We analyse a recent paper in which an alleged devastating criticism of the so called GRW proposal to account for the objectification of the properties of macroscopic systems has been presented and we show that the author has not taken into account the precise implications of the GRW theory. This fact makes his conclusions basically wrong. We also perform a survey of measurement theory aimed to focus better on the physical and the conceptual aspects of the so-called macro-objectification problem.

The formulation of a relativistic theory of state-vector reduction is proposed and analyzed, and its conceptual consequences are elucidated. In particular, a detailed discussion of stochastic invariance and of local and nonlocal aspects at the level of individual systems is presented.

Inspired by possible connections between gravity and foundational question in quantum theory, we consider an approach for the adaptation of objective collapse models to a general relativistic context. We apply these ideas to a list of open problems in cosmology and quantum gravity, such as the emergence of seeds of cosmic structure, the black hole information issue, the problem of time in quantum gravity and, in a more speculative manner, to the nature of dark energy and the origin of (...) the very special initial state of the universe. We conclude that objective collapse models offer a rather promising path to deal with all of these issues. (shrink)

We present the idea of searching for X-rays as a signature of the mechanism inducing the spontaneous collapse of the wave function. Such a signal is predicted by the continuous spontaneous localization theories, which are solving the “measurement problem” by modifying the Schrödinger equation. We will show some encouraging preliminary results and discuss future plans and strategy.

The problem of getting a relativistic generalization of the CSL dynamical reduction model, which has been presented in part I, is discussed. In so doing we have the opportunity to introduce the idea of a stochastically invariant theory. The theoretical model we present, that satisfies this kind of invariance requirement, offers us the possibility to reconsider, from a new point of view, some conceptually relevant issues such as nonlocality, the legitimacy of attributing elements of physical reality to physical (...) systems and the problem of establishing causal relations between physical events. (shrink)

In this part we will consider recent attempts to get a relativistic CSL theory. The problem of getting such a generalization, or at least of making plausible that it exists, is of great interest. J. Bell (1990), after having expressed his dissatisfaction with the fundamental lack of precision of the standard formulation of quantum mechanics and the opinion that the only available acceptable alternatives are the Pilot Wave and the Spontaneous Localization schemes has stated: The big question, in my opinion, (...) is which, if either, of these two precise pictures can be redeveloped in a Lorentz invariant way. The point of view of this paper is that what is most interesting is not a detailed exposition of the formal aspects of the generalization, but some crucial conceptual points which have come into focus in this attempt. (shrink)

In view of the arguments put forward by Clifton and Monton [this volume], we reconsider the alleged conflict of dynamical reduction models with the enumeration principle. We prove that our original analysis of such a problem is correct, that the GRW model does not meet any difficulty and that the reasoning of the above authors is inappropriate since it does not take into account the correct interpretation of the dynamical reduction theories.

In view of the arguments put forward by Clifton and Monton [this volume], we reconsider the alleged conflict of dynamical reduction models with the enumeration principle. We prove that our original analysis of such a problem is correct, that the GRW model does not meet any difficulty and that the reasoning of the above authors is inappropriate since it does not take into account the correct interpretation of the dynamical reduction theories.

In view of the arguments put forward by Clifton and Monton [this volume], we reconsider the alleged conflict of dynamical reduction models with the enumeration principle. We prove that our original analysis of such a problem is correct, that the GRW model does not meet any difficulty and that the reasoning of the above authors is inappropriate since it does not take into account the correct interpretation of the dynamical reduction theories.

The contradictions between food poverty affecting a large section of the global population and the everyday wastage of food, particularly in high income countries, have raised significant academic and public attention. All actors in the food chain have a role to play in food waste prevention and reduction, including farmers, food manufacturers and processors, caterers and retailers and ultimately consumers. Food surplus redistribution is considered by many as a partial solution to food waste reduction and food poverty mitigation, (...) while others criticize charitable initiatives as inadequate responses, that inhibit governments from responsibly protecting the citizens right to food. This paper frames food assistance as “hybrid systems”, situating at the intersection of territorial food, public welfare and third sector voluntary systems. Based on available literature and reflections on previous research examining food banks in Italy, we develop a system dynamics conceptual mapping. The aim is to model a set of relations and dynamic mechanisms associated with variables relevant to food waste generation, food recovery for social purposes and food poverty alleviation. The analysis of feedback interactions highlights the vulnerabilities of food assistance systems that occur when addressing food poverty by reducing food surplus. In summary, as the awareness on food poverty and food surplus arises, incentives to food recovery and redistribution strengthen the role of food assistance actors, increasing their exposure to drivers of change, such as retailers’ standards for food surplus prevention. This paper contributes to the current academic debate on charitable food assistance, with insights for policy makers and other systems’ actors. (shrink)

After more than 70 years of debate about the difficulties that one encounters in working out a coherent view of physical processes based on the standard formulation of quantum mechanics, there is now a widespread belief that such difficulties do not arise from philosophical prejudices but represent precise mathematical and physical challenges which call for a physical solution. As J.S. Bell appropriately stated1 “the way ahead is unromantic in that it requires mathematical work by theoretical physicists, rather than interpretations by (...) philosophers”. It is also encouraging, for those who share this position, to see that now there are explicit proposals indicating possible ways out in which the process of measurement is analysed not in terms of vague assertions or resorting to ill-defined and/or contradictory dualistic evolution processes but in terms of more fundamental physical concepts. In particular, approaches of this kind, which S. Goldstein3 has appropriately denoted as “observer-free formulations of quantum mechanics”, can be grouped in three categories: the pilot-wave theories: the decoherent histories and the spontaneous localization models. (shrink)

