This chapter provides a systematic overview of topological explanations in the philosophy of science literature. It does so by presenting an account of topological explanation that I (Kostić and Khalifa 2021; Kostić 2020a; 2020b; 2018) have developed in other publications and then comparing this account to other accounts of topological explanation. Finally, this appraisal is opinionated because it highlights some problems in alternative accounts of topological explanations, and also it outlines responses to some of (...) the main criticisms raised by the so-called new mechanists. (shrink)

We provide three innovations to recent debates about whether topological or “network” explanations are a species of mechanistic explanation. First, we more precisely characterize the requirement that all topological explanations are mechanistic explanations and show scientific practice to belie such a requirement. Second, we provide an account that unifies mechanistic and non-mechanistic topological explanations, thereby enriching both the mechanist and autonomist programs by highlighting when and where topological explanations are mechanistic. Third, (...) we defend this view against some powerful mechanist objections. We conclude from this that topological explanations are autonomous from their mechanistic counterparts. (shrink)

This paper argues that besides mechanistic explanations, there is a kind of explanation that relies upon “topological” properties of systems in order to derive the explanandum as a consequence, and which does not consider mechanisms or causal processes. I first investigate topological explanations in the case of ecological research on the stability of ecosystems. Then I contrast them with mechanistic explanations, thereby distinguishing the kind of realization they involve from the realization relations entailed by mechanistic (...) explanations, and explain how both kinds of explanations may be articulated in practice. The second section, expanding on the case of ecological stability, considers the phenomenon of robustness at all levels of the biological hierarchy in order to show that topological explanations are indeed pervasive there. Reasons are suggested for this, in which “neutral network” explanations are singled out as a form of topological explanation that spans across many levels. Finally, I appeal to the distinction of explanatory regimes to cast light on a controversy in philosophy of biology, the issue of contingence in evolution, which is shown to essentially involve issues about realization. (shrink)

In the last 20 years or so, since the publication of a seminal paper by Watts and Strogatz :440–442, 1998), an interest in topological explanations has spread like a wild fire over many areas of science, e.g. ecology, evolutionary biology, medicine, and cognitive neuroscience. The topological approach is still very young by all standards, and even within special sciences it still doesn’t have a single methodological programme that is applicable across all areas of science. That is why (...) this special issue is important as a first systematic philosophical study of topological explanations and their relation to a well understood and widespread explanatory strategy, such as mechanistic one. (shrink)

Medical explanations have often been thought on the model of biological ones and are frequently defined as mechanistic explanations of a biological dysfunction. In this paper, I argue that topological explanations, which have been described in ecology or in cognitive sciences, can also be found in medicine and I discuss the relationships between mechanistic and topological explanations in medicine, through the example of network medicine and medical genetics. Network medicine is a recent discipline that (...) relies on the analysis of various disease networks in order to find organizing principles in disease explanation. My aim is to show how topological explanations in network medicine can help solving the conceptual issues that pure mechanistic explanations of the genetics of disease are currently facing, namely the crisis of the concept of genetic disease, the progressive geneticization of diseases and the dissolution of the distinction between monogenic and polygenic diseases. However, I will also argue that topological explanations should not be considered as independent and radically different from mechanistic explanations for at least two reasons. First, in network medicine, topological explanations depend on and use mechanistic information. Second, they leave out some missing gaps in disease explanation that require, in turn, the development of new mechanistic explanations. Finally, I will insist on the specific contribution of topological explanations in medicine: they push us to develop an explanation of disease in general, instead of focusing on single explanations of individual diseases. This last point may have major consequences for biomedical research. (shrink)

It is a well-known fact that mathematics plays a crucial role in physics; in fact, it is virtually impossible to imagine contemporary physics without it. But it is questionable whether mathematical concepts could ever play such a role in psychology or philosophy. In this paper, we set out to examine a rather unobvious example of the application of topology, in the form of the theory of persons proposed by Kurt Lewin in his Principles of Topological Psychology. Our aim is (...) to show that this branch of mathematics can furnish a natural conceptual system for Gestalt psychology, in that it provides effective tools for describing global qualitative aspects of the latter’s object of investigation. We distinguish three possible ways in which mathematics can contribute to this: explanation, explication and metaphor. We hold that all three of these can be usefully characterized as throwing light on their subject matter, and argue that in each case this contrasts with the role of explanations in physics. Mathematics itself, we argue, provides something different from such explanations when applied in the field of psychology, and this is nevertheless still cognitively fruitful. (shrink)

