This fine collection of essays by a leading philosopher of science presents a defence of integrative pluralism as the best description for the complexity of scientific inquiry today. The tendency of some scientists to unify science by reducing all theories to a few fundamental laws of the most basic particles that populate our universe is ill-suited to the biological sciences, which study multi-component, multi-level, evolved complex systems. This integrative pluralism is the most efficient way to understand the different and complex (...) processes - historical and interactive - that generate biological phenomena. This book will be of interest to students and professionals in the philosophy of science. (shrink)

This article introduces and defends the “pathological complexity thesis” as a hypothesis about the evolutionary origins of minimal consciousness, or sentience, that connects the study of animal consciousness closely with work in behavioral ecology and evolutionary biology. I argue that consciousness is an adaptive solution to a design problem that led to the extinction of complex multicellular animal life following the Avalon explosion and that was subsequently solved during the Cambrian explosion. This is the economic trade-off problem of having to (...) deal with a complex body with high degrees of freedom, what I call “pathological complexity.” By modeling the explosion of this computational complexity using the resources of state-based behavioral and life history theory we will be able to provide an evolutionary bottom-up framework to make sense of subjective experience and its function in nature by paying close attention to the ecological lifestyles of different animals. (shrink)

"_The Moment of Complexity_ is a profoundly original work. In remarkable and insightful ways, Mark Taylor traces an entirely new way to view the evolution of our culture, detailing how information theory and the scientific concept of complexity can be used to understand recent developments in the arts and humanities. This book will ultimately be seen as a classic."-John L. Casti, Santa Fe Institute, author of _Gödel: A Life of Logic, the Mind, and Mathematics_ The science of complexity accounts for (...) that inscrutable mix of chaos and order that governs our natural world. Complexity explains how networks emerge and function, how species organize into ecosystems, how stars form into galaxies, and how just a few sequences of DNA can account for so many different life forms. Recently, the idea of complexity has taken the worlds of business and politics by storm. The concept is used to account for phenomena as varied as the behavior of the stock market, the response of voting populations, and the effects of risk management. Even Disney has used complexity theory to manage crowd control at its theme parks. Given the startling development of new information technologies, we now live in a moment of unprecedented complexity, an era in which change occurs faster than our ability to comprehend it. With _The Moment of Complexity_, Mark C. Taylor offers a timely map for this unfamiliar terrain opening in our midst, unfolding an original philosophy through a remarkable synthesis of science and culture. According to Taylor, complexity is not just a breakthrough scientific concept, but the defining quality of the post-Cold War era. The flux of digital currents swirling around us, he argues, has created a new network culture with its own distinctive logic and dynamic. Drawing on resources from information theory and evolutionary biology, Taylor explains the operation of complex adaptive systems in social and cultural processes and captures a whole new zeitgeist in the making. To appreciate the significance of our emerging network culture, he claims, we need not only to understand contemporary scientific and technological transformations, but also to explore the subtle influences of art, architecture, philosophy, religion, and higher education. _The Moment of Complexity_, then, is a remarkable work of cultural analysis on a scale rarely seen today. To follow its trajectory is to learn how we arrived at this critical moment in our culture, and to know where we might head in the twenty-first century. (shrink)

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 idea that consciousness and complexity are closely related has been a major driver of the popularity of integrated information theory of consciousness, despite its major formal, phenomenological, and neuroscientific shortcomings. Here, I argue that we can recover this intuition by replacing its biologically neutral notion of complexity with an evolutionary one that I shall dub “pathological complexity.”.

We propose two alternatives to Xu’s axiomatization of Chellas’s STIT. The first one simplifies its presentation, and also provides an alternative axiomatization of the deliberative STIT. The second one starts from the idea that the historic necessity operator can be defined as an abbreviation of operators of agency, and can thus be eliminated from the logic of Chellas’s STIT. The second axiomatization also allows us to establish that the problem of deciding the satisfiability of a STIT formula without temporal operators (...) is NP-complete in the single-agent case, and is NEXPTIME-complete in the multiagent case, both for the deliberative and Chellas’s STIT. (shrink)