This paper introduces DEMO, a Dynamic Epistemic Modelling tool. DEMO allows modelling epistemic updates, graphical display of update results, graphical display of action models, formula evaluation in epistemic models, translation of dynamic epistemic formulas to PDL formulas, and so on. The paper implements the reduction of dynamic epistemic logic [16, 2, 3, 1] to PDL given in [12]. The reduction of dynamic epistemic logic to automata PDL from [24] is also discussed and implemented. Epistemic models (...) are minimized under bisimulation, and update action models are minimized under action emulation (the appropriate structural notion for having the same update effect, cf. [13]). The paper is an exemplar of tool building for epistemic update logic. It contains the full code of an implementation in Haskell [22], in ‘literate programming’ style [23], of DEMO. (shrink)

With reference to recently proposed theoretical models accounting for reduction in terms of a unified dynamics governing all physical processes, we analyze the problem of working out a worldview accommodating our knowledge about natural phenomena. We stress the relevant conceptual differences between the considered models and standard quantum mechanics. In spite of the fact that both theories describe systems within a genuine Hilbert space framework, the peculiar features of the spontaneous reduction models limit drastically the (...) states which are dynamically stable. This fact by itself allows one to work out an interpretation of the formalism which makes it possible to give a satisfactory description of the world in terms of the values taken by an appropriately defined mass density function in ordinary configuration space. A topology based on this function and which is radically different from the one characterizing the Hilbert space is introduced, and in terms of it the idea of similarity of macroscopic situations is precisely defined. Finally, the formalism and the interpretation are shown to yield a natural criterion for establishing the psychophysical parallelism. The conclusion is that, within the considered theories and at the nonrelativistic level, one can satisfy all sensible requirements for a completely satisfactory macro-objective description of reality. (shrink)

In 1973, Nickles identified two senses in which the term `reduction' is used to describe the relationship between physical theories: namely, the sense based on Nagel's seminal account of reduction in the sciences, and the sense that seeks to extract one physical theory as a mathematical limit of another. These two approaches have since been the focus of most literature on the subject, as evidenced by recent work of Batterman and Butterfield, among others. In this paper, I discuss (...) a third sense in which one physical theory may be said to reduce to another. This approach, which I call `dynamical systems reduction,' concerns the reduction of individual models of physical theories rather than the wholesale reduction of entire theories, and specifically reduction between models that can be formulated as dynamical systems. DS reduction is based on the requirement that there exist a function from the state space of the low-level model to that of the high-level model that satisfies certain general constraints and thereby serves to identify quantities in the low-level model that mimic the behavior of those in the high-level model - but typically only when restricted to a certain domain of parameters and states within the low-level model. I discuss the relationship of this account of reduction to the Nagelian and limit-based accounts, arguing that it is distinct from both but exhibits strong parallels with a particular version of Nagelian reduction, and that the domain restrictions employed by the DS approach may, but need not, be specified in a manner characteristic of the limit-based approach. Finally, I consider some limitations of the account of reduction that I propose and suggest ways in which it might be generalised. I offer a simple, idealised example to illustrate application of this approach; a series of more realistic case studies of DS reduction is presented in another paper. (shrink)

The purpose of this work is reviewing some reduction results to deal with systems of nonautonomous ordinary differential equations with two time scales. They could be included among the so-called approximate aggregation methods. The existence of different time scales in a system, together with some long-term features, are used to build up a simpler system governed by a lesser number of state variables. The asymptotic behavior of the latter system is then used to describe the asymptotic behaviour of the (...) former one. The reduction results are stated in two particular but important cases: periodic systems and asymptotically autonomous systems. The reduction results are illustrated with the help of simple spatial SIS epidemic models including either periodic or asymptotically autonomous terms. (shrink)

A mechanism describing state reduction dynamics in relativistic quantum field theory is outlined. The mechanism involves nonlinear stochastic modifications to the standard description of unitary state evolution and the introduction of a relativistic field in which a quantized degree of freedom is associated to each point in spacetime. The purpose of this field is to mediate in the interaction between classical stochastic influences and conventional quantum fields. The equations of motion are Lorentz covariant, frame independent, and do not result (...) in divergent behavior. It is shown that the mathematical framework permits the specification of unambiguous local properties providing a connection between the model and evidence of real world phenomena. The collapse process is demonstrated for an idealized example. (shrink)

The received view about emergence and reduction is that they are incompatible categories. I argue in this paper that, contrary to the received view, emergence and reduction can hold together. To support this thesis, I focus attention on dynamical systems and, on the basis of a general representation theorem, I argue that, as far as these systems are concerned, the emulation relationship is sufficient for reduction (intuitively, a dynamical system DS1 emulates a second dynamical (...) system DS2 when DS1 exactly reproduces the whole dynamics of DS2). This representational view of reduction, contrary to the standard deductivist one, is compatible with the existence of structural properties of the reduced system that are not also properties of the reducing one. Therefore, under this view, by no means are reduction and emergence incompatible categories but, rather, complementary ones. (shrink)

We take a logical approach to threshold models, used to study the diffusion of e.g. new technologies or behaviors in social net-works. In short, threshold models consist of a network graph of agents connected by a social relationship and a threshold to adopt a possibly cascading behavior. Agents adopt new behavior when the proportion of their neighbors who have already adopted it meets the threshold. Under this adoption policy, threshold models develop dynamically with a guaranteed fixed point. (...) We construct a minimal dynamic propositional logic to describe the threshold dynamics and show that the logic is sound and complete. We then extend this framework with an epistemic dimension and investigate how information about more distant neighbors’ behaviors allows agents to anticipate changes in behavior of their closer neighbors. It is shown that this epistemic prediction dynamics is equivalent to the non-epistemic threshold model dynamics if and only if agents know exactly their neighbors’ behavior. We further show results regarding fixed points and convergence speed,and provide a partial set of reduction laws, venues for further research, and graphical representations of the dynamics. (shrink)

