In this paper, we argue that, contra Strevens (2013), understanding in the sciences is sometimes partially constituted by the possession of abilities; hence, it is not (in such cases) exhausted by the understander’s bearing a particular psychological or epistemic relationship to some set of structured propositions. Specifically, the case will be made that one does not really understand why a modeled phenomenon occurred unless one has the ability to actually work through (meaning run and grasp at each step) a model (...) simulation of the underlying dynamic. (shrink)

This paper focuses on two questions: Is understanding intimately bound up with accurately representing the world? Is understanding intimately bound up with downstream abilities? We will argue that the answer to both these questions is “yes”, and for the same reason-both accuracy and ability are important elements of orthogonal evaluative criteria along which understanding can be assessed. More precisely, we will argue that representational-accuracy and intelligibility are good-making features of a state of understanding. Interestingly, both evaluative claims have been defended (...) by philosophers in the literature on understanding as the criterion of evaluation. We argue that proponents of both approaches have important insights and that, drawing on both their own observations and a few novel arguments, we can construct a more complete picture of understanding evaluation. We thus posit the theory of there being Multiple Understanding Dimensions. The main thing to note about our dualism regarding the evaluative criteria of understanding is that it accounts for the intuitions about cases underlying both previously held positions. (shrink)

This paper brings together several strands of thought from both the analytic and phenomenological traditions in order to critically examine accounts of cognitive enhancement that rely on the idea of cognitive extension. First, I explain the idea of cognitive extension, the metaphysics of mind on which it depends, and how it has figured in recent discussions of cognitive enhancement. Then, I develop ideas from Husserl that emphasize the agential character of thought and the distinctive way that conscious thoughts are related (...) to one another. I argue that these considerations are necessary for understanding why forms of cognitive extension may diminish our cognitive lives in different ways. This does not lead to a categorical rejection of cognitive enhancement as unethical or bad for human flourishing, but does warrant a conservative approach to the design and implementation of cognitive artifacts. (shrink)

One can find in the literature two sets of views concerning the relationship between understanding and explanation: that one understands only if 1) one has knowledge of causes and 2) that knowledge is provided by an explanation. Taken together, these tenets characterize what I call the narrow knowledge account of understanding. While the first tenet has recently come under severe attack, the second has been more resistant to change. I argue that we have good reasons to reject it on the (...) basis of theoretical models that provide how-possibly explanations. These models, while they do not explain in the strict sense, afford understanding. In response, I propose an alternative epistemology of understanding, broad KAU, that takes cases of theoretical modelling into account. (shrink)

One puzzle concerning highly idealized models is whether they explain. Some suggest they provide so-called ‘how-possibly explanations’. However, this raises an important question about the nature of how-possibly explanations, namely what distinguishes them from ‘normal’, or how-actually, explanations? I provide an account of how-possibly explanations that clarifies their nature in the context of solving the puzzle of model-based explanation. I argue that the modal notions of actuality and possibility provide the relevant dividing lines between how-possibly and how-actually explanations. Whereas how-possibly (...) explanations establish claims of possible explanations, how-actually explanations establish claims of actual ones. Models, in turn, simply provide evidence for these claims. (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 medicine. The main hypothesis is that grasping a mechanistic explanation of a condition 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 hypothesis 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)

There is considerable agreement among epistemologists that certain abilities are constitutive of understanding-why. These abilities include: constructing explanations, drawing conclusions, and answering questions. This agreement has led epistemologists to conclude that understanding is a kind of know-how. However, in this paper, I argue that the abilities constitutive of understanding are the same kind of cognitive abilities that we find in ordinary cases of knowledge-that and not the kind of practical abilities associated with know-how. I argue for this by disambiguating between (...) different senses of abilities that are too often lumped together. As a consequence, non-reductionists about understanding—those that claim that understanding-why is not reducible to knowledge-that—need to find another way to motivate the view. In the end, the fact that abilities are constitutive of understanding-why does not give us reason to conclude that understanding is a kind of know-how. (shrink)

What is the relationship between understanding and knowing? This paper offers a defence of reductionism about understanding: the view that instances of understanding reduce to instances of knowing. I argue that knowing is both necessary and sufficient for understanding. I then outline some advantages of reductionism.