In this paper, I present a general theory of topological explanations, and illustrate its fruitfulness by showing how it accounts for explanatory asymmetry. My argument is developed in three steps. In the first step, I show what it is for some topological property A to explain some physical or dynamical property B. Based on that, I derive three key criteria of successful topological explanations: a criterion concerning the facticity of topological explanations, i.e. what (...) makes it true of a particular system; a criterion for describing counterfactual dependencies in two explanatory modes, i.e. the vertical and the horizontal; and, finally, a third perspectival one that tells us when to use the vertical and when to use the horizontal mode. In the second step, I show how this general theory of topological explanations accounts for explanatory asymmetry in both the vertical and horizontal explanatory modes. Finally, in the third step, I argue that this theory is universally applicable across biological sciences, which helps to unify essential concepts of biological networks. (shrink)

Proponents of ontic conceptions of explanation require all explanations to be backed by causal, constitutive, or similar relations. Among their justifications is that only ontic conceptions can do justice to the ‘directionality’ of explanation, i.e., the requirement that if X explains Y , then not-Y does not explain not-X . Using topological explanations as an illustration, we argue that non-ontic conceptions of explanation have ample resources for securing the directionality of explanations. The different ways in which (...) neuroscientists rely on multiplexes involving both functional and anatomical connectivity in their topological explanations vividly illustrate why ontic considerations are frequently (if not always) irrelevant to explanatory directionality. Therefore, directionality poses no problem to non-ontic conceptions of explanation. (shrink)

The relationship between topological explanation and mechanistic explanation is unclear. Most philosophers agree that at least some topological explanations are mechanistic explanations. The crucial question is how to make sense of this claim. Zednik (Philos Psychol 32(1):23–51, 2019) argues that topological explanations are mechanistic if they (i) describe mechanism sketches that (ii) pick out organizational properties of mechanisms. While we agree with Zednik’s conclusion, we critically discuss Zednik’s account and show that it fails as (...) a general account of how and when topological explanations are mechanistic. First, if topological explanations were just mechanism sketches, this implies that they could be enriched by replacing topological terms with mechanistic detail. This, however, conflicts how topological explanations are used in scientific practice. Second, Zednik’s account fails to show how topological properties can be organizational properties of mechanisms that have a place in mechanistic explanation. The core issue is that Zednik’s account ignores that topological properties often are _global_ properties while mechanistic explanantia refer to _local_ properties. We demonstrate how these problems can be solved by a recent account of mechanistic completeness (Craver and Kaplan in Br J Philos Sci 71(1):287–319, 2020; Kohár and Krickel in Calzavarini and Viola (eds) Neural mechanisms—new challenges in the philosophy of neuroscience, Springer, New York, 2021) and use a multilayer network model of Alzheimer’s Disease to illustrate this. (shrink)

I consider recent uses of the notion of neutrality in evolutionary biology and ecology, questioning their relevance to the kind of explanation recently labeled ‘topological explanation’. Focusing on fitness landscapes and genotype-phenotype maps, I explore the explanatory uses of neutral subspaces, as modeled in two perspectives: hyperdimensional fitness landscapes and RNA sequence-structure maps. I argue that topological properties of such spaces account for features of evolutionary systems: respectively, capacity for adaptive evolution toward global optima and mutational robustness of (...) genotypes. Thus many models appealing to “neutral” manifolds provide topological alternatives to hypothetical mechanisms. (shrink)

It is a well-known fact that mathematics plays a crucial role in physics; in fact, it is virtually impossible to imagine contemporary physics without it. But it is questionable whether mathematical concepts could ever play such a role in psychology or philosophy. In this paper, we set out to examine a rather unobvious example of the application of topology, in the form of the theory of persons proposed by Kurt Lewin in his Principles of Topological Psychology. Our aim is (...) to show that this branch of mathematics can furnish a natural conceptual system for Gestalt psychology, in that it provides effective tools for describing global qualitative aspects of the latter’s object of investigation. We distinguish three possible ways in which mathematics can contribute to this: explanation, explication and metaphor. We hold that all three of these can be usefully characterized as throwing light on their subject matter, and argue that in each case this contrasts with the role of explanations in physics. Mathematics itself, we argue, provides something different from such explanations when applied in the field of psychology, and this is nevertheless still cognitively fruitful. (shrink)