This chapter describes the application of reduction concepts in emergence and self organization of complex dynamical system. Condition-dependent laws compress and dynamical equation sets provide implicit compressed representations even when most of that information is not explicitly available without decompression. And, paradoxically, there is still the determined march of fundamental analytical dynamics expanding its compression reach toward a Theory of Everything—even while the more rapidly expanding domain of complex systems dynamics confronts its assumptions and its monolithicity. Nor (...) does science fall apart into a disunified aggregate of particular cases since, with fundamental dynamics as a backbone, complex matching up of models across theoretical and empirical domains then articulates its model-structured skeleton. Discussion provides the delicately entwined dance of emergence and reduction providing constraints on compression that also permit its expansion. However, while the vision is not dead, it is currently substantially more complexly structured through model similarities and differences than that initially envisaged and individuals are left with deep questions about compression unresolved. (shrink)

In this work we study the behavior of a time discrete multiregional stochastic model for a population structured in age classes and spread out in different spatial patches between which individuals can migrate. The dynamics of the population is controlled both by reproduction-survival and by migration. These processes take place at different time scales in the sense of the latter being much faster than the former. We incorporate the effect of demographic stochasticity into the population, which results in both dynamics (...) being modelled by multitype Bienaymé–Galton–Watson branching processes. We present a multitype global model that incorporates the effect of both processes and, making use of the existence of different time scales for demography and migration, build a reduced model in which the variables correspond to the total population in each age class. We extend previous results that relate the behavior of the original and the reduced model showing that, given a large enough separation of time scales between demography and migration, we can obtain information about the behavior of the multitype global model through the study of the simpler reduced model. We concentrate on the case where the two systems are supercritical and therefore the expected number of individuals grows to infinity, and show that we can approximate the asymptotic structure of the population vector and the asymptotic population size of the original system through the study of the reduced model. (shrink)

We apply the distinction between parameter independence and outcome independence to the linear and nonlinear models of a recent nonrelativistic theory of continuous state vector reduction. We show that in the nonlinear model there is a set of realizations of the stochastic process that drives the state vector reduction for which parameter independence is violated for parallel spin components in the EPR-Bohm setup. Such a set has an appreciable probability of occurrence (≈ 1/2). On the other hand, (...) the linear model exhibits only extremely small parameter dependence effects. We investigate some specific features of the models and we recall that, as has been pointed out recently, if one wants to be able to speak of definite outcomes (or equivalently of possessed objective elements of reality) at finite times, one has to slightly change the criteria for their attribution to physical systems. The concluding section is devoted to a detailed discussion of the difficulties which one meets when one tries to take, as a starting point for the formulation of a relativistic theory, a nonrelativistic scheme which exhibits parameter dependence. Here we derive a theorem which identifies the precise sense in which the occurrence of parameter dependence forbids a genuinely relativistic generalization. Finally we show how the appreciable parameter dependence of the nonlinear model gives rise to problems with relativity, while the extremely weak parameter dependence of the linear model does not give rise to any difficulty, provided one takes into account the appropriate criteria for the attribution of definite outcomes. (shrink)

Let κ be a singular cardinal. Karp's notion of a chain model of size κ is defined to be an ordinary model of size κ along with a decomposition of it into an increasing union of length cf. With a notion of satisfaction and -isomorphism such models give an infinitary logic largely mimicking first order logic. In this paper we associate to this logic a notion of a dynamic EF-game which gauges when two chain models are chain-isomorphic. To (...) this game is associated a tree which is a tree of size κ with no κ-branches -branches). The measure of how non-isomorphic the models are is reflected by a certain order on these trees, called reduction. We study the collection of trees of size κ with no κ-branches under this notion and prove that when cf = ω this collection is rather regular; in particular it has universality number exactly κ+. Such trees are then used to develop a descriptive set theory of the space cf κ. The main result of the paper gives in the case of κ strong limit singular an exact connection between the descriptive set-theoretic complexity of the chain isomorphism orbit of a model, the reduction order on the trees and winning strategies in the corresponding dynamic EF games. In particular we obtain a neat analog of the notion of Scott watershed from the Scott analysis of countable models. (shrink)

Traffic congestion is a common problem in many countries, especially in big cities. At present, China’s urban road traffic accidents occur frequently, the occurrence frequency is high, the accident causes traffic congestion, and accidents cause traffic congestion and vice versa. The occurrence of traffic accidents usually leads to the reduction of road traffic capacity and the formation of traffic bottlenecks, causing the traffic congestion. In this paper, the formation and propagation of traffic congestion are simulated by using the improved (...) medium traffic model, and the control strategy of congestion dissipation is studied. From the point of view of quantitative traffic congestion, the paper provides the fact that the simulation platform of urban traffic integration is constructed, and a feasible data analysis, learning, and parameter calibration method based on RBF neural network is proposed, which is used to determine the corresponding decision support system. The simulation results prove that the control strategy proposed in this paper is effective and feasible. According to the temporal and spatial evolution of the paper, we can see that the network has been improved on the whole. (shrink)

According to the received view, reduction is a deductive relation between two formal theories. In this paper, I develop an alternative approach, according to which reduction is a representational relation between models, rather than a deductive relation between theories; more specifically, I maintain that this representational relation is the one of emulation. To support this thesis, I focus attention on mathematical dynamical systems and I argue that, as far as these systems are concerned, the emulation relation (...) is sufficient for reduction. I then extend this representational model-based view of reduction to the case of empirically interpreted dynamical systems, as well as to a treatment of partial, approximate, and asymptotic reduction. (shrink)

