In this paper we consider mechanistic explanations for biologic malfunctions. Drawing on Lipton’s work on difference making, we offer three reasons why one should distinguish i) mechanistic features that only make a difference to the malfunction one aims to explain, from ii) features that make a difference to both the malfunction and normal functioning. Recognition of the distinction is important for a) repair purposes, b) mechanism discovery, and c) understanding. This analysis extends current mechanistic thinking, which fails to appreciate the (...) distinction. We illustrate our contribution with a case on sleeping disorders as arising from disruptions of circadian rhythms. (shrink)

The central aim of this article is to specify the ontological nature of constitutive mechanistic phenomena. After identifying three criteria of adequacy that any plausible approach to constitutive mechanistic phenomena must satisfy, we present four different suggestions, found in the mechanistic literature, of what mechanistic phenomena might be. We argue that none of these suggestions meets the criteria of adequacy. According to our analysis, constitutive mechanistic phenomena are best understood as what we will call ‘object-involving occurrents’. Furthermore, on the basis (...) of this notion, we will clarify what distinguishes constitutive mechanistic explanations from etiological ones. 1 Introduction 2 Criteria of Adequacy 2.1 Descriptive adequacy 2.2 Constitutive–etiological distinction 2.3 Constitution 3 The Ontological Nature of Constitutive Mechanistic Phenomena 3.1 Phenomena as input–output relations 3.2 Phenomena as end states 3.3 Phenomena as dispositions 3.4 Phenomena as behaviours 4 Phenomena as Object-Involving Occurrents 4.1 What object-involving occurrents are and why we need them 4.2 The object in the phenomenon 4.3 The adequacy of option 5 Conclusion. (shrink)

This paper discusses the role of levels and level-bound theoretical terms in neurobiological explanations under the presupposition of a regularity theory of constitution. After presenting the definitions for the constitution relation and the notion of a mechanistic level in the sense of the regularity theory, the paper develops a set of inference rules that allow to determine whether two mechanisms referred to by one or more accepted explanations belong to the same level, or to different levels. The rules are characterized (...) as underlying level distinctions in neuroscience research. (shrink)

The first part of this paper argues that if Craver’s ([2007a], [2007b]) popular mutual manipulability account (MM) of mechanistic constitution is embedded within Woodward’s ([2003]) interventionist theory of causation--for which it is explicitly designed--it either undermines the mechanistic research paradigm by entailing that there do not exist relationships of constitutive relevance or it gives rise to the unwanted consequence that constitution is a form of causation. The second part shows how Woodward’s theory can be adapted in such a way that (...) (MM) neither undermines the mechanistic paradigm nor reduces constitution to causation. However, it turns out that this modified theoretical embedding of (MM) makes it impossible to produce empirical evidence for constitutive relations. The paper ends by suggesting an additional criterion, the fat-handedness criterion, which, when combined with (MM), generates indirect empirical evidence for constitutive relevance. (shrink)

Ordinary Language Philosophy has largely fallen out of favour, and with it the belief in the primary importance of analyses of ordinary language for philosophical purposes. Still, in their various endeavours, philosophers not only from analytic but also from other backgrounds refer to the use and meaning of terms of interest in ordinary parlance. In doing so, they most commonly appeal to their own linguistic intuitions. Often, the appeal to individual intuitions is supplemented by reference to dictionaries. In recent times, (...) Internet search engine queries for expressions of interest have become quite popular. Apparently, philosophers attempt to surpass the limits of their own linguistic intuitions by appealing to experts or to factual uses of language. I argue that this attempt is commendable but that its execution is wanting. Instead of appealing to dictionaries or Internet queries, philosophers should employ computer-based linguistic corpora in order to confirm or falsify hypotheses about the factual use of language. This approach also has some advantages over methods employed by experimental philosophers. If the importance of ordinary language is stressed, the use of linguistic corpora is hardly avoidable. (shrink)

This paper is concerned with the notions of supervenience and mechanistic constitution as they have been discussed in the philosophy of neuroscience. Since both notions essentially involve specific dependence and determination relations among properties and sets of properties, the question arises whether the notions are systematically connected and how they connect to science. In a first step, some definitions of supervenience and mechanistic constitution are presented and tested for logical independence. Afterwards, certain assumptions fundamental to neuroscientific inquiry are made explicit (...) in order to show that the presented definitions of supervenience are virtually uninteresting for theory construction in this field. In a third step, a new formulation of supervenience is developed that makes explicit reference to the notion of constitution and that bridges the gap between the philosophical concepts and explanatory practice in neuroscience. (shrink)