While mechanistic explanation and, to a lesser extent, nomological explanation are well-explored topics in the philosophy of biology, topological explanation is not. Nor is the role of diagrams in topological explanations. These explanations do not appeal to the operation of mechanisms or laws, and extant accounts of the role of diagrams in biological science explain neither why scientists might prefer diagrammatic representations of topological information to sentential equivalents nor how such representations might facilitate important processes (...) of explanatory reasoning unavailable to scientists who restrict themselves to sentential representations. Accordingly, relying upon a case study about immune system vulnerability to attacks on CD4+ T-cells, I argue that diagrams group together information in a way that avoids repetition in representing topological structure, facilitate identification of specific topological properties of those structures, and make available to controlled processing explanatorily salient counterfactual information about topological structures, all in ways that sentential counterparts of diagrams do not. (shrink)

Besides mechanistic explanations of phenomena, which have been seriously investigated in the last decade, biology and ecology also include explanations that pinpoint specific mathematical properties as explanatory of the explanandum under focus. Among these structural explanations, one finds topological explanations, and recent science pervasively relies on them. This reliance is especially due to the necessity to model large sets of data with no practical possibility to track the proper activities of all the numerous entities. The (...) paper first defines topological explanations and then explains why topological explanations and mechanisms are different in principle. Then it shows that they are pervasive both in the study of networks—whose importance has been increasingly acknowledged at each level of the biological hierarchy—and in contexts where the notion of selective neutrality is crucial; this allows me to capture the difference between mechanisms and topological explanations in terms of practical modelling practices. The rest of the paper investigates how in practice mechanisms and topologies are combined. They may be articulated in theoretical structures and explanatory strategies, first through a relation of constraint, second in interlevel theories, or they may condition each other. Finally, I explore how a particular model can integrate mechanistic informations, by focusing on the recent practice of merging networks in ecology and its consequences upon multiscale modelling. (shrink)

Recent philosophical work has explored the distinction between causal and non-causal forms of explanation. In this literature, topological explanation is viewed as a clear example of the non-causal variety–it is claimed that topology lacks temporal information, which is necessary for causal structure. This paper explores the distinction between topological and causal forms of explanation and argues that this distinction is not as clear cut as the literature suggests. One reason for this is that some explanations involve both (...) topological and causal information. In these “borderline” cases scientists explain some outcome by appealing to the causal topology of the system of interest. These cases help clarify a type of topological explanation that is genuinely causal, but that differs from standard topological and interventionist accounts of explanation. (shrink)

So-called ‘distinctively mathematical explanations’ (DMEs) are said to explain physical phenomena, not in terms of contingent causal laws, but rather in terms of mathematical necessities that constrain the physical system in question. Lange argues that the existence of four or more equilibrium positions of any double pendulum has a DME. Here we refute both Lange’s claim itself and a strengthened and extended version of the claim that would pertain to any n-tuple pendulum system on the ground that such (...) class='Hi'>explanations are actually causal explanations in disguise and their associated modal conditionals are not general enough to explain the said features of such dynamical systems. We argue and show that if circumscribing the antecedent for a necessarily true conditional in such explanations involves making a causal analysis of the problem, then the resulting explanation is not distinctively mathematical or non-causal. Our argument generalises to other dynamical systems that may have purported DMEs analogous to the one proposed by Lange, and even to some other counterfactual accounts of non-causal explanation given by Reutlinger and Rice. (shrink)

In this paper, I argue that the newly developed network approach in neuroscience and biology provides a basis for formulating a unique type of realization, which I call topological realization. Some of its features and its relation to one of the dominant paradigms of realization and explanation in sciences, i.e. the mechanistic one, are already being discussed in the literature. But the detailed features of topological realization, its explanatory power and its relation to another prominent view of realization, (...) namely the semantic one, have not yet been discussed. I argue that topological realization is distinct from mechanistic and semantic ones because the realization base in this framework is not based on local realisers, regardless of the scale but on global realizers. In mechanistic approach, the realization base is always at the local level, in both ontic and epistemic accounts. The explanatory power of realization relation in mechanistic approach comes directly from the realization relation-either by showing how a model is mapped onto a mechanism, or by describing some ontic relations that are explanatory in themselves. Similarly, the semantic approach requires that concepts at different scales logically satisfy microphysical descriptions, which are at the local level. In topological framework the realization base can be found at different scales, but whatever the scale the realization base is global, within that scale, and not local. Furthermore, topological realization enables us to answer the “why” questions, which according to Polger 2010 make it explanatory. The explanatoriness of topological realization stems from understanding mathematical consequences of different topologies, not from the mere fact that a system realizes them. (shrink)

