one takes to be the most salient, any pair could be judged more similar to each other than to the third. Goodman uses this second problem to showthat there can be no context-free similarity metric, either in the trivial case or in a scientifically ...

Gases reach equilibrium when left to themselves. Why do they behave in this way? The canonical answer to this question, originally proffered by Boltzmann, is that the systems have to be ergodic. This answer has been criticised on different grounds and is now widely regarded as flawed. In this paper we argue that some of the main arguments against Boltzmann's answer, in particular, arguments based on the KAM-theorem and the Markus-Meyer theorem, are beside the point. We then argue that something (...) close to Boltzmann's original proposal is true for gases: gases behave thermodynamic-like if they are epsilon-ergodic, i.e., ergodic on the entire accessible phase space except for a small region of measure epsilon. This answer is promising because there are good reasons to believe that relevant systems in statistical mechanics are epsilon-ergodic. (shrink)

The traditional use of ergodic theory in the foundations of equilibrium statistical mechanics is that it provides a link between thermodynamic observables and microcanonical probabilities. First of all, the ergodic theorem demonstrates the equality of microcanonical phase averages and infinite time averages (albeit for a special class of systems, and up to a measure zero set of exceptions). Secondly, one argues that actual measurements of thermodynamic quantities yield time averaged quantities, since measurements take a long time. The combination of these (...) two points is held to be an explanation why calculating microcanonical phase averages is a successful algorithm for predicting the values of thermodynamic observables. It is also well-known that this account is problematic.

This survey intends to show that ergodic theory nevertheless may have important roles to play, and it explores three other uses of ergodic theory. Particular attention is paid, firstly, to the relevance of specific interpretations of probability, and secondly, to the way in which the concern with systems in thermal equilibrium is translated into probabilistic language. With respect to the latter point, it is argued that equilibrium should not be represented as a stationary probability distribution as is standardly done; instead, a weaker definition is presented. (shrink)

This is an extensive review of recent work on the foundations of statistical mechanics.

If one formulates Helmholtz's ideas about perception in terms of modern-day theories one arrives at a model of perceptual inference and learning that can explain a remarkable range of neurobiological facts. Using constructs from statistical physics it can be shown that the problems of inferring what cause our sensory inputs and learning causal regularities in the sensorium can be resolved using exactly the same principles. Furthermore, inference and learning can proceed in a biologically plausible fashion. The ensuing scheme rests on (...) Empirical Bayes and hierarchical models of how sensory information is generated. The use of hierarchical models enables the brain to construct prior expectations in a dynamic and context-sensitive fashion. This scheme provides a principled way to understand many aspects of the brain's organisation and responses. In this paper, we suggest that these perceptual processes are just one emergent property of systems that conform to a free-energy principle. The free-energy considered here represents a bound on the surprise inherent in any exchange with the environment, under expectations encoded by its state or configuration. A system can minimise free-energy by changing its configuration to change the way it samples the environment, or to change its expectations. These changes correspond to action and perception, respectively, and lead to an adaptive exchange with the environment that is characteristic of biological systems. This treatment implies that the system's state and structure encode an implicit and probabilistic model of the environment. We will look at models entailed by the brain and how minimisation of free-energy can explain its dynamics and structure. (shrink)

We argue that, contrary to some analyses in the philosophy of science literature, ergodic theory falls short in explaining the success of classical equilibrium statistical mechanics. Our claim is based on the observations that dynamical systems for which statistical mechanics works are most likely not ergodic, and that ergodicity is both too strong and too weak a condition for the required explanation: one needs only ergodic-like behaviour for the finite set of observables that matter, but the behaviour must ensure that (...) the approach to equilibrium for these observables is on the appropriate time-scale. (shrink)

A proposal for the biological grounding of intrinsic teleology and sense-making through the theory of autopoiesis is critically evaluated. Autopoiesis provides a systemic language for speaking about intrinsic teleology but its original formulation needs to be elaborated further in order to explain sense-making. This is done by introducing adaptivity, a many-layered property that allows organisms to regulate themselves with respect to their conditions of viability. Adaptivity leads to more articulated concepts of behaviour, agency, sense-construction, health, and temporality than those given (...) so far by autopoiesis and enaction. These and other implications for understanding the organismic generation of values are explored. (shrink)