According to cognitive psychology, virtually every sensory system influences the way in which flavours are experienced. However, it is less clear which systems are actually constitutive of flavour perception and which have merely causal influence. The paper focuses on the status of vision and audition, which are usually not treated as constitutive in the context of flavour perception. First, it is proposed that the mechanistic explanation debate provides conceptual resources which allow the constitutivity of sensory systems to be assessed. Second, (...) it is argued that the contemporary state of the art provides reasons for accepting the constitutive role of audition, but analogous evidence is not available in the case of vision. (shrink)

In his “New Consensus” on explanation, Wesley Salmon (1989) famously argued that there are two kinds of scientific explanation: global, derivational, and unifying explanations, and then local, ontic explanations backed by causal relations. Following Salmon’s New Consensus, the dominant view in philosophy of science is what I term “neo-Causalism” which assumes that all ontic explanations of singular fact/event are causal explanations backed by causal relations, and that scientists only search for causal patterns or relations and only offer causal explanations of (...) singular facts/events. I argue that there are foundational, and fatal, flaws in the neo-Causal picture. The relations backing constitutive mechanistic explanations of activities of wholes using activities of parts, as well as other species of compositional explanation, cannot be causal relations. Treating them as causal or causation-like is therefore plausibly a category mistake. Compositional explanations in the sciences represent instead a sui generis kind of ontic explanation of singular fact/event backed by sui generis compositional relations. We thus need a pluralistic revision of Salmon’s New Consensus on explanation to reflect these findings. (shrink)

Some New Mechanists have proposed that claims of compositional relations are justified by combining the results of top-down and bottom-up interlevel interventions. But what do scientists do when they can perform, say, a cellular intervention, but not a subcellular detection? In such cases, paired interlevel interventions are unavailable. We propose that scientists use abduction and we illustrate its use through a case study of the ionic theory of resting and action potentials.

An adequate understanding of the ubiquitous practice of mechanistic explanation requires an account of what Craver termed “constitutive relevance.” Entities or activities are constitutively relevant to a phenomenon when they are parts of the mechanism responsible for that phenomenon. Craver’s mutual manipulability account extended Woodward’s account of manipulationist counterfactuals to analyze how interlevel experiments establish constitutive relevance. Critics of MM argue that applying Woodward’s account to this philosophical problem conflates causation and constitution, thus rendering the account incoherent. These criticisms, we (...) argue, arise from failing to distinguish the semantic, epistemic, and metaphysical aspects of the problem of constitutive relevance. In distinguishing these aspects of the problem and responding to these critics accordingly, we amend MM into a refined epistemic criterion, the “matched interlevel experiments” account. Further, we explain how this epistemological thesis is grounded in the plausible metaphysical thesis that constitutive relevance is causal betweenness. (shrink)

One of Stuart Glennan's most prominent contributions to the new mechanist debate consists in his reductive analysis of higher-level causation in terms of mechanisms (Glennan, 1996). In this paper I employ the causal Bayes net framework to reconstruct his analysis. This allows for specifying general assumptions which have to be satis ed to get Glennan's approach working. I show that once these assumptions are in place, they imply (against the background of the causal Bayes net machinery) that higher-level causation indeed (...) reduces to interactions between component parts of mechanisms. I also briefly discuss the plausibility of these assumptions and some consequences for the mechanism debate. (shrink)

Certain hypotheses cannot be directly confirmed for theoretical, practical, or moral reasons. For some of these hypotheses, however, there might be a workaround: confirmation based on analogical reasoning. In this paper we take up Dardashti, Hartmann, Thébault, and Winsberg’s (in press) idea of analyzing confirmation based on analogical inference Baysian style. We identify three types of confirmation by analogy and show that Dardashti et al.’s approach can cover two of them. We then highlight possible problems with their model as a (...) general approach to analogical inference and argue that these problems can be avoided by supplementing Bayesian update with Jeffrey conditionalization. (shrink)