We derive for Bohmian mechanics topological factors for quantum systems with a multiply-connected configuration space Q. These include nonabelian factors corresponding to what we call holonomy-twisted representations of the fundamental group of Q. We employ wave functions on the universal covering space of Q. As a byproduct of our analysis, we obtain an explanation, within the framework of Bohmian mechanics, of the fact that the wave function of a system of identical particles is either symmetric or anti-symmetric.

This article examines the use of mathematical concepts in philosophy, focusing on topology, which may be viewed as a modern supplement to geometry. We show that Plato and Parmenides were already employing geometric ideas in their research, and discuss three examples of the application of topology to philosophical problems: the first concerns the analysis of the Cartesian distinction between res extensa and res cogitans, the second the ontology of possible worlds of Wittgenstein's Tractatus, and the third Leibniz's monadology. We also (...) consider the role of topology in mathematical explanations of the sort found in science, arguing that it can perform a role in philosophy that is of comparable importance. (shrink)

We address the question of whether and to what extent explanatory and modelling strategies in systems biology are mechanistic. After showing how dynamic mathematical models are actually required for mechanistic explanations of complex systems, we caution readers against expecting all systems biology to be about mechanistic explanations. Instead, the aim may be to generate topological explanations that are not standardly mechanistic, or to arrive at design principles that explain system organization and behaviour in general, but not (...) specific mechanisms. These abstraction strategies serve various aims, including prediction and control, that are central to understanding the epistemic diversity of systems biology. (shrink)

definitions and explanations frequently come together and permeate almost all fields of knowledge. This does not exclude mathematics, even when these definitions hold clear links and close connections with our physical world. Here we propose a rather different perspective. Making operational physical assumptions, we show how it is possible to rigorously reconstruct some features of both geometry and topology. Broadly speaking, assuming this operational and more concrete philosophy we not only are capable of defining primitive concepts like points, straight (...) lines, planes, angles and spaces, but we also go all the way up to more complex constructions. We show that within our method it is also possible to come up with what we call a compass-based topology as well as a normed and a metric space. We hope this operationalist point-of-view can assist other researchers and students to have a clearer understanding of these quite abstract concepts. (shrink)

In this paper, I outline a heuristic for thinking about the relation between explanation and understanding that can be used to capture various levels of “intimacy”, between them. I argue that the level of complexity in the structure of explanation is inversely proportional to the level of intimacy between explanation and understanding, i.e. the more complexity the less intimacy. I further argue that the level of complexity in the structure of explanation also affects the explanatory depth in a similar way (...) to intimacy between explanation and understanding, i.e. the less complexity the greater explanatory depth and vice versa. (shrink)

The epistemological foundation of unity of knowledge is used to formulate a system-model of participatory socioeconomic development. The micro-properties of such a participatory development approach are deeply ethical in nature. In order to bring out the endogenous role of ethics derived from the moral law in reference to the epistemic foundation, and thereby explain their impact on the socioeconomic development experience, the methods of topological space and topological mappings are found to be appropriate for formalizing the complex nature (...) of participatory dynamics. They emerge in the midst of institutional and organic interaction, integration, and evolution. The application of topological methods to participatory socioeconomic development thus opens up a field that is rarely used by mathematical economists. In this sense this article is an original contribution to the area of ethical development theory and its topological explanation and application. (shrink)