Much has been written about the free energy principle (FEP), and much misunderstood. The principle has traditionally been put forth as a theory of brain function or biological self-organisation. Critiques of the framework have focused on its lack of empirical support and a failure to generate concrete, falsifiable predictions. I take both positive and negative evaluations of the FEP thus far to have been largely in error, and appeal to a robust literature on scientific modelling to rectify the situation. A (...) prominent account of scientific modelling distinguishes between model structure and model construal. I propose that the FEP be reserved to designate a model structure, to which philosophers and scientists add various construals, leading to a plethora of models based on the formal structure of the FEP. An entailment of this position is that demands placed on the FEP that it be falsifiable or that it conform to some degree of biological realism rest on a category error. To this end, I deliver first an account of the phenomenon of model transfer and the breakdown between model structure and model construal. In the second section, I offer an overview of the formal elements of the framework, tracing their history of model transfer and illustrating how the formalism comes apart from any interpretation thereof. Next, I evaluate existing comprehensive critical assessments of the FEP, and hypothesise as to potential sources of existing confusions in the literature. In the final section, I distinguish between what I hold to be the FEP—taken to be a modelling language or modelling framework—and what I term “FEP models.”. (shrink)

Biological evolution is a complex blend of ever changing structural stability, variability and emergence of new phe- notypes, niches, ecosystems. We wish to argue that the evo- lution of life marks the end of a physics world view of law entailed dynamics. Our considerations depend upon dis- cussing the variability of the very ”contexts of life”: the in- teractions between organisms, biological niches and ecosys- tems. These are ever changing, intrinsically indeterminate and even unprestatable: we do not know ahead of (...) time the ”niches” which constitute the boundary conditions on selec- tion. More generally, by the mathematical unprestatability of the ”phase space”, no laws of mo- tion can be formulated for evolution. We call this radical emergence, from life to life. The purpose of this paper is the integration of variation and diversity in a sound concep- tual frame and situate unpredictability at a novel theoretical level, that of the very phase space. Our argument will be carried on in close comparisons with physics and the mathematical constructions of phase spaces in that discipline. The role of symmetries as invariant preserving transformations will allow us to under- stand the nature of physical phase spaces and to stress the differences required for a sound biological theoretizing. In this frame, we discuss the novel notion of ”enablement”. Life lives in a web of enablement and radical emergence. This will restrict causal analyses to differential cases. Mutations or other causal differ- ences will allow us to stress that ”non conservation princi- ples” are at the core of evolution, in contrast to physical dynamics, largely based on conservation principles as sym- metries. Critical transitions, the main locus of symmetry changes in physics, will be discussed, and lead to ”extended criticality” as a conceptual frame for a better understanding of the living state of matter. (shrink)

Symmetries play a major role in physics, in particular since the work by E. Noether and H. Weyl in the first half of last century. Herein, we briefly review their role by recalling how symmetry changes allow to conceptually move from classical to relativistic and quantum physics. We then introduce our ongoing theoretical analysis in biology and show that symmetries play a radically different role in this discipline, when compared to those in current physics. By this comparison, we stress that (...) symmetries must be understood in relation to conservation and stability properties, as represented in the theories. We posit that the dynamics of biological organisms, in their various levels of organization, are not just processes, but permanent (extended, in our terminology) critical transitions and, thus, symmetry changes. Within the limits of a relative structural stability (or interval of viability), variability is at the core of these transitions. (shrink)

We study the Johansen–Ledoit–Sornette model of financial market crashes :219–255, 2000). On our view, the JLS model is a curious case from the perspective of the recent philosophy of science literature, as it is naturally construed as a “minimal model” in the sense of Batterman and Rice :349–376, 2014) that nonetheless provides a causal explanation of market crashes, in the sense of Woodward’s interventionist account of causation.