A longstanding criticism of Ernest Nagel's model of reduction is that it fails to take theory change into account. This criticism builds on the received view that Nagelian reductions are incompatible with theory change. This article challenges the received view by showing that Nagel's model can easily accommodate theory change. Indeed, Nagel's model is essentially static as it only gives unchanging formal and nonformal conditions for reduction; in contrast, theory change belongs to the dynamic history of science; as (...) a result, the application of Nagel's model to scientific knowledge from different historical periods yields a series of Nagelian reductions of different degrees of reductive success. This Nagelian treatment of theory change is illustrated by considering the enterprise of reducing thermodynamics to statistical mechanics in the late nineteenth century. It is also contended that, in handling theory change Nagel's model has greater merits than subsequent models (exemplified by Kenneth Schaffner's general reduction-replacement model). This article concludes by suggesting that Nagel's model of reduction deals with theory change exactly in the same way as logical empiricism does with historicism. (shrink)

As a result of the complexity inherent in some natural systems, mathematical models employed in ecology are often governed by a large number of variables. For instance, in the study of population dynamics we often find multiregional models for structured populations in which individuals are classified regarding their age and their spatial location. Dealing with such structured populations leads to high dimensional models. Moreover, in many instances the dynamics of the system is controlled by processes whose time (...) scales are very different from each other. For example, in multiregional models migration is often a fast process in comparison to the growth of the population.Approximate reduction techniques take advantage of the presence of different time scales in a system to introduce approximations that allow one to transform the original system into a simpler low dimensional system. In this way, the dynamics of the original system can be approximated in terms of that of the reduced system. This work deals with the study of that approximation. In particular, we work with a non-autonomous discrete time model previously presented in the literature and obtain different bounds for the error we incur when we describe the dynamics of the original system in terms of the reduced one. (shrink)

A conventional wisdom about the progress of physics holds that successive theories wholly encompass the domains of their predecessors through a process that is often called reduction. While certain influential accounts of inter-theory reduction in physics take reduction to require a single "global" derivation of one theory's laws from those of another, I show that global reductions are not available in all cases where the conventional wisdom requires reduction to hold. However, I argue that a weaker (...) "local" form of reduction, which defines reduction between theories in terms of a more fundamental notion of reduction between models of a single fixed system, is available in such cases and moreover suffices to uphold the conventional wisdom. To illustrate the sort of fixed-system, inter-model reduction that grounds inter-theoretic reduction on this picture, I specialize to a particular class of cases in which both models are dynamical systems. I show that reduction in these cases is underwritten by a mathematical relationship that follows the broad prescriptions of Nagel/Schaffner reduction, and support this claim with several examples. Moreover, I show that this broadly Nagelian analysis of inter-model reduction encompasses several cases that are sometimes cited as instances of the "physicist's" limit-based notion of reduction. (shrink)

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)

Coherence and correspondence are classical contenders as theories of truth. In this paper we examine them instead as interacting factors in the dynamics of belief across epistemic networks. We construct an agent-based model of network contact in which agents are characterized not in terms of single beliefs but in terms of internal belief suites. Individuals update elements of their belief suites on input from other agents in order both to maximize internal belief coherence and to incorporate ‘trickled in’ elements of (...) truth as correspondence. Results, though often intuitive, prove more complex than in simpler models (Hegselmann & Krause 2002, 2006; Grim, Singer, Reade & Fisher 2015). The optimistic finding is that pressures toward internal coherence can exploit and expand on small elements of truth as correspondence is introduced into epistemic networks. Less optimistic results show that pressures for coherence can also work directly against the incorporation of truth, particularly when coherence is established first and new data is introduced later. (shrink)

We investigate the discrete (finite) case of the Popper–Renyi theory of conditional probability, introducing discrete conditional probabilistic models for knowledge and conditional belief, and comparing them with the more standard plausibility models. We also consider a related notion, that of safe belief, which is a weak (non-negatively introspective) type of “knowledge”. We develop a probabilistic version of this concept (“degree of safety”) and we analyze its role in games. We completely axiomatize the logic of conditional belief, knowledge and (...) safe belief over conditional probabilistic models. We develop a theory of probabilistic dynamic belief revision, introducing probabilistic “action models” and proposing a notion of probabilistic update product, that comes together with appropriate reduction laws. (shrink)

Statements not only update our current knowledge, but also have other dynamic effects. In particular, suggestions or commands ?upgrade' our preferences by changing the current order among worlds. We present a complete logic of knowledge update plus preference upgrade that works with dynamic-epistemic-style reduction axioms. This system can model changing obligations, conflicting commands, or ?regret'. We then show how to derive reduction axioms from arbitrary definable relation changes. This style of analysis also has a product update version with (...) preferences between actions, as well as worlds. Some illustrations are presented involving defaults and obligations. We conclude that our dynamic framework is viable, while admitting a further extension to more numerical ?utility update'. (shrink)

We show how belief revision can be treated systematically in the format of dynamicepistemic logic, when operators of conditional belief are added. The core engine consists of definable update rules for changing plausibility relations between worlds, which have been proposed independently in the dynamic-epistemic literature on preference change. Our analysis yields two new types of modal result. First, we obtain complete logics for concrete mechanisms of belief revision, based on compositional reduction axioms. Next, we show how various abstract postulates (...) for belief revision can be analyzed by standard modal frame correspondences for model-changing operations. (shrink)

I propose a semi-eliminative reduction of Fodors concept of module to the concept of attractor basin which is used in Cognitive Dynamic Systems Theory (DST). I show how attractor basins perform the same explanatory function as modules in several DST based research program. Attractor basins in some organic dynamic systems have even been able to perform cognitive functions which are equivalent to the If/Then/Else loop in the computer language LISP. I suggest directions for future research programs which could find (...) similar equivalencies between organic dynamic systems and other cognitive functions. This type of research could help us discover how (and/or if) it is possible to use Dynamic Systems Theory to more accurately model the cognitive functions that are now being modeled by subroutines in Symbolic AI computer models. If such a reduction of subroutines to basins of attraction is possible, it could free AI from the limitations that prompted Fodor to say that it was impossible to model certain higher level cognitive functions. (shrink)