In the last two decades, philosophy of neuroscience has predominantly focused on explanation. Indeed, it has been argued that mechanistic models are the standards of explanatory success in neuroscience over, among other things, topological models. However, explanatory power is only one virtue of a scientific model. Another is its predictive power. Unfortunately, the notion of prediction has received comparatively little attention in the philosophy of neuroscience, in part because predictions seem disconnected from interventions. In contrast, we argue that (...) class='Hi'>topological predictions can and do guide interventions in science, both inside and outside of neuroscience. Topological models allow researchers to predict many phenomena, including diseases, treatment outcomes, aging, and cognition, among others. Moreover, we argue that these predictions also offer strategies for useful interventions. Topology-based predictions play this role regardless of whether they do or can receive a mechanistic interpretation. We conclude by making a case for philosophers to focus on prediction in neuroscience in addition to explanation alone. (shrink)

Philippe Huneman has recently questioned the widespread application of mechanistic models of scientific explanation based on the existence of structural explanations, i.e. explanations that account for the phenomenon to be explained in virtue of the mathematical properties of the system where the phenomenon obtains, rather than in terms of the mechanisms that causally produce the phenomenon. Structural explanations are very diverse, including cases like explanations in terms of bowtie structures, in terms of the topological properties (...) of the system, or in terms of equilibrium. The role of mathematics in bowtie structured systems and in topologically constrained systems has recently been examined in different papers. However, the specific role that mathematical properties play in equilibrium explanations requires further examination, as different authors defend different interpretations, some of them closer to the new-mechanistic approach than to the structural model advocated by Huneman. In this paper, we cover this gap by investigating the explanatory role that mathematics play in Blaser and Kirschner’s nested equilibrium model of the stability of persistent long-term human-microbe associations. We argue that their model is explanatory because: i) it provides a mathematical structure in the form of a set of differential equations that together satisfy an ESS; ii) that the nested nature of the ESSs makes the explanation of host-microbe persistent associations robust to any perturbation; iii) that this is so because the properties of the ESS directly mirror the properties of the biological system in a non-causal way. The combination of these three theses make equilibrium explanations look more similar to structural explanations than to causal-mechanistic explanation. (shrink)

What does our naïve conception of a conscious subject demand of the nature of conscious beings? In a series of recent papers David Barnett has argued that a range of powerful intuitions in the philosophy of mind are best explained by the hypothesis that our naïve conception imposes a requirement of mereological simplicity on the nature of conscious beings. It is argued here that there is a much more plausible explanation of the intuitions in question. Our naïve conception of a (...) conscious subject imposes a requirement of topological integrity. (shrink)

In this work we show that our self-awareness and perception may be successfully explained using two dimensional holistic structures with closed topology embedded into our brains - elastic membranes. These membranes are able to preserve their structure during conscious processes. Their elastic oscillations may be associated with our perceptions, where the frequency of the oscillations is responsible for the perception of different colors, sounds and other stimuli, while the amplitude of the oscillations is responsible for the feeling of a distance. (...) According to the model the squeezed regions of a membrane correspond to the brain zones involved into awareness and attention. The model may be useful for prediction, explanation and interpretation of various conscious phenomena. (shrink)

This work is mainly concerned with the notion of hierarchical modularity and its use in explaining structure and dynamical behavior of complex systems by means of hierarchical modular models, as well as with a concept of my proposal, antimodularity, tied to the possibility of the algorithmic detection of hierarchical modularity. Specifically, I highlight the pragmatic bearing of hierarchical modularity on the possibility of scientific explanation of complex systems, that is, systems which, according to a chosen basic description, can be considered (...) as composed of elementary, discrete, interrelated parts. I stress that hierarchical modularity is also required by the experimentation aimed to discover the structure of such systems. Algorithmic detection of hierarchical modularity turns out to be a task plagued by the demonstrated computational intractability of the search for the best hierarchical modular description, and by the high computational expensiveness of even approximated detection methods. Antimodularity consists in the lack of a modular description fitting the needs of the observer, a lack due either to absence of modularity in the system’s chosen basic description, or to the impossibility, due to the excessive size of the system under assessment in relation to the computational cost of algorithmic methods, to algorithmically produce a valid hierarchical description. I stress that modularity and antimodularity depend on the pragmatic choice of a given basic description of the system, a choice made by the observer based on explanatory goals. I show how antimodularity hinders the possibility of applying at least three well-known types of explanation: mechanistic, deductive-nomological and computational. A fourth type, topological explanation, remains unaffected. I then assess the presence of modularity in biological systems, and evaluate the possible consequences, and the likelihood, of incurring in antimodularity in biology and other sciences, concluding that this eventuality is quite likely, at least in systems biology. I finally indulge in some metaphysical and historical speculations: metaphysically, antimodularity seems to suggest a possible position according to which natural kinds are detected modules, and as such, due to the computational hardness of the detection of the best hierarchical modular description, they are unlikely to be the best possible way to describe the world, because the modularity of natural kinds quite probably does not reflect the best possible modularity of the world. From an historical point of view, the growing use of computational methods for modularity detection or simulation of complex systems, especially in certain areas of scientific research, hints at the envisioning of a multiplicity of emerging scientific disciplines guided by a self- sustained, growing production of possibly human-unintelligible explanations. This, I suggest, would constitute an historical change in science, which, if has not already occurred, could well be on the verge of happening. (shrink)

