It is proposed that we use the term “approximation” for inexact description of a target system and “idealization” for another system whose properties also provide an inexact description of the target system. Since systems generated by a limiting process can often have quite unexpected, even inconsistent properties, familiar limit systems used in statistical physics can fail to provide idealizations, but are merely approximations. A dominance argument suggests that the limiting idealizations of statistical physics should be demoted to approximations.

This article examines ontological/dynamical aspects of emergence, specifically the micro-macro relation in cases of universal behavior. I discuss superconductivity as an emergent phenomenon, showing why microphysical features such as Cooper pairing are not necessary for deriving characteristic properties such as infinite conductivity. I claim that the difficulties surrounding the thermodynamic limit in explaining phase transitions can be countered by showing how renormalization group techniques facilitate an understanding of the physics behind the mathematics, enabling us to clarify epistemic and ontological aspects (...) of emergence. I close with a discussion of the impact of these issues for questions concerning natural kinds. (shrink)

Despite the close connection between the central limit theorem and renormalization group (RG) methods, the latter should be considered fundamentally distinct from the kind of probabilistic framework associated with statistical mechanics, especially the notion of averaging. The mathematics of RG is grounded in dynamical systems theory rather than probability, which raises important issues with respect to the way RG generates explanations of physical phenomena. I explore these differences and show why RG methods should be considered not just calculational tools but (...) the basis for a physical understanding of complex systems in terms of structural properties and relations. (shrink)

The concept of mechanism is analyzed in terms of entities and activities, organized such that they are productive of regular changes. Examples show how mechanisms work in neurobiology and molecular biology. Thinking in terms of mechanisms provides a new framework for addressing many traditional philosophical issues: causality, laws, explanation, reduction, and scientific change.

It is shown that three common conditions for scientific explanations are violated by a widely used class of domain-independent explanations. These explanations can accommodate both complex and noncomplex systems and do not require the use of detailed models of system-specific processes for their effectiveness, although they are compatible with such model-based explanations. The approach also shows how a clean separation can be maintained between mathematical representations and empirical content.

Philosophers of science typically associate the causal-mechanical view of scientific explanation with the work of Railton and Salmon. In this paper I shall argue that the defects of this view arise from an inadequate analysis of the concept of mechanism. I contrast Salmon's account of mechanisms in terms of the causal nexus with my own account of mechanisms, in which mechanisms are viewed as complex systems. After describing these two concepts of mechanism, I show how the complex-systems approach avoids certain (...) objections to Salmon's account of causal-mechanical explanation. I conclude by discussing how mechanistic explanations can provide understanding by unification. (shrink)

Philosophers of science typically associate the causal-mechanical view of scientific explanation with the work of Railton and Salmon. In this paper I shall argue that the defects of this view arise from an inadequate analysis of the concept of mechanism. I contrast Salmon's account of mechanisms in terms of the causal nexus with my own account of mechanisms, in which mechanisms are viewed as complex systems. After describing these two concepts of mechanism, I show how the complex-systems approach avoids certain (...) objections to Salmon's account of causal-mechanical explanation. I conclude by discussing how mechanistic explanations can provide understanding by unification. (shrink)

The last decade and a half has seen an ardent development of self-organised criticality, a new approach to complex systems, which has become important in many domains of natural as well as social science, such as geology, biology, astronomy, and economics, to mention just a few. This has led many to adopt a generalist stance towards SOC, which is now repeatedly claimed to be a universal theory of complex behaviour. The aim of this paper is twofold. First, I provide a (...) brief and non-technical introduction to SOC. Second, I critically discuss the various bold claims that have been made in connection with it. Throughout, I will adopt a rather sober attitude and argue that some people have been too readily carried away by fancy contentions. My overall conclusion will be that none of these bold claims can be maintained. Nevertheless, stripped of exaggerated expectations and daring assertions, many SOC models are interesting vehicles for promising scientific research.Author Keywords: Self-organised criticality; Scaling law; Models; Formal analogy. (shrink)

Philosophers of science typically associate the causal‐mechanical view of scientific explanation with the work of Railton and Salmon. In this paper I shall argue that the defects of this view arise from an inadequate analysis of the concept of mechanism. I contrast Salmon’s account of mechanisms in terms of the causal nexus with my own account of mechanisms, in which mechanisms are viewed as complex systems. After describing these two concepts of mechanism, I show how the complex‐systems approach avoids certain (...) objections to Salmon’s account of causal‐mechanical explanation. I conclude by discussing how mechanistic explanations can provide understanding by unification. (shrink)

This is one of two papers about emergence, reduction and supervenience. It expounds these notions and analyses the general relations between them. The companion paper analyses the situation in physics, especially limiting relations between physical theories. I shall take emergence as behaviour that is novel and robust relative to some comparison class. I shall take reduction as deduction using appropriate auxiliary definitions. And I shall take supervenience as a weakening of reduction, viz. to allow infinitely long definitions. The overall claim (...) of this paper will be that emergence is logically independent both of reduction and of supervenience. In particular, one can have emergence with reduction, as well as without it; and emergence without supervenience, as well as with it. Of the subsidiary claims, the four main ones are: : I defend the traditional Nagelian conception of reduction ; : I deny that the multiple realizability argument causes trouble for reductions, or ``reductionism'' ; : I stress the collapse of supervenience into deduction via Beth's theorem ; : I adapt some examples already in the literature to show supervenience without emergence and vice versa. (shrink)

The robust behavior of the patent citation network is a complex target of recent bottom-up models in science. This paper investigates the purpose and testing of three especially simple bottom-up models of the citation count distribution observed in the patent citation network. The complex causal webs in the models generate weakly emergent patterns of behavior, and this explains both the need for empirical observation of computer simulations of the models and the epistemic harmlessness of the resulting epistemic opacity.

Explanations in the life sciences frequently involve presenting a model of the mechanism taken to be responsible for a given phenomenon. Such explanations depart in numerous ways from nomological explanations commonly presented in philosophy of science. This paper focuses on three sorts of differences. First, scientists who develop mechanistic explanations are not limited to linguistic representations and logical inference; they frequently employ diagrams to characterize mechanisms and simulations to reason about them. Thus, the epistemic resources for presenting mechanistic explanations are (...) considerably richer than those suggested by a nomological framework. Second, the fact that mechanisms involve organized systems of component parts and operations provides direction to both the discovery and testing of mechanistic explanations. Finally, models of mechanisms are developed for specific exemplars and are not represented in terms of universally quantified statements. Generalization involves investigating both the similarity of new exemplars to those already studied and the variations between them. (shrink)

A traditional view of mathematical modeling holds, roughly, that the more details of the phenomenon being modeled that are represented in the model, the better the model is. This paper argues that often times this ‘details is better’ approach is misguided. One ought, in certain circumstances, to search for an exactly solvable minimal model—one which is, essentially, a caricature of the physics of the phenomenon in question.