Although there is a substantial philosophical literature on dynamical systems theory in the cognitive sciences, the same is not the case for neuroscience. This paper attempts to motivate increased discussion via a set of overlapping issues. The first aim is primarily historical and is to demonstrate that dynamical systems theory is currently experiencing a renaissance in neuroscience. Although dynamical concepts and methods are becoming increasingly popular in contemporary neuroscience, the general approach should not be viewed as something (...) entirely new to neuroscience. Instead, it is more appropriate to view the current developments as making central again approaches that facilitated some of neuroscience’s most significant early achievements, namely, the Hodgkin–Huxley and FitzHugh–Nagumo models. The second aim is primarily critical and defends a version of the “dynamical hypothesis” in neuroscience. Whereas the original version centered on defending a noncomputational and nonrepresentational account of cognition, the version I have in mind is broader and includes both cognition and the neural systems that realize it as well. In view of that, I discuss research on motor control as a paradigmatic example demonstrating that the concepts and methods of dynamical systems theory are increasingly and successfully being applied to neural systems in contemporary neuroscience. More significantly, such applications are motivating a stronger metaphysical claim, that is, understanding neural systems as being dynamical systems, which includes not requiring appeal to representations to explain or understand those phenomena. Taken together, the historical claim and the critical claim demonstrate that the dynamical hypothesis is undergoing a renaissance in contemporary neuroscience. (shrink)

Carbon emission has negative externalities, which will cause severe natural and social problems. In recent years, more and more attention has been paid to carbon emission reduction issue both in academic and application fields. This paper aims to explore the impact of punitive carbon tax and incentive carbon emission reduction subsidy on economy and environment through the dynamic stochastic general equilibrium framework. The results show that both carbon tax and carbon emission reduction subsidy policies can help to (...) reduce carbon emissions and to improve environment quality. In addition, carbon emission reduction subsidy has a positive impact on economy, while carbon tax has the opposite impact. It follows that the incentive carbon emission reduction policy is more conducive to the coordinated development of economy and environment. This research can be a guideline for the government to formulate carbon emission abatement policies from the perspective of coordinated development. (shrink)

This essay analyzes and develops recent views about explanation in biology. Philosophers of biology have parted with the received deductive-nomological model of scientific explanation primarily by attempting to capture actual biological theorizing and practice. This includes an endorsement of different kinds of explanation (e.g., mathematical and causal-mechanistic), a joint study of discovery and explanation, and an abandonment of models of theory reduction in favor of accounts of explanatory reduction. Of particular current interest are philosophical accounts of complex (...) explanations that appeal to different levels of organismal organization and use contributions from different biological disciplines. The essay lays out one model that views explanatory integration across different disciplines as being structured by scientific problems. I emphasize the philosophical need to take the explanatory aims pursued by different groups of scientists into account, as explanatory aims determine whether different explanations are competing or complementary and govern the dynamics of scientific practice, including interdisciplinary research. I distinguish different kinds of pluralism that philosophers have endorsed in the context of explanation in biology, and draw several implications for science education, especially the need to teach science as an interdisciplinary and dynamic practice guided by scientific problems and explanatory aims. (shrink)

This thesis is on information dynamics modeled using *dynamic epistemic logic*. It takes the simple perspective of identifying models with maps, which under a suitable topology may be analyzed as *topological dynamical systems*. It is composed of an introduction and six papers. The introduction situates DEL in the field of formal epistemology, exemplifies its use and summarizes the main contributions of the papers.Paper I models the information dynamics of the *bystander effect* from social psychology. It shows how (...) augmenting the standard machinery of DEL with a decision making framework yields mathematically self-contained models of dynamic processes, a prerequisite for rigid model comparison.Paper II extrapolates from Paper I's construction, showing how the augmentation and its natural peers may be construed as maps. It argues that under the restriction of dynamics produced by DEL dynamical systems still falls a collection rich enough to be of interest. Paper III compares the approach of Paper II with *extensional protocols*, the main alternative augmentation to DEL. It concludes that both have benefits, depending on application. In favor of the DEL dynamical systems, it shows that extensional protocols designed to mimic simple, DEL dynamical systems require infinite representations. Paper IV focuses on *topological dynamical systems*. It argues that the *Stone topology* is a natural topology for investigating logical dynamics as, in it, *logical convergence* coinsides with topological convergence. It investigates the recurrent behavior of the maps of Papers II and III, providing novel insigths on their long-term behavior, thus providing a proof of concept for the approach.Paper V lays the background for Paper IV, starting from the construction of metrics generalizing the Hamming distance to infinite strings, inducing the Stone topology. It shows that the Stone topology is unique in making logical and topological convergens coinside, making it the natural topology for logical dynamics. It further includes a metric-based proof that the hitherto analyzed maps are continuous with respect to the Stone topology. Paper VI presents two characterization theorems for the existence of *reduction laws*, a common tool in obtaining complete dynamic logics. In the compact case, continuity in the Stone topology characterizes existence, while a strengthening is required in the non-compact case. The results allow the recasting of many logical dynamics of contemporary interest as topological dynamical systems. (shrink)

In this work, our aim is to investigate the impact of a non-Kolmogorov predator-prey-subsidy model incorporating nonlinear prey refuge and the effect of fear with Holling type II functional response. The model arises from the study of a biological system involving arctic foxes, lemmings, and seal carcasses. The positivity and asymptotically uniform boundedness of the solutions of the system have been derived. Analytically, we have studied the criteria for the feasibility and stability of different equilibrium points. In addition, we have (...) derived sufficient conditions for the existence of local bifurcations of codimension 1. It is also observed that there is some time lag between the time of perceiving predator signals through vocal cues and the reduction of prey’s birth rate. So, we have analyzed the dynamical behaviour of the delayed predator-prey-subsidy model. Numerical computations have been performed using MATLAB to validate all the analytical findings. Numerically, it has been observed that the predator, prey, and subsidy can always exist at a nonzero subsidy input rate. But, at a high subsidy input rate, the prey population cannot persist and the predator population has a huge growth due to the availability of food sources. (shrink)