In the last couple of years, a few seemingly independent debates on scientific explanation have emerged, with several key questions that take different forms in different areas. For example, the questions what makes an explanation distinctly mathematical and are there any non-causal explanations in sciences (i.e., explanations that don’t cite causes in the explanans) sometimes take a form of the question of what makes mathematical models explanatory, especially whether highly idealized models in science can be explanatory and in (...) virtue of what they are explanatory. These questions raise further issues about counterfactuals, modality, and explanatory asymmetries: i.e., do mathematical and non-causal explanations support counterfactuals, and how ought we to understand explanatory asymmetries in non-causal explanations? Even though these are very common issues in the philosophy of physics and mathematics, they can be found in different guises in the philosophy of biology where there is the statistical interpretation of the Modern Synthesis theory of evolution, according to which the post-Darwinian theory of natural selection explains evolutionary change by citing statistical properties of populations and not the causes of changes. These questions also arise in philosophy of ecology or neuroscience in regard to the nature of topological explanations. The question here is can the mathematical (or more precisely topological) properties in network models in biology, ecology, neuroscience, and computer science be explanatory of physical phenomena, or are they just different ways to represent causal structures. The aim of this special issue is to unify all these debates around several overlapping questions. These questions are: are there genuinely or distinctively mathematical and non-causal explanations?; are all distinctively mathematical explanations also non-causal; in virtue of what they are explanatory; does the instantiation, implementation, or in general, applicability of mathematical structures to a variety of phenomena and systems play any explanatory role? This special issue provides a platform for unifying the debates around several key issues and thus opens up avenues for better understanding of mathematical and non-causal explanations in general, but also, it will enable even better understanding of key issues within each of the debates. (shrink)

Most philosophers of the self would take what David Barnett calls ‘The Datum’—that “pairs of people themselves are incapable of experience”—to merit its name. Barnett argues abductively from The Datum to Simplicity, the view that conscious beings must be simple. The truth of Simplicity would upend almost all materialist accounts of what we are, so Barnett’s argument and attempted rebuttals of it merit scrutiny. Rory Madden charges Barnett with overlooking a rival, better explanation, deriving from Integrity: the thesis that our (...) naïve conception of a conscious subject demands that conscious beings be topologically integrated. The content of this naïve conception is supposed to be superior to Simplicity in explaining The Datum. I argue here that Madden is mistaken: the requirement of topological integration cannot explain The Datum, and Barnett’s argument survives Madden’s challenge. (shrink)

In non-causal explanations, some non-causal facts (such as mathematical, modal or metaphysical) are used to explain some physical facts. However, precisely because these explanations abstract away from causal facts, they face two challenges: 1) it is not clear why would one rather than the other non-causal explanantia be relevant for the explanandum; and 2) why would standing in a particular explanatory relation (e.g., “counterfactual dependence”, “constraint”, “entailment”, “constitution”, “grounding”, and so on), and not in some other, be explanatory. (...) I develop an explanatory relevance account which is based on erotetic constraints and show how it addresses these two challenges. (shrink)