Within the modeling literature, there is often an implicit assumption about the relationship between a given model and a scientific explanation. The goal of this article is to provide a unified framework with which to analyze the myriad relationships between a model and an explanation. Our framework distinguishes two fundamental kinds of relationships. The first is metaphysical, where the model is identified as an explanation or as a partial explanation. The second is epistemological, where the model produces understanding that is (...) related to the explanation of interest. Our analysis reveals that the epistemological relationships are not always dependent on the metaphysical relationships, contrary to what has been assumed by many philosophers of science. Moreover, we identify several importantly different ways that scientific models instantiate these relationships. We argue that our framework provides novel insights concerning the nature of models, explanation, idealization, and understanding. (shrink)

Catherine Elgin has recently argued that a nonfactive conception of understanding is required to accommodate the epistemic successes of science that make essential use of idealizations and models. In this paper, I argue that the fact that our best scientific models and theories are pervasively inaccurate representations can be made compatible with a more nuanced form of scientific realism that I call Understanding Realism. According to this view, science aims at (and often achieves) factive scientific understanding of natural phenomena. I (...) contend that this factive scientific understanding is provided by grasping a set of true modal information about the phenomenon of interest. Furthermore, contrary to Elgin’s view, I argue that the facticity of this kind of scientific understanding can be separated from the inaccuracy of the models and theories used to produce it. (shrink)

This paper analyzes two ways idealized biological models produce factive scientific understanding. I then argue that models can provide factive scientific understanding of a phenomenon without providing an accurate representation of the features of their real-world target system. My analysis of these cases also suggests that the debate over scientific realism needs to investigate the factive scientific understanding produced by scientists’ use of idealized models rather than the accuracy of scientific models themselves.

In this note I defend nonreductionism about understanding by arguing that knowledge is neither necessary nor sufficient for understanding. To do so, I examine Paulina Sliwa’s recent (Sliwa 2015, 2017) defence of knowledge-based Reductionism (Reductionism for short). Sliwa claims that one understands why p if and only if one has a sufficient amount of knowledge why p. Sliwa also contends that Reductionism is supported by intuitive verdicts about our uses of ‘understanding why’ and ‘knowing why’. In reply, I first argue (...) that Sliwa’s Reductionism leads to a vicious infinite regress. Secondly, I defuse the motivation in favour of Reductionism by showing how the linguistic data can be accommodated within a Nonreductionist framework. (shrink)

In this article I develop a model of theoretical understanding in science. This is a philosophical theory that specifies the conditions that are both necessary and sufficient for a scientist to satisfy the construction ‘S understands theory T ’. I first consider how this construction is preferable to others, then build a model of the requisite conditions on the basis of examples from elementary physics. I then show how this model of theoretical understanding can be made philosophically robust and provide (...) a more sophisticated account than we see from models of a similar kind developed by those working in the psychology of physics and artificial intelligence. 1 Introduction2 The Explicandum/Analysandum3 Analysis of ‘S understands T’ 4 The Inferential Model4.1 Which problems are we talking about?4.2 Does the solution have to be true?4.3 Does each cycle have to be correct for S to understand T?4.4 What is problem-solving reliability?4.5 Does every specific inference of a cycle have to be correct?4.6 Does each inference have to use a principle that is part of the theory?5 Theoretical Understanding and Conceptual Expertise: Empirical Considerations6 Conclusion: Inferential Model of Scientific Understanding and Our Traditional Problems. (shrink)

I argue for an account of grasping, or understanding that, on which we grasp via a higher-order mental act of Husserlian fulfillment. Fulfillment is the act of matching up the objects of our phenomenally presentational experiences with those of our phenomenally representational thought. Grasping-by-fulfilling is importantly different from standard epistemic aims, in part because it is phenomenal rather than inferential. (I endorse Bourget’s 2017 arguments to that effect.) I show that grasping-by-fulfilling cannot be a species of propositional knowledge or belief, (...) and that it is not essentially connected to justification. I motivate a revisionary epistemology on which achieving propositional knowledge and coming to grasp are dual epistemic aims. My account makes sense of a common occurrence—that we are often unmoved to act on our beliefs until we come to phenomenally experience them in some way. It also explains puzzling features of human inquiry. (shrink)

