The general problem of visual search can be shown to be computationally intractable in a formal, complexity-theoretic sense, yet visual search is extensively involved in everyday perception, and biological systems manage to perform it remarkably well. Complexity level analysis may resolve this contradiction. Visual search can be reshaped into tractability through approximations and by optimizing the resources devoted to visual processing. Architectural constraints can be derived using the minimum cost principle to rule out a large class of potential (...) solutions. The evidence speaks strongly against bottom-up approaches to vision. In particular, the constraints suggest an attentional mechanism that exploits knowledge of the specific problem being solved. This analysis of visual search performance in terms of attentional influences on visual information processing and complexity satisfaction allows a large body of neurophysiological and psychological evidence to be tied together. (shrink)

The arbitrariness of a signal has long been seen as a theoretically important but difficult to pin down notion. In this article, we suggest there are at least two different notions of arbitrariness at play in philosophical and scientific debates concerning the use of arbitrary signals, and work towards improved analyses of both. We then consider how these different types of arbitrariness can co-occur and come apart. Finally, we examine the connections between these two types of arbitrariness and the cognitive (...) complexity of signal users with an eye towards better evaluating one possible form of human-nonhuman communicative continuity. We show that each type of arbitrariness bears its own nuanced relationship to cognitive complexity, demonstrating the theoretical importance of keeping these two notions separate. (shrink)

It is often claimed that one cannot locate a notion of causation in fundamental physical theories. The reason most commonly given is that the dynamics of those theories do not support any distinction between the past and the future, and this vitiates any attempt to locate a notion of causal asymmetry—and thus of causation—in fundamental physical theories. I argue that this is incorrect: the ubiquitous generation of entanglement between quantum systems grounds a relevant asymmetry in the dynamical evolution of quantum (...) systems. I show that by exploiting a connection between the amount of entanglement in a quantum state and the algorithmic complexity of that state, one can use recently developed tools for causal inference to identify a causal asymmetry—and a notion of causation—in the dynamical evolution of quantum systems. (shrink)

In this paper, we investigate the implications that a general view of complexity - i.e. the view that complex phenomena are irreducible - hold for our understanding of ethics. In this view, ethics should be conceived of as constitutive of knowledge and identity, rather than as a normative system that dictates right action. Using this understanding, we elaborate on the ethics of complexity and the complexity of ethics. Whilst the former concerns the nature and the status of (...) our modelling choices, the latter denotes a contingent and recursive understanding of ethics. Although the complexity of ethics cannot be captured in a substantive normative model, we argue that this view of ethics nevertheless commits one to, what we term, ‘the provisional imperative’. Like Kant’s categorical imperative, the provisional imperative is substantively- empty; however, unlike Kant’s imperative, our imperative cannot be used to generate universal ethical principles. As such, the provisional imperative simultaneously demands that we must be guided by it, whilst drawing attention to the exclusionary nature of all imperatives. We further argue that the provisional imperative urges us to adopt a certain attitude with regard to ethical decision-making, and that this attitude is supported and nurtured by provisionality, transgressivity, irony, and imagination. (shrink)

Multinational corporations are operating in complex business environments. They are confronted with contradictory institutional demands that often represent mutually incompatible expectations of various audiences. Managing these demands poses new organizational challenges for the corporation. Conducting an empirical case study at the sportswear manufacturer Puma, we explore how multinational corporations respond to institutional complexity and what legitimacy strategies they employ to maintain their license to operate. We draw on the literature on institutional theory, contingency theory, and organizational paradoxes. The results (...) of our qualitative longitudinal study show that managing corporate legitimacy is a dynamic process in which corporations adapt organizational capacities, structures, and procedures. (shrink)

Let [Formula: see text] be an integer. We show that the set of real numbers that are Poisson generic in base [Formula: see text] is [Formula: see text]-complete in the Borel hierarchy of subsets of the real line. Furthermore, the set of real numbers that are Borel normal in base [Formula: see text] and not Poisson generic in base [Formula: see text] is complete for the class given by the differences between [Formula: see text] sets. We also show that the (...) effective versions of these results hold in the effective Borel hierarchy. (shrink)