In the last couple of years a few seemingly independent debates on scientific explanation have emerged, with several key questions that take different forms in different areas. For example, the question what makes an explanation distinctly mathematical and are there any non-causal explanations in sciences (i.e. explanations that don’t cite causes in the explanans) sometimes take a form of the question what makes mathematical models explanatory, especially whether highly idealized models in science can be explanatory and in virtue (...) of what they are explanatory. These questions raise further issues about counterfactuals, modality and explanatory asymmetries, i.e. do mathematical and non-causal explanations support counterfactuals, and how to understand explanatory asymmetries in non-causal explanations. Even though these are very common issues in the philosophy of physics and mathematics, they can be found in different guises in the philosophy of biology, where there is the statistical interpretation of the Modern Synthesis theory of evolution, according to which the post-Darwinian theory of natural selection explains evolutionary change by citing statistical properties of populations and not the causes of changes. These questions also arise in philosophy of ecology or neuroscience in regard to the nature of topological explanations. The question here is whether in network models in biology, ecology, neuroscience and computer science the mathematical or more precisely topological properties can be explanatory of physical phenomena, or they are just different ways to represent causal structures. The aim of the special issue is to unify all these debates around several overlapping questions. (shrink)

There have been recent disagreements in the philosophy of neuroscience regarding which sorts of scientific models provide mechanistic explanations, and which do not. These disagreements often hinge on two commonly adopted, but conflicting, ways of understanding mechanistic explanations: what I call the “representation-as” account, and the “representation-of” account. In this paper, I argue that neither account does justice to neuroscientific practice. In their place, I offer a new alternative that can defuse some of these disagreements. I argue that (...) individual models do not provide mechanistic explanations by themselves. Instead, individual models are always used to complement a huge body of background information and pre-existing models about the target system. With this in mind, I argue that mechanistic explanations are distributed across sets of different, and sometimes contradictory, scientific models. Each of these models contributes limited, but essential, information to the same mechanistic explanation, but none can be considered a mechanistic explanation in isolation of the others. (shrink)

This paper is a culmination of our new foundations for recursive analysis through recursive topology as reported in Kalantari and Welch 125; 98 87). While in those papers we developed groundwork for an approach to point free analysis and applied recursion theory, in this paper we blend techniques of recursion theory with those of topology to establish new findings. We present several new techniques different from existing ones which yield interesting results. Incidental to our work is a unifying explanation of (...) various schools of study for recursive analysis. (shrink)

The concepts of atoms and bonds in molecules which appeared in chemistry during the nineteenth century are unavoidable to explain the structure and the reactivity of the matter at a chemical level of understanding. Although they can be criticized from a strict reductionist point of view, because neither atoms nor bonds are observable in the sense of quantum mechanics, the topological and statistical interpretative approaches of quantum chemistry (quantum theory of atoms in molecules, electron localization function and maximum probability (...) domain) provide consistent definitions which accommodate chemistry and quantum mechanics. (shrink)

Two approaches to understanding the idealizations that arise in the Aharonov–Bohm effect are presented. It is argued that a common topological approach, which takes the non-simply connected electron configuration space to be an essential element in the explanation and understanding of the effect, is flawed. An alternative approach is outlined. Consequently, it is shown that the existence and uniqueness of self-adjoint extensions of symmetric operators in quantum mechanics have important implications for philosophical issues. Also, the alleged indispensable explanatory role (...) of said idealizations is examined via a minimal model explanatory scheme. Last, the idealizations involved in the AB effect are placed in a wider philosophical context via a short survey of part of the literature on infinite and essential idealizations. (shrink)

Over the last two decades, network-focused approaches have become highly popular in diverse fields of biology, including neuroscience, ecology, molecular biology and genetics. While the network approach continues to grow very rapidly, some of its conceptual and methodological aspects still require a programmatic foundation. This challenge particularly concerns the question of whether a generalized account of explanatory, organisational and descriptive levels of networks can be applied universally across biological sciences. Consequently, the central focus of this theme issue will be on (...) the definition, motivation and application of key concepts in biological network science, such as levels, hierarchies, and explanatory directionality. A unification will be achieved by formulating norms for delimiting the distinctively network-topological class of explanations that connect general as well as very specific biological research questions. The impact of this theme issue is broad and encompassing, as it is highly interdisciplinary and opens a uniquely normative perspective on the foundational aspects of network-based explanations and modelling. This theme issue is intended to become a landmark publication for practical research as well as funding policy decisions, by unifying network approaches in biological sciences in terms of fundamental concepts and informing the public understanding of the network science. (shrink)