This paper discusses two challenges for a Boolean method for establishing constitutive regularity statements which, according to the regularity theory of mechanistic constitution, form the core of any mechanistic explanation in neuroscience. After presenting the regularity definition for the constitution relation and a methodology for constitutive inference, the paper discusses the problem of full variation of tested mechanistic factors and the problem of informational redundancy. A solution is offered for each problem. The first requires some adjustments to the original theory (...) by introducing the technical notion of a set of types satisfying independent instantiability. The second one is resolved by demonstrating that the problem of informational redundancy is based on a confusion that fails to challenge the theory. It is concluded that the methodology of constitutive inference is consistent and plausible with respect to actual practice in neuroscience. (shrink)

According to the new mechanistic approach, an acting entity is at a lower mechanistic level than another acting entity if and only if the former is a component in the mechanism for the latter. Craver and Bechtel :547–563, 2007. doi:10.1007/s10539-006-9028-8) argue that a consequence of this view is that there cannot be causal interactions between acting entities at different mechanistic levels. Their main reason seems to be what I will call the Metaphysical Argument: things at different levels of a mechanism (...) are related as part and whole; wholes and their parts cannot be related as cause and effect; hence, interlevel causation in mechanisms is impossible. I will analyze this argument in more detail and show under which conditions it is valid. This analysis will reveal that interlevel causation in mechanisms is indeed possible, if we take seriously the idea that the relata of the mechanistic level relation are acting entities and accept a slightly modified notion of a mechanistic level that is highly plausible in the light of the first clarification. (shrink)

Constitutive mechanistic explanations are said to refer to mechanisms that constitute the phenomenon-to-be-explained. The most prominent approach of how to understand this constitution relation is Carl Craver’s mutual manipulability approach to constitutive relevance. Recently, the mutual manipulability approach has come under attack (Leuridan 2012; Baumgartner and Gebharter 2015; Romero 2015; Harinen 2014; Casini and Baumgartner 2016). Roughly, it is argued that this approach is inconsistent because it is spelled out in terms of interventionism (which is an approach to causation), whereas (...) constitutive relevance is said to be a non-causal relation. In this paper, I will discuss a strategy of how to resolve this inconsistency, so-called fat-handedness approaches (Baumgartner and Gebharter 2015; Casini and Baumgartner 2016; Romero 2015). I will argue that these approaches are problematic. I will present a novel suggestion of how to consistently define constitutive relevance in terms of interventionism. My approach is based on a causal interpretation of mutual manipulability, where manipulability is interpreted as a causal relation between the mechanism’s components and temporal parts of the phenomenon. (shrink)

Mechanisms are said to consist of two kinds of components, entities and activities. In the first half of this chapter, I examine what entities and activities are, how they relate to well-known ontological categories, such as processes or dispositions, and how entities and activities relate to each other (e.g., can one be reduced to the other or are they mutually dependent?). The second part of this chapter analyzes different criteria for individuating the components of mechanisms and discusses how real the (...) boundaries of mechanisms are. (shrink)

In this paper, I evaluate recently defended mechanistic accounts of the unity of neuroscience from a metaphysical point of view. Considering the mechanistic framework in general , I argue that explanations of this kind are essentially reductive . The reductive character of mechanistic explanations provides a sufficiency criterion, according to which the mechanism underlying a certain phenomenon is sufficient for the latter. Thus, the concept of supervenience can be used in order to describe the relation between mechanisms and phenomena . (...) Against this background, I show that the mechanistic framework is subject to the causal exclusion problem and faces the classical metaphysical options when it comes to the relations obtaining between different levels of mechanisms . Finally, an attempt to improve the metaphysics of mechanisms is made and further difficulties are pointed out. (shrink)

Distributive egalitarians believe that distributive justice is to be explained by the idea of distributive equality (DE) and that DE is of intrinsic value. The socio-relational critique argues that distributive egalitarianism does not account for the “true” value of equality, which rather lies in the idea of “equality as a substantive social value” (ESV). This paper examines the socio-relational critique and argues that it fails because – contrary to what the critique presupposes –, first, ESV is not conceptually distinct from (...) DE, and second, the idea of ESV cannot serve as a “foundation” or “root” of distributive egalitarianism. (shrink)