This Special Issue addresses a range of educational issues linked to main themes from our 2019 book The Emergence of Complexity: Rethinking Education as a Social Science. This book elaborated two major theses that raise fundamental questions for philosophy of education. First, that learning by groups is typically a distinctive kind of learning that is not reducible to learning by individuals. Second, that a degree of holism, as against a focus on individuals, is essential for achieving a convincing understanding (...) of this distinctive type of group learning. These two theses are of direct interest to philosophy of education since they challenges the resources of received theories of learning. Yet this kind of group learning characterises the vast bulk of human learning situations that occur outside of formal education systems. In this Special Issue introductory article we, firstly, introduce some basic principles of complexity theory, and demonstrate that, together with the concept of a ‘co-present group’ (between 2 and about 12 individuals), these ideas offer develop novel understandings of the distinctive learning that occurs within such groups. Secondly, we outline and illustrate with further examples the main features of co-present groups. Thirdly, we consolidate our conceptual work by showing five ways in which our account of group learning serves to refurbish the concept of ‘learning’. (shrink)

The main claim of this paper is that notions of implementation based on an isomorphic correspondence between physical and computational states are not tenable. Rather, ``implementation'' has to be based on the notion of ``bisimulation'' in order to be able to block unwanted implementation results and incorporate intuitions from computational practice. A formal definition of implementation is suggested, which satisfies theoretical and practical requirements and may also be used to make the functionalist notion of ``physical realization'' precise. The upshot of (...) this new definition of implementation is that implementation cannot distinguish isomorphic bisimilar from non-isomporphic bisimilar systems anymore, thus driving a wedge between the notions of causal and computational complexity. While computationalism does not seem to be affected by this result, the consequences for functionalism are not clear and need further investigations. (shrink)

The concept of disease has been the subject ofa vast, vivid and versatile debate. Categoriessuch as ``realist'', ``nominalist'', ``ontologist'',``physiologist'', ``normativist'' and``descriptivist'' have been applied to classifydisease concepts. These categories refer tounderlying theoretical frameworks of thedebate. The objective of this review is toanalyse these frameworks. It is argued that thecategories applied in the debate refer toprofound philosophical issues, and that thecomplexity of the debate reflects thecomplexity of the concept itself: disease is acomplex concept, and does not easily lenditself to definition.

Over the past decades, the modernization of agriculture in the Western world has contributed not only to a rapid increase in food production but also to environmental and societal concerns over issues such as greenhouse gas emissions, soil quality and biodiversity loss. Many of these concerns, for example those related to animal welfare or labor conditions, are stuck in controversies and apparently deadlocked debates. As a result we observe a paradox in which a wide range of corporate social responsibility initiatives, (...) originally seeking to reconnect agriculture and society, frequently provoke debate, conflict, and protests. In order to make sense of this pattern, the present paper contends that Western agriculture is marked by moral complexity, i.e., the tendency of multiple legitimate moral standpoints to proliferate without the realistic prospect of a consensus. This contention is buttressed by a conceptual framework that draws inspiration the contemporary business ethics and systems-theoretic scholarship. From the systems-theoretic point of view, the evolution of moral complexity is traced back to the processes of agricultural modernization, specialization, and differentiation, each of which suppresses the responsiveness of the economic and legal institutions to the full range of societal and environmental concerns about agriculture. From the business ethics point of view, moral complexity is shown to prevent the transformation of the ethical responsibilities into the legal and economic responsibilities despite the ongoing institutionalization of CSR. Navigating moral complexity is shown to require moral judgments which are necessarily personal and contestable. These judgments are implicated in those CSR initiatives that require dealing with trade-offs among the different sustainability issues. (shrink)

This fascinating popular science journey explores key concepts in information theory in terms of Conway's "Game of Life" program. The author explains the application of natural law to a random system and demonstrates the necessity of limits. Other topics include the limits of knowledge, paradox of complexity, Maxwell's demon, Big Bang theory, and much more. 1985 edition.