The philosophical literature on scientific explanation in neuroscience has been dominated by the idea of mechanisms. The mechanist philosophers often claim that neuroscience is in the business of finding mechanisms. This view has been challenged in numerous ways by showing that there are other successful and widespread explanatory strategies in neuroscience. However, the empirical evidence for all these claims was hitherto lacking. Empirical evidence about the pervasiveness and uses of various explanatory strategies in neuroscience is particularly needed because examples and (...) case studies that are used to illustrate philosophical claims so far tend to be hand-picked. The risk of confirmation bias is therefore considerable: when looking for white swans, all one finds is that swans are white. The more systematic quantitative and qualitative bibliometric study of a large body of relevant literature that we present in this paper can put such claims into perspective. Using bibliometric tools, we identify the typical linguistic patterns used in the alleged mechanistic, dynamical, and topological explanations in the literature, their preponderance and how they change over time. Our findings show abundant use of mechanistic language, but also the presence of a significant neuroscience literature using topological and dynamical explanatory language, which grows over time and increasingly differentiates from each other and from mechanistic explanations. (shrink)

Over the last decades, network-based approaches have become highly popular in diverse fields of biology, including neuroscience, ecology, molecular biology and genetics. While these approaches continue to grow very rapidly, some of their conceptual and methodological aspects still require a programmatic foundation. This challenge particularly concerns the question of whether a generalized account of explanatory, organisational and descriptive levels of networks can be applied universally across biological sciences. To this end, this highly interdisciplinary theme issue focuses on the definition, motivation (...) and application of key concepts in biological network science, such as explanatory power of distinctively network explanations, network levels, and network hierarchies. (shrink)

The mathematical structure of realist quantum theories has given rise to a debate about how our ordinary 3-dimensional space is related to the 3N-dimensional configuration space on which the wave function is defined. Which of the two spaces is our (more) fundamental physical space? I review the debate between 3N-Fundamentalists and 3D-Fundamentalists and evaluate it based on three criteria. I argue that when we consider which view leads to a deeper understanding of the physical world, especially given the deeper (...) class='Hi'>topological explanation from the unordered configurations to the Symmetrization Postulate, we have strong reasons in favor of 3D-Fundamentalism. I conclude that our evidence favors the view that our fundamental physical space in a quantum world is 3-dimensional rather than 3N-dimensional. I outline lines of future research where the evidential balance can be restored or reversed. Finally, I draw lessons from this case study to the debate about theoretical equivalence. (shrink)

This paper is concerned with a quality space model as an account of the intelligibility of explanation. I argue that descriptions of causal or functional roles (Chalmers Levine, 2001) are not the only basis for intelligible explanations. If we accept that phenomenal concepts refer directly, not via descriptions of causal or functional roles, then it is difficult to find role fillers for the described causal roles. This constitutes a vagueness constraint on the intelligibility of explanation. Thus, I propose to (...) use quality space models to develop a systematic way of studying different modalities of perception and feelings, e.g., visual and auditory perception, pain, and emotion, that can reveal some structural relations among these modalities. It might turn out that topological explanation can be more intelligible than causal explanation in this case. I discuss two accounts of a quality space for color vision (Clark, 2000; Rosenthal, 2010) and propose how to construct a quality space for pain. Daniel Kostic is Associated Researcher at Berlin School of Mind and Brain. (shrink)

Borsboom and colleagues have recently proposed a “network theory” of psychiatric disorders that conceptualizes psychiatric disorders as relatively stable networks of causally interacting symptoms. They have also claimed that the network theory should include non-symptom variables such as environmental factors. How are environmental factors incorporated in the network theory, and what kind of explanations of psychiatric disorders can such an “extended” network theory provide? The aim of this article is to critically examine what explanatory strategies the network theory that (...) includes both symptoms and environmental factors can accommodate. We first analyze how proponents of the network theory conceptualize the relations between symptoms and between symptoms and environmental factors. Their claims suggest that the network theory could provide insight into the causal mechanisms underlying psychiatric disorders. We assess these claims in light of network analysis, Woodward’s interventionist theory, and mechanistic explanation, and show that they can only be satisfied with additional assumptions and requirements. Then, we examine their claim that network characteristics may explain the dynamics of psychiatric disorders by means of a topological explanatory strategy. We argue that the network theory could accommodate topological explanations of symptom networks, but we also point out that this poses some difficulties. Finally, we suggest that a multilayer network account of psychiatric disorders might allow for the integration of symptoms and non-symptom factors related to psychiatric disorders and could accommodate both causal/mechanistic and topological explanations. (shrink)