Grounding theorists insist that grounding and explanation are intimately related. This claim could be understood as saying either that grounding ‘inherits’ its properties from explanation or it could be interpreted as saying that grounding plays an important—possibly an indispensable—role in metaphysical explanation. Or both. I argue that saying that grounding ‘inherits’ its properties from explanation can only be justified if grounding is explanatory by nature, but that this view is untenable. We ought therefore to be ‘separatists’ and view grounding and (...) explanation as distinct. As it turns out, though, once grounding has been in this sense distinguished from the explanation it backs, the view that the role grounding plays in explanation justifies its introduction ends up in serious trouble. I conclude that the role grounding plays in explanation does not justify attributing to grounding whatever nature we think it has, and it most likely does not give us any special reason to think grounding exists. (shrink)

How is grounding related to metaphysical explanation? The standard view is that the former somehow “backs”, “undergirds” or “underlies” the latter. This view fits into a general picture of explanation, according to which explanations in general hold in virtue of a certain elite group of “explanatory relations” or “determinative relations” that back them. This paper turns the standard view on its head: grounding doesn't “back” metaphysical explanation but is in an important sense downstream from it. I call this view “grounding (...) idealism”, since it structurally resembles an analogous view about causation that is known as “causal idealism” and has been endorsed by philosophers like Michael Scriven and Philip Kitcher. I formulate a specific version of grounding idealism, Metaphysical Explanation‐First Idealism (MEFI), according to which the semantic value of ‘grounding’ is an abundant, gerrymandered relation settled by the metaphysical explanation facts. Then I offer some theoretical considerations that support MEFI over rival accounts of the relation between grounding and metaphysical explanation. Finally, I address the question of what role is left for grounding to play, if not that of “backing” metaphysical explanations. (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 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 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)

Recently, it has been debated as to whether understanding is a species of explanatory knowledge. Those who deny this claim frequently argue that understanding, unlike knowledge, can be lucky. In this paper I argue that current arguments do not support this alleged compatibility between understanding and epistemic luck. First, I argue that understanding requires reliable explanatory evaluation, yet the putative examples of lucky understanding underspecify the extent to which subjects possess this ability. In the course of defending this claim, I (...) also provide a new account of the kind of ‘grasping’ taken to be central to understanding. Second, I show that putative examples of lucky understanding unwittingly deploy a kind of luck that is compatible with knowledge. Finally, appealing to a number of works on explanation and its attendant epistemology, I argue that alleged instances of lucky understanding that overcome these two obstacles will invariably violate certain norms of explanatory inquiry – our paradigmatic understanding-oriented practice. By contrast, knowledge of the same information is immune to these criticisms. Consequently, if understanding is environmentally lucky, it is always inferior to the understanding that a corresponding case of knowledge would provide. (shrink)

The literature on the nature of understanding can be divided into two broad camps. Explanationists believe that it is knowledge of explanations that is key to understanding. In contrast, their manipulationist rivals maintain that understanding essentially involves an ability to manipulate certain representations. The aim of this paper is to provide a novel knowledge based account of understanding. More specifically, it proposes an account of maximal understanding of a given phenomenon in terms of fully comprehensive and maximally well-connected knowledge of (...) it and of degrees of understanding in terms of approximations to such knowledge. It is completed by a contextualist semantics for outright attributions of understanding according to which an attribution of understanding is true of one just in case one knows enough about it to perform some contextually determined task. It is argued that this account has an edge over both its explanationist and manipulationist competitors. (shrink)

This paper connects two important debates in epistemology—to wit, on the goal of inquiry and on the nature of understanding—and offers a unified knowledge-based account of both.

Reformulating a scientific theory often leads to a significantly different way of understanding the world. Nevertheless, accounts of both theoretical equivalence and scientific understanding have neglected this important aspect of scientific theorizing. This essay provides a positive account of how reformulation changes our understanding. My account simultaneously addresses a serious challenge facing existing accounts of scientific understanding. These accounts have failed to characterize understanding in a way that goes beyond the epistemology of scientific explanation. By focusing on cases in which (...) we have differences in understanding without differences in explanation, I show that understanding does not reduce to explanation. (shrink)

We argue that the robustness analysis of idealized models can have confirmational power. This responds to concerns recently raised in the literature, according to which the robustness analysis of models whose idealizations are not discharged is unable to confirm the causal mechanisms underlying these models, and the robustness analysis of models whose idealizations are discharged is unnecessary. In response, we make clear that, where idealizations sweep out, in a specific way, the space of possibilities— which is sometimes, though not always, (...) the case—they can be holistically discharged. In turn, this can be used to show that the robustness analysis of idealized models can have confirmational force after all. (shrink)