Within contemporary philosophy of perception, it is commonly claimed that flavour experiences are paradigmatic examples of multimodal perceptual experiences. In fact, virtually any sensory system, including vision and audition, is believed to influence how we experience flavours. However, there is a strong intuition, often expressed in these works, that not all of these sensory systems make an equal contribution to the phenomenology of flavour experiences. More specifically, it seems that the activities of some sensory systems are constitutive for flavour perception (...) while others merely influence how we experience flavours. This paper aims to answer the question regarding the constitutive factors of flavour perception in a twofold way. First, a theoretical framework is developed, relying on debates regarding constitutivity in analytic metaphysics and philosophy of science, which defines the stronger and weaker senses in which the activities of sensory systems may be constitutive for flavour perception. Second, relying on empirical results in flavour science, the constitutive status of activities related to distinct sensory systems in the context of flavour perception is investigated. (shrink)

Gebharter has proposed using one of the best known Bayesian network causal discovery algorithms, PC, to identify the constitutive dependencies underwriting mechanistic explanations. His proposal assumes that mechanistic constitution behaves like deterministic direct causation, such that PC is directly applicable to mixed variable sets featuring both causal and constitutive dependencies. Gebharter claims that such mixed sets, under certain restrictions, comply with PC’s background assumptions. The aim of this article is to show that Gebharter’s proposal incurs severe problems, ultimately rooted in (...) the widespread non-compliance of mechanistic systems with PC’s assumptions. This casts severe doubts on the attempt to implicitly define constitution as a form of deterministic direct causation complying with PC’s assumptions. (shrink)

Entities that are, in ordinary perceptual situations, veridically presented as objects can be called ‘perceptual objects’. In the philosophical literature, one can find various approaches to the crucial features that distinguish the class of perceptual objects. While these positions differ in many respects, they share an important general feature: they all characterize perceptual objects as largely subject-independent. More specifically, they do not attribute a significant constitutive role to the perceptual relation connecting a fragment of the environment with a perceiving subject. (...) Fragments of the environment are perceptual objects no matter whether they stand in a perceptual relation to any subject, mainly by virtue of having a certain physical structure. I question this common assumption, relying on Green’s ( 2019 ) definition of perceptual objects, arguing that a proper theory of perceptual objects should accommodate the constitutive role of perceptual relations. This is because there exist fragments of the environment that are perceptual objects only when they stand in a perceptual relation to a subject. (shrink)

Alexander Gebharter has recently proposed to use Bayesian network causal discovery methods to identify the constitutive dependencies that underwrite mechanistic explanations. The proposal depends on using the assumptions of the causal Bayesian network framework to implicitly define mechanistic constitution as a kind of deterministic direct causal dependence. The aim of this paper is twofold. In the first half, we argue that Gebharter’s proposal incurs severe conceptual problems. In the second half, we present an alternative way to bring Bayesian network tools (...) to bear on the issue of understanding mechanistic constitution. More precisely, our proposal interprets constitution as the relation explaining why a target phenomenon has its characteristic causal role in terms of the causal roles of some of its spatiotemporal parts---where the notion of causal role is probabilistically understood. (shrink)

In this paper I address the current debate on ontic versus epistemic conceptualizations of mechanistic explanation in the mechanisms literature. Illari recently argued that good explanations are subject to both ontic and epistemic constraints: they must describe mechanisms in the world (ontic aim) in such fashion that they provide understanding of their workings (epistemic aim). Elaborating upon Illari’s ‘integration’ account, I argue that causal role function discovery of mechanisms and their components is an epistemic prerequisite for achieving these two aims. (...) This analysis extends Illari’s account in important ways, putting more pressure on ontic readings of mechanistic explanation and providing an answer to the question how ontic and epistemic constraints on mechanistic explanation are related. I argue these point in terms of cases on memory research drawn from neuroscience and research on extinct neurogenetic mechanisms from early nervous systems biology. (shrink)

While ideal interventions are acknowledged by many as valuable tools for the analysis of causation, recent discussions have shown that, since there are no ideal interventions on upper-level phenomena that non-reductively supervene on their underlying mechanisms, interventions cannot—contrary to a popular opinion—ground an informative analysis of constitution. This has led some to abandon the project of analyzing constitution in interventionist terms. By contrast, this paper defines the notion of a horizontally surgical intervention, and argues that, when combined with some innocuous (...) metaphysical principles about the relation between upper and lower levels of mechanisms, that notion delivers a sufficient condition for constitution. This, in turn, strengthens the case for an interventionist analysis of constitution. (shrink)

