notion of ‘structured variable’, in order to compare Russell's and Tarski's conceptions of variables. The framework of syntactic fibrations, coming from categorical logic, is used as a common setting. The main objective of this paper is to make sense of the notion of structured variable beyond the context of Russell's theory, to question the Tarskian way of understanding what it is to be a possible value for a variable, and to bring (...) out semantically structured variables as a renewed and fruitful way of conceiving of logical structure. (shrink)