We investigate, in a logical setting, the expressivist proposal that assertion primarily functions to express and coordinate doxastic states and that ‘might’ fundamentally expresses lack of belief. We provide a formal model of an agent’s doxastic state and novel assertability conditions for an associated formal language. We thereby prove that an arbitrary assertion always succeeds in expressing a well-defined doxastic state, and propose a fully general and intuitive update operation as a model of an agent coming to accept an arbitrary (...) assertion. Leaving a comprehensive philosophical and linguistic defense for elsewhere, we explore technical aspects of our framework, providing, for instance, a complete logic of assertability and reduction axioms for the novel update operations related to our proposal. Finally, we contrast our work with related proposals in the logic literature. (shrink)

To model the organization of levels' of cortical dynamics, at least some general scheme for hierarchy, functional diversity, and proper intrinsic control must be provided. Rhythmic control forces the system to iterate its state by short trajectories, which makes it much more stable and predictable without discarding the desirable ability of chaotic systems to make rapid phase transitions. Rhythmic control provides a fundamentally different systems dynamics, one not provided by models that allow the emergence of continuous trajectories in the (...) systems state space. (shrink)

In this paper we reconsider the constraints which are imposed by relativistic requirements to any model of dynamical reduction. We review the debate on the subject and we call attention on the fundamental contributions by Aharonov and Albert. Having done this we present a new formulation, which is much simpler and more apt for our analysis, of the proposal put forward by these authors to perform measurements of nonlocal observables by means of local interactions and detections. We take (...) into account recently proposed relativistic models of dynamical reduction and we show that, in spite of some mathematical difficulties related to the appearence of divergences, they represent a perfectly appropriate conceptual framework which meets all necessary requirements for a relativistic account of wave packet reduction. Subtle questions like the appropriate way to deal with counterfactual reasoning in a relativistic and nonlocal context are also analyzed in detail. (shrink)

Whether financial inclusion and economic growth can sustainably release poverty alleviation effects in long term has been the focus of academia and government sector. This article uses provincial panel data from 2004 to 2019 to examine the dynamic nonlinear connectedness between the financial inclusion, economic growth, income inequality, and poverty alleviation; the main objective is to reveal the direction and intensity of the long-term and short-term impact of each factor on poverty alleviation. By building a panel vector autoregression model, the (...) comparison analyses of national, eastern, central, and western sample groups verify the existence of dynamic nonlinear connectedness among the four variables. The study found that there is complex bidirectional causality between these variables, financial inclusion has the long-term impact on promoting poverty alleviation in China, the impact of economic growth is relatively weak, and income inequality has weakened the positive impact of financial inclusion on poverty alleviation. Through the analysis of impulse response function, variance decomposition, and time-varying nonparametric estimates in different economic regions, we find that the impact of financial inclusion on poverty alleviation presents a U-shaped characteristic, and the contribution of financial inclusion to poverty alleviation in western regions is significant, but poverty reduction in eastern and central region mainly depends on economic growth. For policymakers, financial inclusion can be an effective way to alleviate relative poverty, but the poverty governance should focus more on reducing income inequality in China. (shrink)

The aim of this essay is a criticism of reductionism ? both in its ?static? interpretation (usually referred to as the layer model or level?picture of science) and in its ?dynamic? interpretation (as a theory of the growth of scientific knowledge), with emphasis on the latter ? from the point of view of Popperian fallibilism and Feyerabendian pluralism, but without being committed to the idiosyncrasies of these standpoints. In both aspects of criticism, the rejection is based on the proposal of (...) a global alternative. Hummell and Opp's research programme for the reduction of sociology to psychology is used as a starting?point and taken as the primary object of criticism. Following the introductory Section I, Section II analyses the three crucial notions of Hummell and Opp's research programme ? their explications of the notions of ?sociology?, ?psychology? and the concept of reduction itself ? and criticizes the authors? deficient ?logic of reduction?. Although the ?local? shortcomings of our authors? ?logic of reduction? do not affect reductionism as such, i.e. logically sound versions of reductionism as devised by Kemeny, Nagel, Oppenheim, Putnam, Woodger et al., it is argued that the logical soundness of sophisticated reductionism cannot compensate for its additional epistemological and methodological deficiencies. Section III analyses the ?dynamic? interpretation of reductionism as a particular developmental pattern of scientific growth. It is argued that even reductionism at its best can produce only cumulative progress, thus ?a priori? excluding scientific revolutions which are inevitably counter?inductive as well as counter?reductive. Section IV discusses the philosophical background of modern reductionism, and examines the effects both of reductionism and of anti?reductionistic pluralism on the autonomy of scientific fields. It is argued that pluralistic anti?reductionism undermines spurious claims for autonomy much more effectively than reductionism. As a ?local? improvement of the reductionistic research programme, the replacement of the predominant one?way reductionism by a less restrictive many?way reductionism is proposed. It is argued that the appropriate treatment for an allegedly backward science (say sociology) is not its reduction to an allegedly more advanced science (say psychology) but its non?reductive replacement by new theories (of the same or of another field) that do not incorporate the older ones. As a ?global? alternative to the reduction of sociology to psychology, the frontier?crossing direct application of psychological theories to sociological phenomena is proposed. A plea is made for a pluralistic science without reduction, based on intra? and interscientific criticism as the proper method for the advancement of knowledge. (shrink)