The free-energy principle states that all systems that minimize their free energy resist a tendency to physical disintegration. Originally proposed to account for perception, learning, and action, the free-energy principle has been applied to the evolution, development, morphology, anatomy and function of the brain, and has been called a postulate, an unfalsifiable principle, a natural law, and an imperative. While it might afford a theoretical foundation for understanding the relationship between environment, life, and mind, its epistemic status is unclear. Also (...) unclear is how the free-energy principle relates to prominent theoretical approaches to life science phenomena, such as organicism and mechanism. This paper clarifies both issues, and identifies limits and prospects for the free-energy principle as a first principle in the life sciences. (shrink)

This work addresses the autonomous organization of biological systems. It does so by considering the boundaries of biological systems, from individual cells to Home sapiens, in terms of the presence of Markov blankets under the active inference scheme—a corollary of the free energy principle. A Markov blanket defines the boundaries of a system in a statistical sense. Here we consider how a collective of Markov blankets can self-assemble into a global system that itself has a Markov blanket; thereby providing an (...) illustration of how autonomous systems can be understood as having layers of nested and self-sustaining boundaries. This allows us to show that: (i) any living system is a Markov blanketed system and (ii) the boundaries of such systems need not be co-extensive with the biophysical boundaries of a living organism. In other words, autonomous systems are hierarchically composed of Markov blankets of Markov blankets—all the way down to individual cells, all the way up to you and me, and all the way out to include elements of the local environment. (shrink)

This paper considers questions about continuity and discontinuity between life and mind. It begins by examining such questions from the perspective of the free energy principle (FEP). The FEP is becoming increasingly influential in neuroscience and cognitive science. It says that organisms act to maintain themselves in their expected biological and cognitive states, and that they can do so only by minimizing their free energy given that the long-term average of free energy is entropy. The paper then argues that there (...) is no singular interpretation of the FEP for thinking about the relation between life and mind. Some FEP formulations express what we call an independence view of life and mind. One independence view is a cognitivist view of the FEP. It turns on information processing with semantic content, thus restricting the range of systems capable of exhibiting mentality. Other independence views exemplify what we call an overly generous non-cognitivist view of the FEP, and these appear to go in the opposite direction. That is, they imply that mentality is nearly everywhere. The paper proceeds to argue that non-cognitivist FEP, and its implications for thinking about the relation between life and mind, can be usefully constrained by key ideas in recent enactive approaches to cognitive science. We conclude that the most compelling account of the relationship between life and mind treats them as strongly continuous, and that this continuity is based on particular concepts of life (autopoiesis and adaptivity) and mind (basic and non-semantic). (shrink)

In this paper, I compare the use of the thermodynamic limit in the theory of phase transitions with the infinite-time limit in the explanation of equilibrium statistical mechanics. In the case of phase transitions, I will argue that the thermodynamic limit can be justified pragmatically since the limit behavior also arises before we get to the limit and for values of N that are physically significant. However, I will contend that the justification of the infinite-time limit is less straightforward. In (...) fact, I will point out that even in cases where one can recover the limit behavior for finite t, i.e. before we get to the limit, one cannot recover this behavior for realistic time scales. I will claim that this leads us to reconsider the role that the rate of convergence plays in the justification of infinite limits and calls for a revision of the so-called Butterfield’s principle. (shrink)

This paper addresses the question of what organisms are and therefore what kinds of biological entities qualify as organisms. For some time now, the concept of organismality has been eclipsed by the notion of individuality. Biological individuals are those systems that are units of selection. I develop a conception of organismality that does not rely on evolutionary considerations, but instead draws on development and ecology. On this account, organismality and individuality can come apart. Organisms, in my view, are as Godfrey-Smith (...) puts it “essentially persisters.” I argue that persistence is underpinned by differentiation, integration, development, and the constitutive embeddedness of organisms in their worlds. I examine two marginal cases, the Portuguese Man O’ War and the honey bee colony, and show that both count as organisms in light of my analysis. Next, I examine the case of holobionts, hosts plus their microsymbionts, and argue that they can be counted as organisms even though they may not be biological individuals. Finally, I consider the question of whether other, less tightly integrated biological systems might also be treated as organisms. (shrink)

Science is the study of our world, as it is in its messy reality. Nonetheless, science requires idealization to function—if we are to attempt to understand the world, we have to find ways to reduce its complexity. Idealization and the Aims of Science shows just how crucial idealization is to science and why it matters. Beginning with the acknowledgment of our status as limited human agents trying to make sense of an exceedingly complex world, Angela Potochnik moves on to explain (...) how science aims to depict and make use of causal patterns—a project that makes essential use of idealization. She offers case studies from a number of branches of science to demonstrate the ubiquity of idealization, shows how causal patterns are used to develop scientific explanations, and describes how the necessarily imperfect connection between science and truth leads to researchers’ values influencing their findings. The resulting book is a tour de force, a synthesis of the study of idealization that also offers countless new insights and avenues for future exploration. (shrink)