Concerns with the use of engineering approaches in biology have recently been raised. I examine two related challenges to biological research that I call the synchronic and diachronic underdetermination problem. The former refers to challenges associated with the inference of design principles underlying system capacities when the synchronic relations between lower-level processes and higher-level systems capacities are degenerate. The diachronic underdetermination problem regards the problem of reverse engineering a system where the non-linear relations between system capacities and lower-level mechanisms are (...) changing over time. Braun and Marom argue that recent insights to biological complexity leave the aim of reverse engineering hopeless - in principle as well as in practice. While I support their call for systemic approaches to capture the dynamic nature of living systems, I take issue with the conflation of reverse engineering with naïve reductionism. I clarify how the notion of design principles can be more broadly conceived and argue that reverse engineering is compatible with a dynamic view of organisms. It may even help to facilitate an integrated account that bridges the gap between mechanistic and systems approaches. (shrink)

This paper starts from the observation that the standard arguments for compositionality are really arguments for the computability of semantics. Since computability does not entail compositionality, the question of what justifies compositionality recurs. The paper then elaborates on the idea of recursive semantics as corresponding to computable semantics. It is then shown by means of time complexity theory and with the use of term rewriting as systems of semantic computation, that syntactically unrestricted, noncompositional recursive semantics leads to computational explosion (...) (factorial complexity). Hence, with combinatorially unrestricted syntax, semantics with tractable time complexity is compositional. (shrink)

The relationship between intelligent systems and their environment is at the forefront of research in cognitive science. The Unexplained Intellect: Complexity, Time, and the Metaphysics of Embodied Thought shows how computational complexity theory and analytic metaphysics can together illuminate long-standing questions about the importance of that relationship. It argues that the most basic facts about a mind cannot just be facts about mental states, but must include facts about the dynamic, interactive mental occurrences that take place when a (...) creature encounters its environment. In a discussion that is organised into four clear parts, Christopher Mole begins by examining the mathematics of computational complexity, arguing that the results from complexity theory create a puzzle about how human intelligence could possibly be explained. Mole then uses the tools of analytic metaphysics to draw a distinction between mental states and dynamic mental entities, and shows that, in order to answer the complexity-theoretic puzzle, dynamic entities must be understood to be among the most basic of mental phenomena. The picture of the mind that emerges has important implications for our understanding of intelligence, of action, and of the mind’s relationship to the passage of time. The Unexplained Intellect is the first book to bring insights from the mathematics of computational complexity to bear in an enquiry into the metaphysics of the mind. It will be essential reading for scholars and researchers in the philosophy of mind and psychology, for cognitive scientists, and for those interested in the philosophical importance of complexity. (shrink)

This volume presents a selection of the Proceedings of the Workshop on Anticipation, Agency and Complexity held in Trento on April 2017. The contributions contained in the book brilliantly revolve around three core concepts: agency, complexity and anticipation, giving precious insights to further define the discipline of anticipation. In a world that moves increasingly fast, constantly on the verge of disruptive events, more and more scholars and practitioners in any field feel in need of new approaches to make (...) sense of the complexity and uncertainty that the future seems to bear. The theory of anticipation tries to describe how possible futures are intrinsically intertwined with the present. (shrink)

Many contemporary philosophers writing on punishment seek to show that much of the dispute between retributionists and utilitarians springs from a failure on the part of both parties to elucidate the concept of punishment. The writers are usually utilitarians who seek to show that what is true in the retributive theory is simply a point about the concept of punishment, and that for the rest, the morality of punishment is to be explained in terms of the utilitarian theory. Those who (...) attempt to destroy the retributive theory by reducing its element of truth to a mere conceptual point about the concept of punishment, seek to argue that the notion of being guilty of an offence is part of the concept of punishment. Against this kind of approach, I wish to consider whether a general theory of punishment is possible, and if so, what are its basic concepts—punishment, deserving of punishment, deserved, or justifiable punishment—and how they are to be elucidated. I shall be concerned to argue that much contemporary writing on punishment commits the Platonic fallacy of assuming that there is a single, core, paradigm use of ‘punishment’ which is to be found by elucidating the concept of legal punishment. (shrink)