This paper discusses the relevance of models for cognitive science that integrate mechanistic and computational aspects. Its main hypothesis is that a model of a cognitive system is satisfactory and explanatory to the extent that it bridges phenomena at multiple mechanistic levels, such that at least several of these mechanistic levels are shown to implement computational processes. The relevant parts of the computation must be mapped onto distinguishable entities and activities of the mechanism. The ideal is contrasted with two other (...) accounts of modeling in cognitive science. The first has been presented by David Marr in combination with a distinction of “levels of computation”. The second builds on a hierarchy of “mechanistic levels” in the sense of Carl Craver. It is argued that neither of the two accounts secures satisfactory explanations of cognitive systems. The mechanistic-computational ideal can be thought of as resulting from a fusion of Marr’s and Craver’s ideals. It is defended as adequate and plausible in light of scientific practice, and certain metaphysical background assumptions are discussed. (shrink)

Most defenders of the new mechanistic approach accept ontic constraints for successful scientific explanation (Illari 2013; Craver 2014). The minimal claim is that scientific explanations have objective truthmakers, namely mechanisms that exist in the physical world independently of any observer and that cause or constitute the phenomena-to- be-explained. How can this idea be applied to type-level explanations? Many authors at least implicitly assume that in order for mechanisms to be the truthmakers of type-level explanation they need to be regular (Andersen (...) 2012; Sheredos 2015). One problem of this assumption is that most mechanisms are (highly) stochastic in the sense that they “fail more often than they succeed” (Bogen 2005; Andersen 2012). How can a mechanism type whose instances are more likely not to produce an instance of a particular phenomenon type be the truthmaker of the explanation of that particular phenomenon type? In this paper, I will give an answer to this question. I will analyze the notion of regularity and I will discuss Andersen's suggestion for how to cope with stochastic mechanisms. I will argue that her suggestion cannot account for all kinds of stochastic mechanisms and does not provide an answer as to why regularity grounds type-level explanation. According to my analysis, a mechanistic type- level explanation is true if and only if at least one of the following two conditions is satisfied: the mechanism brings about the phenomenon more often than any other phenomenon (comparative regularity) or the phenomenon is more often brought about by the mechanism than by any other mechanism/causal sequence (comparative reverse regularity). (shrink)

A popular view presents explanations in the cognitive sciences as causal or mechanistic and argues that an important feature of such explanations is that they allow us to manipulate and control the explanandum phenomena. Nonetheless, whether there can be explanations in the cognitive sciences that are neither causal nor mechanistic is still under debate. Another prominent view suggests that both causal and non-causal relations of counterfactual dependence can be explanatory, but this view is open to the criticism that it is (...) not clear how to distinguish explanatory from non-explanatory relations. In this paper, I draw from both views and suggest that, in the cognitive sciences, relations of counterfactual dependence that allow manipulation and control can be explanatory even when they are neither causal nor mechanistic. Furthermore, the ability to allow manipulation can determine whether non-causal counterfactual dependence relations are explanatory. I present a preliminary framework for manipulation relations that includes some non-causal relations and use two examples from the cognitive sciences to show how this framework distinguishes between explanatory and non-explanatory, non-causal relations. The proposed framework suggests that, in the cognitive sciences, causal and non-causal relations have the same criterion for explanatory value, namely, whether or not they allow manipulation and control. (shrink)

In contemporary philosophy of science, the consensus view seems to be that scientific explanations describe mechanisms responsible for the phenomena to be explained. Two kinds of explanatory relevance figure in mechanistic accounts of explanation: causal and constitutive. Following prominent accounts, it seems natural to analyze both these relations in terms of systematic interventions into some factor X with respect to another factor Y. However, such interventions are tailored to uncover causal relations only. Construing the constitutive relationship between parts and wholes (...) in terms of interventions thus raises metaphysical, conceptual, and epistemological questions. We here review the barriers that intervention-based inquiry into mechanisms encounters and consider some solutions. (shrink)