If one formulates Helmholtz’s ideas about perception in terms of modern-day theories one arrives at a model of perceptual inference and learning that can explain a remarkable range of neurobiological facts. Using constructs from statistical physics it can be shown that the problems of inferring what cause our sensory inputs and learning causal regularities in the sensorium can be resolved using exactly the same principles. Furthermore, inference and learning can proceed in a biologically plausible fashion. The ensuing scheme rests on (...) Empirical Bayes and hierarchical models of how sensory information is generated. The use of hierarchical models enables the brain to construct prior expectations in a dynamic and context-sensitive fashion. This scheme provides a principled way to understand many aspects of the brain’s organisation and responses. In this paper, we suggest that these perceptual processes are just one emergent property of systems that conform to a free-energy principle. The free-energy considered here represents a bound on the surprise inherent in any exchange with the environment, under expectations encoded by its state or configuration. A system can minimise free-energy by changing its configuration to change the way it samples the environment, or to change its expectations. These changes correspond to action and perception, respectively, and lead to an adaptive exchange with the environment that is characteristic of biological systems. This treatment implies that the system’s state and structure encode an implicit and probabilistic model of the environment. We will look at models entailed by the brain and how minimisation of free-energy can explain its dynamics and structure. (shrink)

The increasing application of network models to interpret biological systems raises a number of important methodological and epistemological questions. What novel insights can network analysis provide in biology? Are network approaches an extension of or in conflict with mechanistic research strategies? When and how can network and mechanistic approaches interact in productive ways? In this paper we address these questions by focusing on how biological networks are represented and analyzed in a diverse class of case studies. Our examples span from (...) the investigation of organizational properties of biological networks using tools from graph theory to the application of dynamical systems theory to understand the behavior of complex biological systems. We show how network approaches support and extend traditional mechanistic strategies but also offer novel strategies for dealing with biological complexity. (shrink)

Predictive processing approaches to the mind are increasingly popular in the cognitive sciences. This surge of interest is accompanied by a proliferation of philosophical arguments, which seek to either extend or oppose various aspects of the emerging framework. In particular, the question of how to position predictive processing with respect to enactive and embodied cognition has become a topic of intense debate. While these arguments are certainly of valuable scientific and philosophical merit, they risk underestimating the variety of approaches gathered (...) under the predictive label. Here, we first present a basic review of neuroscientific, cognitive, and philosophical approaches to PP, to illustrate how these range from solidly cognitivist applications—with a firm commitment to modular, internalistic mental representation—to more moderate views emphasizing the importance of ‘body-representations’, and finally to those which fit comfortably with radically enactive, embodied, and dynamic theories of mind. Any nascent predictive processing theory must take into account this continuum of views, and associated theoretical commitments. As a final point, we illustrate how the Free Energy Principle attempts to dissolve tension between internalist and externalist accounts of cognition, by providing a formal synthetic account of how internal ‘representations’ arise from autopoietic self-organization. The FEP thus furnishes empirically productive process theories by which to guide discovery through the formal modelling of the embodied mind. (shrink)

In many fields in the life sciences investigators refer to downward or top-down causal effects. Craver and Bechtel defended the view that such cases should be understood in terms of a constitution relation between levels in a mechanism and causation as solely an intra-level relation. Craver and Bechtel, however, provided insufficient specification as to when entities constitute a higher-level mechanism. In this paper I appeal to graph-theoretic representations of networks that are now widely employed in systems biology and neuroscience to (...) identify mechanisms with the modules that exhibit high clustering. As a result of the interconnections of nodes in these modules/mechanisms, they often exhibit complex dynamic behaviors that constrain how the individual components respond to external inputs, an important feature of cases viewed as involving top-down causation. (shrink)