Einstein’s razor, a corollary of Ockham’s razor, is often paraphrased as follows: make everything as simple as possible, but not simpler. This rule of thumb describes the challenge that designers of a legal system face—to craft simple laws that produce desired ends, but not to pursue simplicity so far as to undermine those ends. Complexity, simplicity’s inverse, taxes cognition and increases the likelihood of suboptimal decisions. In addition, unnecessary legal complexity can drive a misallocation of human capital toward (...) comprehending and complying with legal rules and away from other productive ends. While many scholars have offered descriptive accounts or theoretical models of legal complexity, most empirical research to date has been limited to simple measures of size, such as the number of pages in a bill. No extant research rigorously applies a meaningful model to real data. As a consequence, we have no reliable means to determine whether a new bill, regulation, order, or precedent substantially effects legal complexity. In this paper, we begin to address this need by developing a proposed empirical framework for measuring relative legal complexity. This framework is based on “knowledge acquisition”, an approach at the intersection of psychology and computer science, which can take into account the structure, language, and interdependence of law. We then demonstrate the descriptive value of this framework by applying it to the U.S. Code’s Titles, scoring and ranking them by their relative complexity. We measure various features of a title including its structural size, the net flow of its intra-title citations and its linguistic entropy. Our framework is flexible, intuitive, and transparent, and we offer this approach as a first step in developing a practical methodology for assessing legal complexity. (shrink)

Let$ \le _c $be computable the reducibility on computably enumerable equivalence relations. We show that for every ceerRwith infinitely many equivalence classes, the index sets$\left\{ {i:R_i \le _c R} \right\}$,$\left\{ {i:R_i \ge _c R} \right\}$, and$\left\{ {i:R_i \equiv _c R} \right\}$are${\rm{\Sigma }}_3^0$complete, whereas in caseRhas only finitely many equivalence classes, we have that$\left\{ {i:R_i \le _c R} \right\}$is${\rm{\Pi }}_2^0$complete, and$\left\{ {i:R \ge _c R} \right\}$ is${\rm{\Sigma }}_2^0$complete. Next, solving an open problem from [1], we prove that the index set of (...) the effectively inseparable ceers is${\rm{\Pi }}_4^0$complete. Finally, we prove that the 1-reducibility preordering on c.e. sets is a${\rm{\Sigma }}_3^0$complete preordering relation, a fact that is used to show that the preordering relation$ \le _c $on ceers is a${\rm{\Sigma }}_3^0$complete preordering relation. (shrink)

Modern mathematical sciences are hard to imagine without appeal to efficient computational algorithms. We address several conceptual problems arising from this interaction by outlining rival but complementary perspectives on mathematical tractability. More specifically, we articulate three alternative characterizations of the complexity hierarchy of mathematical problems that are themselves based on different understandings of computational constraints. These distinctions resolve the tension between epistemic contexts in which exact solutions can be found and the ones in which they cannot; however, contrary to (...) a persistent myth, we conclude that having an exact solution is not generally more epistemologically beneficial than lacking one. (shrink)

With their focus on human production and consumption activities, cities incur massive energy consumption and CO2 emissions. An intercity connection is a typical complex system in which the interaction between cities is crucial for developing low-carbon outputs within the urban agglomeration. This paper presents the construction of the CO2 emission network of an urban agglomeration in the Yangtze River middle reaches megalopolis, based on the gravity model. Combined with social network analysis, a multilevel analysis framework is proposed to deal with (...) the complexity, spatiality, and visualization of the CO2 emission network with reference to the network features, structural equivalence, and the rich-club phenomenon. The following results emerged: firstly, the spatial structure of the CO2 emissions was characterized by low robustness and compactness, indicating disunity among the studied cities. Secondly, there was found to be a strong correlation between regionalism and intercity connections, with geographically close cities playing a similar role in the network. Thirdly, the “rich-club” cities, including Wuhan, Changsha, Xiaogan, and Zhuzhou, dominated the connections, covering more than 87.1% of the network in the Yangtze River Middle Reaches Megalopolis. (shrink)

The study of human behavior is severely hampered by logistical problems, ethical and legal constraints, and funding shortfalls. However, the biggest difficulty of conducting social and behavioral research is the extraordinary complexity of the study phenomena. In this article, we review the impact of complexity on research design, hypothesis testing, measurement, data analyses, reproducibility, and the communication of findings in psychological science. The systematic investigation of the world often requires different approaches because of the variability in complexity. (...) Confirmatory testing, multi-factorial designs, survey methods, large samples, and modeling are frequently needed to study complex social and behavioral topics. Complexity impedes the measurement of general constructs, the reproducibility of results and scientific reporting, and the general rigor of research. Many of the benchmarks established by classic work in physical science are not attainable in studies of more complex phenomena. Consequently, the standards used to evaluate scientific research should be tethered to the complexity of the study topic. (shrink)