In computational complexity theory, decision problems are divided into complexity classes based on the amount of computational resources it takes for algorithms to solve them. In theoretical computer science, it is commonly accepted that only functions for solving problems in the complexity class P, solvable by a deterministic Turing machine in polynomial time, are considered to be tractable. In cognitive science and philosophy, this tractability result has been used to argue that only functions in P can feasibly work as computational (...) models of human cognitive capacities. One interesting area of computational complexity theory is descriptive complexity, which connects the expressive strength of systems of logic with the computational complexity classes. In descriptive complexity theory, it is established that only first-order (classical) systems are connected to P, or one of its subclasses. Consequently, second-order systems of logic are considered to be computationally intractable, and may therefore seem to be unfit to model human cognitive capacities. This would be problematic when we think of the role of logic as the foundations of mathematics. In order to express many important mathematical concepts and systematically prove theorems involving them, we need to have a system of logic stronger than classical first-order logic. But if such a system is considered to be intractable, it means that the logical foundation of mathematics can be prohibitively complex for human cognition. In this paper I will argue, however, that this problem is the result of an unjustified direct use of computational complexity classes in cognitive modelling. Placing my account in the recent literature on the topic, I argue that the problem can be solved by considering computational complexity for humanly relevant problem solving algorithms and input sizes. (shrink)

This paper studies two dual notions in module theory—namely, radicals and socles—from the standpoint of reverse mathematics. We first consider radicals of Z-modules, where the radical of a Z-module M is defined as the intersection of pM={px:x∈M} with p taken from all primes. It shows that ACA0 is equivalent to the existence of radicals of Z-modules over RCA0. We then study socles of modules over commutative rings with identity. The socle of an R-module M is the largest semisimple submodule of (...) M. We show that the existence of socles of modules over a commutative ring with identity is equivalent to ACA0 over RCA0. Vector spaces are semisimple modules over fields. In general, semisimple modules possess nice properties of vector spaces. Lastly, we study characterizations of semisimple modules over commutative rings using techniques of reverse mathematics. (shrink)

(2013). Complexity and Transdisciplinarity: Reflections on Theory and Practice. World Futures: Vol. 69, The Complexity of Life and Lives of Complexity, pp. 200-230.

The complexity approach to political economy suggests that radical uncertainty is a necessary feature of a complex and evolving socioeconomic landscape. Radical uncertainty raises various adaptive challenges that are likely to escalate in the coming decades under the “Fourth Industrial Revolution.” It jeopardizes the wellbeing of ordinary citizens, whose welfare prospects, job opportunities, and income stream are rendered insecure. It also renders precarious the robust implementation of universal human rights, including the right to social security. In fact, it will be (...) argued that human rights cannot be institutionally secured unless they are implemented in a “complexity aware” way that takes account of the uncertainty of the socioeconomic order. In particular, in order to better protect the dignity of rights holders, and to allow them to survive and thrive in the face of radical uncertainty, governments ought to explore various institutional alternatives to existing schemes. It will be suggested that most existing conditional welfare policies systematically fall short of complexity-aware institutional implementation to the extent that they rely on unreasonable assumptions regarding the availability of salient technocratic control over the complex socioeconomic order. Some economists and philosophers have suggested that UBI (Universal Basic Income) might be a viable way to implement the right to social security today. I propose that some of UBI’s most ethically and economically controversial features, such as unconditionality and universality, appear relatively appealing in light of the complexity perspective. In the absence of better alternatives, UBI might even be a requirement of a robust implementation of the human right to social security – a right that welfare states are already committed to on the level of ideal theory but predictably fail to respect in practice due to policy incoherence. However, open questions remain about whether UBI can be transformed from an ideal model into a pragmatic policy. (shrink)

In their simplest form, hybrid languages are propositional modal languages which can refer to states. They were introduced by Arthur Prior, the inventor of tense logic, and played an important role in his work: because they make reference to specific times possible, they remove the most serious obstacle to developing modal approaches to temporal representation and reasoning. However very little is known about the computational complexity of hybrid temporal logics.In this paper we analyze the complexity of the satisfiability problem of (...) a number of hybrid temporal logics: the basic hybrid language over transitive trees; nominal Until logic; and referential interval logic. We discuss the effects of including nominals, the @ operator, the somewhere modality E, and the difference operator D. Adding nominals to tense logic leads for several frame-classes to an increase in complexity of the satisfiability problem from PSPACE to EXPTIME. On transitive trees, however, the satisfiability problem for this language can be decided in PSPACE. Along the way we make a detour through hybrid propositional dynamic logic: we establish upper bounds for a number of temporal logics by generalizing results due to Passy and Tinchev [29] and De Giacomo [16]. We conclude with some remarks on the relevance of our results to description logic, and draw attention to the utility of the spypoint technique for proving upper and lower bounds. (shrink)