Biological regulation is what allows an organism to handle the effects of a perturbation, modulating its own constitutive dynamics in response to particular changes in internal and external conditions. With the central focus of analysis on the case of minimal living systems, we argue that regulation consists in a specific form of second-order control, exerted over the core regime of production and maintenance of the components that actually put together the organism. The main argument is that regulation requires a distinctive (...) architecture of functional relationships, and specifically the action of a dedicated subsystem whose activity is dynamically decoupled from that of the constitutive regime. We distinguish between two major ways in which control mechanisms contribute to the maintenance of a biological organisation in response to internal and external perturbations: dynamic stability and regulation. Based on this distinction an explicit definition and a set of organisational requirements for regulation are provided, and thoroughly illustrated through the examples of bacterial chemotaxis and the lac-operon. The analysis enables us to mark out the differences between regulation and closely related concepts such as feedback, robustness and homeostasis. (shrink)

Didier Sornette boldly applies his varied experience in many areas to propose a simple, powerful, and general theory of how, why, and when stock markets crash.

The paper discusses how systems biology is working toward complex accounts that integrate explanation in terms of mechanisms and explanation by mathematical models—which some philosophers have viewed as rival models of explanation. Systems biology is an integrative approach, and it strongly relies on mathematical modeling. Philosophical accounts of mechanisms capture integrative in the sense of multilevel and multifield explanations, yet accounts of mechanistic explanation have failed to address how a mathematical model could contribute to such explanations. I discuss how mathematical (...) equations can be explanatorily relevant. Several cases from systems biology are discussed to illustrate the interplay between mechanistic research and mathematical modeling, and I point to questions about qualitative phenomena, where quantitative models are still indispensable to the explanation. Systems biology shows that a broader philosophical conception of mechanisms is needed, which takes into account functional-dynamical aspects, interaction in complex networks with feedback loops, system-wide functional properties such as distributed functionality and robustness, and a mechanism’s ability to respond to perturbations. I offer general conclusions for philosophical accounts of explanation. (shrink)

Robert Batterman examines a form of scientific reasoning called asymptotic reasoning, arguing that it has important consequences for our understanding of the scientific process as a whole. He maintains that asymptotic reasoning is essential for explaining what physicists call universal behavior. With clarity and rigor, he simplifies complex questions about universal behavior, demonstrating a profound understanding of the underlying structures that ground them. This book introduces a valuable new method that is certain to fill explanatory gaps across disciplines.

The life–mind continuity thesis is difficult to study, especially because the relation between life and mind is not yet fully understood, and given that there is still no consensus view neither on what qualifies as life nor on what defines mind. Rather than taking up the much more difficult task of addressing the many different ways of explaining how life relates to mind, and vice versa, this paper considers two influential accounts addressing how best to understand the life–mind continuity thesis: (...) first, the theory of autopoiesis (AT) developed in biology and in enactivist theories of mind; and second, the recently formulated free energy principle in theoretical neurobiology, with roots in thermodynamics and statistical physics. This paper advances two claims. The first is that the free energy principle (FEP) should be preferred to the theory of AT, as classically formulated. The second is that the FEP and the recently formulated framework of autopoietic enactivism can be shown to be genuinely continuous on a number of central issues, thus raising the possibility of a joint venture when it comes to answering the life–mind continuity thesis. (shrink)

What is the function of cognition? On one influential account, cognition evolved to co-ordinate behaviour with environmental change or complexity. Liberal interpretations of this view ascribe cognition to an extraordinarily broad set of biological systems—even bacteria, which modulate their activity in response to salient external cues, would seem to qualify as cognitive agents. However, equating cognition with adaptive flexibility per se glosses over important distinctions in the way biological organisms deal with environmental complexity. Drawing on contemporary advances in theoretical biology (...) and computational neuroscience, we cash these distinctions out in terms of different kinds of generative models, and the representational and uncertainty-resolving capacities they afford. This analysis leads us to propose a formal criterion for delineating cognition from other, more pervasive forms of adaptive plasticity. On this view, biological cognition is rooted in a particular kind of functional organisation; namely, that which enables the agent to detach from the present and engage in counterfactual inference. (shrink)