Analysis of the adequacy of engineering design methods, as well as analysis of the utility of concepts of function often invoked in these methods, is a neglected topic in both philosophy of technology and in engineering proper. In this paper, I present an approach—dubbed an explanationist perspective—for assessing the adequacy of function-based design methods. Engineering design is often intertwined with explanation, for instance, in reverse engineering and subsequent redesign, knowledge base-assisted designing, and diagnostic reasoning. I argue that the presented approach (...) is useful for validating function-based design methods with respect to their explanatory elements and that it supports assessment of the explanatory and design utility of “function”, and the different conceptualizations thereof, as used in such engineering design methods. I deploy two key desiderata from the explanation literature to assess the viability of function-based design methods: explanatorily relevant difference-making factors and counterfactual understanding defined in terms of what-if-things-had-been-different questions. I explicate the approach and its merits in terms of two case studies drawn from the engineering functional modeling literature: reverse engineering and redesign and malfunction analysis. I close the paper by discussing ramifications of the presented approach for the philosophy of design and the philosophy of explanation. (shrink)

One reason for the popularity of Craver’s mutual manipulability account of constitutive relevance is that it seems to make good sense of the experimental practices and constitutive reasoning in the life sciences. Two recent papers propose a theoretical alternative to in light of several important conceptual objections. Their alternative approach, the no de-coupling account, conceives of constitution as a dependence relation that once postulated provides the best explanation of the impossibility of breaking the common cause coupling of a macro-level mechanism (...) and its micro-level components. This entails an abductive view of constitutive inference. Proponents of the NDC or abductive account recognize that their discussion leaves open a big question concerning the practical dimension of the notion of constitutive relevanssssce: Is it possible to faithfully reconstruct constitutional reasoning in science in terms of a failure to de-couple, via interlevel experiments, phenomena from their mechanistic constituents? Focusing on the field of memory and long-term potential research, this article argues that the abductive account provides a more adequate description of interlevel experiments in neuroscience. We also suggest that the account highlights some significant practical recommendations of how to interpret the findings of interlevel experiments. 1Introduction 2Mutual Manipulability and Constitutive Relevance 2.1Constitutive relevance through an interventionist lens 2.2Mutual manipulability: A methodological application 3Trouble for the Mutual Manipulability Account 4The Abductive Account of Constitution 5The Abductive Account: A Methodological Application 5.1Long-term potential and memory experiments 5.2A comparative summary 6Conclusions. (shrink)

Over the past three decades, the discourse on the mechanistic approach to scientific modelling and explanation has notably sidestepped the topic of simplicity and fit within the process of model selection. This paper aims to rectify this disconnect by delving into the topic of simplicity and fit within the context of mechanistic explanations. More precisely, our primary objective is to address whether simplicity metrics hold any significance within mechanistic explanations. If they do, then our inquiry extends to the suitability of (...) the Akaike Information Criterion (AIC), the Bayesian Information Criterion (BIC), and related criteria in determining the optimal balance of fit and simplicity of mechanistic models. As our main claims, we argue that mechanistic models inherently lend themselves to considerations of simplicity, and that the AIC and BIC and related criteria are applicable to some submodels of certain kinds of mechanistic models. However, these criteria and related criteria designed for curve fitting and causal modelling are of little help for a comparative assessment of full mechanistic models, and a fundamentally different approach is needed to make determinations of this kind. (shrink)

The mechanistic framework traditionally comes bundled with a multi-level view. Some ascribe ontological weight to these levels, whereas others claim that characterising a higher-level entity and the corresponding lower-level mechanism are only different descriptions of the same thing. The goal of this paper is to develop a consistent metaphysical picture that can underly the latter position. According to this flat view, wholes and their parts are embedded in the same network of interacting units. The flat view preserves the original virtues (...) of the mechanistic approach and is able to avoid the problems associated with the multi-level view. (shrink)

It is often argued that constitution and causation are different kinds of metaphysical relations. Constitution, like other grounding relations, is assumed to be synchronic, while causation is diachronic. It is this synchronic-diachronic division that, more than other difference-makers, is argued to distinguish grounding relations such as constitution from causation. This paper develops an account of a species of constitution that happens over time. We call this type of constitution, diachronic constitution. We show how diachronic constitution is a consequence of a (...) common type of causation, often ignored in metaphysical discussions of causation: continuous reciprocal causation. Hence, constitution is not only sometimes like causation; it can also be a form of causation. We argue that temporalising the constitution relation is neither as remarkable nor as problematic as it might initially seem. It is inevitable, given local interactions between microscale and macroscale states in dynamical systems. (shrink)