Many scholars have conducted in-depth research on the evaluation and prediction of scholars’ scientific impact and meanwhile discovered various factors that affect the success of scholars. Among all these relevant factors, scholars’ ages have been universally acknowledged as one of the most important factors for it can shed light on many practical issues, e.g., finding supervisors, discovering rising stars, and research funding or award applications. However, due to the inaccessibility or the privacy issues of acquiring scholars’ personal data, there is (...) little research to explore the true ages of scholars currently. Alternatively, scholars’ publications’ information can be obtained through various digital libraries. Inspired by this fact, we propose a novel scholar’s age prediction method based on their articles’ information. Our method first classifies factors that affect scholars’ ages into intuitive and complex types according to their computational complexity and then apply machine learning algorithms to predict the ages of scholars based on these factors. The experimental results on the real dataset demonstrate that our method can effectively predict the true ages of scholars. Given that there is no completely accurate dataset because of the continuous publication of academic papers, we then apply our method on the incomplete dataset. Nevertheless, our method still has high prediction accuracy in such situations. (shrink)

Angelaki, Volume 17, Issue 2, Page 169-176, June 2012.

A t-tautology is a propositional formula which is a tautology in all fuzzy logics defined by continuous triangular norms. In this paper we show that the problem of recognizing t-tautologies is coNP complete, and thus decidable.

Some things look more complex than others. For example, a crenulate and richly organized leaf may seem more complex than a plain stone. What is the nature of this experience—and why do we have it in the first place? Here, we explore how object complexity serves as an efficiently extracted visual signal that the object merits further exploration. We algorithmically generated a library of geometric shapes and determined their complexity by computing the cumulative surprisal of their internal skeletons—essentially quantifying the (...) “amount of information” within each shape—and then used this approach to ask new questions about the perception of complexity. Experiments 1–3 asked what kind of mental process extracts visual complexity: a slow, deliberate, reflective process (as when we decide that an object is expensive or popular) or a fast, effortless, and automatic process (as when we see that an object is big or blue)? We placed simple and complex objects in visual search arrays and discovered that complex objects were easier to find among simple distractors than simple objects are among complex distractors—a classic search asymmetry indicating that complexity is prioritized in visual processing. Next, we explored the function of complexity: Why do we represent object complexity in the first place? Experiments 4–5 asked subjects to study serially presented objects in a self‐paced manner (for a later memory test); subjects dwelled longer on complex objects than simple objects—even when object shape was completely task‐irrelevant—suggesting a connection between visual complexity and exploratory engagement. Finally, Experiment 6 connected these implicit measures of complexity to explicit judgments. Collectively, these findings suggest that visual complexity is extracted efficiently and automatically, and even arouses a kind of “perceptual curiosity” about objects that encourages subsequent attentional engagement. (shrink)

Poststructuralism and complexity are plural and diverse modes of thought that share a common subscription to the `anteriority of radical relationality'. They nonetheless subscribe to a different ethic of life because they address the anteriority of radical relationality in different ways. Complexity remains strategic in its bid to become a power-knowledge of the laws of becoming. It derives that strategic ethic from its scientific interest in the implicate order of non-linearity that is said to subvert Newtonian science. Poststructuralism is poetic. (...) It derives its poetic ethic from Heidegger and from the reworking of orphic and tragic sensibilities to radical relationality with the radically non-relational. Observing that all poetry is complexity avant la lettre, the article illustrates these points with the Odyssey and concludes that while complexity is ultimately concerned with fitness, poststructuralism is preoccupied with justice. (shrink)

Biological systems exhibit complexity at all levels of organization. It has recently been argued by Michael Behe that at the biochemical level a type of complexity exists--irreducible complexity--that cannot possibly have arisen as the result of natural, evolutionary processes and must instead be the product of (supernatural) intelligent design. Recent work on self-organizing chemical reactions calls into question Behe's analysis of the origins of biochemical complexity. His central interpretative metaphor for biochemical complexity, that of the well-designed mousetrap that ceases to (...) function if critical parts are absent, is undermined by the observation that typical biochemical systems exhibit considerable redundancy and overlap of function. Real biochemical systems, we argue, manifest redundant complexity--a characteristic result of evolutionary processes. (shrink)

Veit’s central claims are, first, that the function of valenced consciousness is to deal with pathological complexity, and, second, that pathological complexity is a trade-off problem associated with maximizing fitness. I argue that Veit’s hints about what pathological complexity amounts to pull in conflicting directions, and that the specific contribution of consciousness to dealing with a computational problem is under-motivated.