In lieu of an abstract, here is a brief excerpt of the content:Philosophy, Psychiatry, & Psychology 12.3 (2005) 229-234 [Access article in PDF] Nonlinear Dynamics at the Cutting Edge of Modernity: A Postmodern View Gordon Globus Keywords nonlinear dynamics, modernity, postmodernity, quantum brain theory, free will, self-organization, autopoiesis, autorhoesis Although nonlinear dynamical conceptu-alizations have been applied to psychia-try for over 20 years,1 they have not had significant impact on the field. Unfortunately Heinrichs' very thoughtful contribution to the discussion is (...) unlikely to move such disinterest. Pragmatically successful paradigms in the phase of Kuhnian "normal science" are highly resistant to change. There is no crisis that besets triumphalist biological psychiatry that might lead to clinical or scientific revolution. At the same time, as I suggest at the end of this commentary, the ideas of nonlinear dynamics may not be revolutionary enough, remaining staunchly within the framework of modernity.In what follows I discuss four issues related to Heinrichs' article. First, I try to enrich his presentation of nonlinear dynamics by bringing in the role of self-organization in the evolution of nonlinear dynamical brain systems and by making the nonlinear dynamics "tunable." Second, I discuss whether Heinrichs succeeds in avoiding the dualism of the biopsychosocial model that he criticizes. Third, I look at the issue of "free will," which Heinrichs would understandably like to avoid. Finally, I mention a new form of dynamics, namely thermofield dynamics, which I think is more promising than nonlinear dynamics. Self-Organizing Self-Tuning Nonlinear Dynamical Systems In the case of psychiatry, we are not considering nonlinear dynamical systems like the weather or an ecosystem, but the brain's neural networks in terms of nonlinear dynamics with all its chaos. There is a principle of such systems of neural networks that Heinrichs does not bring out, although it is extremely important for them. These systems are self-organizing under a Hamiltonian principle of "least energy." To use Hopfield and Tank's (1986) terms, nonlinear dynamical neural networks self-organize toward attractors that minimize the "computational energy" of the system, or for Smolensky (1988), self-organize toward "harmony," or for Globus (1995, 2003), in a Heideggerian vein, self-organize to maximize "belonging-together." In this elaborated framework, rational deliberation is one constraint among many on a self-organizing nonlinear dynamical process. [End Page 229]Heinrichs brings out beautifully the nonlinear dynamical way of thinking clinically. This is not the dynamics of mechanistic psychodynamics, which features psychological forces in vectorial conflict—id versus superego and their compromises—but a flowing evolution of states in which small changes in initial state may have large effects (nonlinearity) on the state trajectory. To live a life is often to feel surprise, which nonlinear dynamics with its chaotic regimes well portrays.But there is a way that classical Freud and nonlinear dynamical neural networks do come together—in the "economics," discharges and conservations of libidinal energy, expenditures and credits in Derrida's (1978) accounting. Heinrichs does not mention this similarity. The economic principles differ between Freud's late nineteenth-century thermodynamics and Heinrichs' late twentieth-century nonlinear dynamics, it is true, but it is all economics.Freud called this economic functioning the "pleasure principle" in which "libido" seeks to discharge its instinctual energy store, reducing the level of instinctual tension. This "primary process" proceeds to an attractor by the quickest, most direct way possible, whereas the "secondary process" defers reduction in instinctual tension, subjecting the primary process to thought. Self-organizing directly to the attractor is the primary process with which the secondary process interferes, introducing deferral.The economy of nonlinear dynamics pictures a "landscape," a variegated topography with peaks and valleys. Each point on the topography represents a state. Peak points are repellors—for example, states in which the phobic object is approached—and the lowest points of the valleys are attractors—for example, obsessions and compulsions. The path of occupied states self-organizes away from repellors and toward attractors. This topography is an energy landscape. Its dynamics spontaneously tends—"self-organizes"—toward least energy/high-constraint satisfaction. Freud's pleasure principle is just the Hamiltonian least energy... (shrink)

Recent computational models of perception conceptualize auditory oddball responses as signatures of a learning process, in line with the influential view of the mismatch negativity as a prediction error signal. Novel MMN experimental paradigms have put an emphasis on neurophysiological effects of manipulating regularity and predictability in sound sequences. This raises the question of the contextual adaptation of the learning process itself, which on the computational side speaks to the mechanisms of gain-modulated prediction error. In this study using electrocorticographic (...) signals, we manipulated the predictability of oddball sound sequences with two objectives: Uncovering the computational process underlying trial-by-trial variations of the cortical responses. The fluctuations between trials, generally ignored by approaches based on averaged evoked responses, should reflect the learning involved. We used a general linear model and Bayesian Model Reduction to assess the respective contributions of experimental manipulations and learning mechanisms under probabilistic assumptions. To validate and expand on previous findings regarding the effect of changes in predictability using simultaneous EEG-MEG recordings. Our trial-by-trial analysis revealed only a few stimulus-responsive sensors but the measured effects appear to be consistent over subjects in both time and space. In time, they occur at the typical latency of the MMN. In space, we found a dissociation between time-independent effects in more anterior temporal locations and time-dependent effects in more posterior locations. However, we could not observe any clear and reliable effect of our manipulation of predictability modulation onto the above learning process. Overall, these findings clearly demonstrate the potential of trial-to-trial modeling to unravel perceptual learning processes and their neurophysiological counterparts. (shrink)

The reduction from Einstein's to Newton's gravitation theories (and intermediate steps) is used to exemplify reduction in physical theories. Both dimensionless and dimensional reduction are presented, and the advantages and disadvantages of each are pointed out. It is concluded that neither a completely reductionist nor a completely antireductionist view can be maintained. Only the mathematical structure is strictly reducible. The interpretation (the model, the central concepts) of the superseded theory T′ can at best only partially be derived (...) directly from the superseding theory T; it is severely constrained by the mathematical structure, and it can involve qualitatively different central terms that cannot be logically related between T and T′. (shrink)

