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)

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)

Berichte zur Wissenschaftsgeschichte, Volume 45, Issue 3, Page 373-383, September 2022.

Berichte zur Wissenschaftsgeschichte, Volume 45, Issue 3, Page 373-383, September 2022.

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 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... (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)

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)

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)

This study clarifies the need for a renewed account of the body in physiotherapy to fill sizable gaps between physiotherapeutical theory and practice. Physiotherapists are trained to approach bodily functioning from an objectivist perspective; however, their therapeutic interactions with patients are not limited to the provision of natural-scientific explanations. Physiotherapists’ practice corresponds well to theorisation of the body as the bearer of original bodily intentionality, as outlined by Merleau-Ponty and elaborated upon by enactivists. We clarify how physiotherapeutical practice corroborates Merleau-Ponty’s (...) critical arguments against objectivist interpretations of the body; particularly, his analyses demonstrate that norms of optimal corporeal functioning are highly individual and variable in time and thus do not directly depend on generic physiological structures. In practice, objectively measurable physical deviations rarely correspond to specific subjective difficulties and, similarly, patients’ reflective insights into their own motor deficiencies do not necessarily produce meaningful motor improvements. Physiotherapeutical procedures can be understood neither as mechanical manipulations of patients’ machine-like bodies by experts nor as a process of such manipulation by way of instructing patients’ explicit conscious awareness. Rather, physiotherapeutical practice and theory can benefit from the philosophical interpretation of motor disorders as modifications of bodily intentionality. Consequently, motor performances addressed in physiotherapy are interpreted as relational features of a living organism coupled with its environment, and motor disorders are approached as failures to optimally manage the motor requirements of a given situation owing to a relative loss of the capacity to structure one’s relation with their environment through motor action. Building on this, we argue that the process of physiotherapy is most effective when understood as a bodily interaction to guide patients towards discovering better ways of grasping a situation as meaningful through bodily postures and movements. (shrink)

This paper aims to clarify the nature of understanding in medicine. The first part describes in more detail what it means to understand something and links a type of understanding (i.e., objectual understanding) to explanations. The second part proceeds to investigate what objectual understanding of a disease (i.e., biomedical understanding) requires by considering the case of scurvy from the history of medi- cine. The main hypothesis is that grasping a mechanistic explanation of a condi- tion is necessary for a biomedical (...) understanding of that condition. The third part of the paper argues that biomedical understanding is necessary, but not sufficient for understanding in a clinical context (i.e., clinical understanding). The hypothe- sis is that clinical understanding combines biomedical understanding of a disease or pathological condition with understanding illness, which involves some degree of personal understanding of the patient. It is argued that, in many cases, clinical understanding necessitates adopting a particular second-personal stance and using cognitive resources in addition to those involved in biomedical understanding. (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)