Following Marr’s famous three-level distinction between explanations in cognitive science, it is often accepted that focus on modeling cognitive tasks should be on the computational level rather than the algorithmic level. When it comes to mathematical problem solving, this approach suggests that the complexity of the task of solving a problem can be characterized by the computational complexity of that problem. In this paper, I argue that human cognizers use heuristic and didactic tools and thus engage in cognitive processes that (...) make their problem solving algorithms computationally suboptimal, in contrast with the optimal algorithms studied in the computational approach. Therefore, in order to accurately model the human cognitive tasks involved in mathematical problem solving, we need to expand our methodology to also include aspects relevant to the algorithmic level. This allows us to study algorithms that are cognitively optimal for human problem solvers. Since problem solving methods are not universal, I propose that they should be studied in the framework of enculturation, which can explain the expected cultural variance in the humanly optimal algorithms. While mathematical problem solving is used as the case study, the considerations in this paper concern modeling of cognitive tasks in general. (shrink)

Increasingly organizations have dedicated systems and personnel (recipients) to receive and handle internal whistleblower reports. Yet, the complexity of handling whistleblower reports is often underestimated, and there is a dearth of literature that attempts to describe or analyse the challenges internal recipients face. This paper uses an agency theory inspired lens to provide insight into the complexity of internal whistleblowing, with the aim to identify focal points for improving internal whistleblowing processes. We conceive of internal recipients as agents of two (...) principals in the event of whistleblowing: owner/top management as well as whistleblowers. We identify sources of agency problems and agency costs within these double-agent relationships. We provide avenues for solving these problems and reducing the agency costs. We close by offering paths for future research. (shrink)

Complexity science is an investigative framework that stems from a number of tried and tested disciplines—including systems theory, nonlinear dynamical systems theory, and synergetics—and extends a common set of concepts, methods, and principles to understand how natural systems operate. By quantitatively employing concepts, such as emergence, nonlinearity, and self‐organization, complexity science offers a way to understand the structures and operations of natural cognitive systems in a manner that is conceptually compelling and mathematically rigorous. Thus, complexity science both transforms understandings of (...) cognition and reframes more traditional approaches. Consequently, if cognitive systems are indeed complex systems, then cognitive science ought to consider complexity science as a centerpiece of the discipline. (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)

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.

In many simple integral domains, such as Z or Z[i], there is a straightforward procedure to determine if an element is prime by simply reducing to a direct check of finitely many potential divisors. Despite the fact that such a naive approach does not immediately translate to integral domains like Z[x] or the ring of integers in an algebraic number field, there still exist computational procedures that work to determine the prime elements in these cases. In contrast, we will show (...) how to computably extend Z in such a way that we can control the ordinary integer primes in any Π20 way, all while maintaining unique factorization. As a corollary, we establish the existence of a computable unique factorization domain such that the set of primes is Π20-complete in every computable presentation. (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)

In this paper I discuss how, given the complexity of biological systems, reliance on theoretical models in the development and testing of biological theories leads to an uncomfortable form of anti-realism. I locate the source of this discomfort in the uniqueness and hence diversity of biological phenomena, in contrast with the simplicity and uniformity of the subject matter of physics. I have argued elsewhere that the use of theoretical models creates an unresolvable tension between the explanatory strength and predictive power (...) of hypotheses, and I review this argument again here. My discussion parallels that of Nancy Cartwright, who claims that the use of ceteris paribus laws in physics creates an antagonism between truth and explanation that requires theoretical models to figure centrally in scientific explanation, thereby precluding realism. I argue instead that in biology it is the use of theoretical models that creates this conflict, and conclude that adequate biological explanation cannot rely on the modeling approach alone. Finally, I claim that if we accept the semantic view of theories, which makes theoretical models an integral part of our conception of theories, we must accept anti-realism as well. (shrink)

We prove that the sets of standard tautologies of predicate Product Logic and of predicate Basic Logic, as well as the set of standard-satisfiable formulas of predicate Basic Logic are not arithmetical, thus finding a rather satisfactory solution to three problems proposed by Hájek in [H01].