In his 1966 paper “The Strategy of model-building in Population Biology”, Richard Levins argues that no single model in population biology can be maximally realistic, precise and general at the same time. This is because these desirable model properties trade-off against one another. Recently, philosophers have developed Levins’ claims, arguing that trade-offs between these desiderata are generated by practical limitations on scientists, or due to formal aspects of models and how they represent the world. However this project is not complete. (...) The trade-offs discussed by Levins had a noticeable effect on modelling in population biology, but not on other sciences. This raises questions regarding why such a difference holds. I claim that in order to explain this finding, we must pay due attention to the properties of the systems, or targets modelled by the different branches of science.Keywords: Trade-offs; Population biology; Scientific models; Generality; Precision. (shrink)

The free energy principle says that any self-organising system that is at nonequilibrium steady-state with its environment must minimize its free energy. It is proposed as a grand unifying principle for cognitive science and biology. The principle can appear cryptic, esoteric, too ambitious, and unfalsifiable—suggesting it would be best to suspend any belief in the principle, and instead focus on individual, more concrete and falsifiable ‘process theories’ for particular biological processes and phenomena like perception, decision and action. Here, I explain (...) the free energy principle, and I argue that it is best understood as offering a conceptual and mathematical analysis of the concept of existence of self-organising systems. This analysis offers a new type of solution to long-standing problems in neurobiology, cognitive science, machine learning and philosophy concerning the possibility of normatively constrained, self-supervised learning and inference. The principle can therefore uniquely serve as a regulatory principle for process theories, to ensure that process theories conforming to it enable self-supervision. This is, at least for those who believe self-supervision is a foundational explanatory task, good reason to believe the free energy principle. (shrink)

In this fascinating read, Kauffman concludes that the development of life on earth is not entirely predictable, because no theory could ever fully account for the limitless variations of evolution. Sure to cause a stir, this book will be discussed for years to come and may even set the tone for the next "great thinker.".

While the fundamental laws of physics are time-reversal invariant, most macroscopic processes are irreversible. Given that the fundamental laws are taken to underpin all other processes, how can the fundamental time-symmetry be reconciled with the asymmetry manifest elsewhere? In statistical mechanics, progress can be made with this question. What I dub the ‘Zwanzig–Zeh–Wallace framework’ can be used to construct the irreversible equations of SM from the underlying microdynamics. Yet this framework uses coarse-graining, a procedure that has faced much criticism. I (...) focus on two objections in the literature: claims that coarse-graining makes time-asymmetry ‘illusory’ and ‘anthropocentric’. I argue that these objections arise from an unsatisfactory justification of coarse-graining prevalent in the literature, rather than from coarse-graining itself. This justification relies on the idea of measurement imprecision. By considering the role that abstraction and autonomy play, I provide an alternative justification and offer replies to the illusory and anthropocentric objections. Finally, I consider the broader consequences of this alternative justification: the connection to debates about inter-theoretic reduction and the implication that the time-asymmetry in SM is weakly emergent. 1Introduction 1.1Prospectus2The Zwanzig–Zeh–Wallace Framework3Why Does This Method Work? 3.1The special conditions account3.2When is a density forwards-compatible?4Anthropocentrism and Illusion: Two Objections 4.1The two objections in more detail4.2Against the justification by measurement imprecision5An Alternative Justification 5.1Abstraction and autonomy5.2An illustration: the Game of Life6Reply to Illusory7Reply to Anthropocentric8The Wider Landscape: Concluding Remarks 8.1Inter-theoretic relations8.2The nature of irreversibility. (shrink)

A hallmark of ecological research is dealing with complexity in the systems under investigation. One strategy is to diminish this complexity by constructing models and theories that are general. Alternatively, ecologists can constrain the scope of their generalizations to particular phenomena or types of systems. However, research employing the second strategy is often met with scathing criticism. I offer a theoretical argument in support of moderate generalizations in ecological research, based on the notions of interdependence and causal heterogeneity and their (...) effect on the trade-off between generality and realism. (shrink)

- A recent debate has touched upon the question of whether diseases can be understood as dysfunctional mechanisms or whether there are "pathological" mechanisms that deserve to be investigated and explained independently (Nervi 2010; Moghaddam Taaheri 2011). Here I suggest that both views tell us something important about disease but that in many instances only a systemic view can shed light on the relationship between physiology and pathology. I provide examples from the literature in systems biology in support of my (...) position. As a result of my analysis, I conclude that a perspective narrowly focusing on mechanisms is insufficient if the goal is to get a comprehensive picture of disease. (shrink)