Economics is a culturally and politically powerful and contested discipline, and it has been that way as long as it has existed. For some commentators, economics is the "queen of the social sciences", while others view it as a "dismal science" (and both of these epithets allow for diverse interpretations; see Mäki 2002). Economics is also a discipline that deals with a dynamically complex subject matter and has a tradition of reducing this complexity by using systematic procedures of simplification. Nowadays, (...) these procedures involve for the most part building and using mathematical models (for an overview of the philosophical issues, see Morgan and Knuuttila 2011). In the dominant circles of the discipline, one is not regarded as a serious economist having a professional expert view on any given economic or social issue without having a model about it. Much of the power of the discipline and its characteristic contestations therefore involve models and modelling: the successes and failures of the dismal queen are those of modeling. The issues involved in conomic modeling have been made particularly acute once again by the financial crisis of 2008-2009 and its aftermath: the discipline of economics is among the candidates for the major blame for failure. I will first outline some thoughts about the characteristics disciplinary conventions that guide and constrain modeling in economics. I will then summarize my account of the very ideas of models and modeling. Finally, within the framework of that account, I will highlight some major issues of contestation and sketch the respective notions of potential success and failure in economic modeling with illustrations. These notions are motivated by my subscription to a (flexible and discipline-sensitive) realist philosophy of science (e.g. Mäki 2005). (shrink)

Research on natural and artificial brains is proceeding at a rapid pace. However, the understanding of the essence of consciousness has changed slightly over the millennia, and only the last decade has brought some progress to the area. Scientific ideas emerged that the soul could be a product of the material body and that calculating machines could imitate brain processes. However, the authors of this book reject the previously common dualism—the view that the material and spiritual-psychic processes are separate and (...) require a completely different substance as their foundation. -/- Reductive Model of the Conscious Mind is a forward-thinking book wherein the authors identify processes that are the essence of conscious thinking and place them in the imagined, simplified structure of cells able to memorize and transmit information in the form of impulses, which they call neurons. The purpose of the study is to explain the essence of consciousness to the degree of development of natural sciences, because only the latter can find a way to embed the concept of the conscious mind in material brains. The book is divided into three parts. Part 1 works to convince readers that the emergence of consciousness does not require detailed knowledge of the structure and morphology of the brain, with the exception of some specific properties of the neural network structure that the authors attempt to point out. Part 2 proves that the biological structure of many natural brains fulfills the necessary conditions for consciousness and intelligent thinking. Similarly, Part 3 shows the ways in which artificial creatures imitating natural brains can meet these conditions, which gives great hopes for building artificially intelligent beings endowed with consciousness. Covering topics that include cognitive architecture, the embodied mind, and machine learning, this book is ideal for cognitive scientists, philosophers of mind, neuroscientists, psychologists, researchers, academicians, and advanced-level students. The book can also help to focus the research of linguists, neurologists, and biophysicists on the biophysical basis of postulated information processing into knowledge structures. (shrink)

Chapter V attempts to provide the elements of a solution to the problem of how terms in theoretical sciences acquire their reference. Its proposal is that a theory of reference-acquisition for theoretical terms should acknowledge the fact that what fixes the reference of a theoretical term is typically the embedding theory as a whole, not an austere causal description like 'the item causally responsible for event E.' It is argued that there are epistemic reasons for the existence of this phenomenon, (...) and an attempt is made to show how, by appealing to these reasons, it is nonetheless possible to understand the reference-determining role of theories in such a way that occurrences of a term embedded in incompatible theoretical frameworks can often be interpreted as co-referential. ;Chapter IV is an interlude. It argues for the relevance of the theory of reference to the topic of intertheoretic reduction. It does this by attempting to demonstrate that intertheoretic reduction in the natural sciences requires intertheoretic identities involving theoretical terms, and that making sense of such identities demands a theory of reference-acquisition for theoretical terms. The chapter also argues that the problem of how mathematical terms secure their reference precludes an obvious extension of this model to examples of reduction in mathematics. It further criticizes attempts to make sense of mathematical reductions in terms of concepts of ontological reduction, and it suggests that much recent work on ontological reduction, especially the attempt to exclude all-out 'Pythagorean' reductions, is flawed through its failure to take referential semantics seriously. ;Chapter II contains exposition and criticism of both the descriptivist account of reference and Kripke's version of the 'causal' account of reference. The latter account is represented as a recursive account, with a base clause specifying how terms initially acquire their reference and a recursion clause specifying how the ability to use a term with a certain reference is transmitted to other users . It is argued that the Kripkean formulation of referential intentions at the reference-transmission stage is flawed, in part because the formulation makes his account unable to capture the dynamics of the way in which a person's use of a term may undergo reference-shifts without these shifts in reference being intended. ;The third chapter suggests an alternative account. It motivates and sketches a mixed causal-descriptivist theory speaker's reference, formulated in terms of first-order referential intentions, and then uses this theory to sketch aspects of a mixed causal-descriptivist account of term reference, formulated in terms of second-order intentions to intend the 'right' object . It is argued that such an account provides a plausible solution to a number of problems confronting Kripke's account, including that of unintended reference-shifts. ;This dissertation consists of five chapters whose unifying theme is the theory of term-reference. The first chapter offers an overview and critical comparison of two opposing approaches to the topic of reference: the semantic holism of Quine-Davidson, and the semantic atomism of those who treat reference as a relation that grounds the assignment of truth-conditions to sentences. The chapter argues that the apparent theoretical importance of referential intentions, emphasised in Saul Kripke's work on reference and argued for in detail in chapter III of the dissertation, provides strong support for semantic atomism, since such intentions are used to explain reference-assignments and, indirectly, truth-conditions. (shrink)