What is scientific progress? On Alexander Bird’s epistemic account of scientific progress, an episode in science is progressive precisely when there is more scientific knowledge at the end of the episode than at the beginning. Using Bird’s epistemic account as a foil, this paper develops an alternative understanding-based account on which an episode in science is progressive precisely when scientists grasp how to correctly explain or predict more aspects of the world at the end of the episode than at the (...) beginning. This account is shown to be superior to the epistemic account by examining cases in which knowledge and understanding come apart. In these cases, it is argued that scientific progress matches increases in scientific understanding rather than accumulations of knowledge. In addition, considerations having to do with minimalist idealizations, pragmatic virtues, and epistemic value all favor this understanding-based account over its epistemic counterpart. (shrink)

Deductive Cogency holds that the set of propositions towards which one has, or is prepared to have, a given type of propositional attitude should be consistent and closed under logical consequence. While there are many propositional attitudes that are not subject to this requirement, e.g. hoping and imagining, it is at least prima facie plausible that Deductive Cogency applies to the doxastic attitude involved in propositional knowledge, viz. belief. However, this thought is undermined by the well-known preface paradox, leading a (...) number of philosophers to conclude that Deductive Cogency has at best a very limited role to play in our epistemic lives. I argue here that Deductive Cogency is still an important epistemic requirement, albeit not as a requirement on belief. Instead, building on a distinction between belief and acceptance introduced by Jonathan Cohen and recent developments in the epistemology of understanding, I propose that Deductive Cogency applies to the attitude of treating propositions as given in the context of attempting to understand a given phenomenon. I then argue that this simultaneously accounts for the plausibility of the considerations in favor of Deductive Cogency and avoids the problematic consequences of the preface paradox. (shrink)

This paper presents and argues for an account of objectual understanding that aims to do justice to the full range of cases of scientific understanding, including cases in which one does not have an explanation of the understood phenomenon. According to the proposed account, one understands a phenomenon just in case one grasps a sufficiently accurate and comprehensive model of the ways in which it or its features are situated within a network of dependence relations; one’s degree of understanding is (...) proportional to the comprehensiveness and accuracy of such a model. I compare this account with accounts of scientific understanding that explicate understanding in terms of having an explanation of the understood phenomenon. I discuss three distinct types of cases in which scientific understanding does not amount to possessing an explanation of any kind, and argue that the proposed model-based account can accommodate these cases while still retaining a strong link between understanding and explanation. (shrink)

This is a teaching and learning guide to accompany "Explanation in Mathematics: Proofs and Practice".

Gauss’s quadratic reciprocity theorem is among the most important results in the history of number theory. It’s also among the most mysterious: since its discovery in the late 18th century, mathematicians have regarded reciprocity as a deeply surprising fact in need of explanation. Intriguingly, though, there’s little agreement on how the theorem is best explained. Two quite different kinds of proof are most often praised as explanatory: an elementary argument that gives the theorem an intuitive geometric interpretation, due to Gauss (...) and Eisenstein, and a sophisticated proof using algebraic number theory, due to Hilbert. Philosophers have yet to look carefully at such explanatory disagreements in mathematics. I do so here. According to the view I defend, there are two important explanatory virtues—depth and transparency—which different proofs (and other potential explanations) possess to different degrees. Although not mutually exclusive in principle, the packages of features associated with the two stand in some tension with one another, so that very deep explanations are rarely transparent, and vice versa. After developing the theory of depth and transparency and applying it to the case of quadratic reciprocity, I draw some morals about the nature of mathematical explanation. (shrink)

Mathematicians distinguish between proofs that explain their results and those that merely prove. This paper explores the nature of explanatory proofs, their role in mathematical practice, and some of the reasons why philosophers should care about them. Among the questions addressed are the following: what kinds of proofs are generally explanatory (or not)? What makes a proof explanatory? Do all mathematical explanations involve proof in an essential way? Are there really such things as explanatory proofs, and if so, how do (...) they relate to the sorts of explanation encountered in philosophy of science and metaphysics? (shrink)

In this paper, I give an overview of different models of understanding attribution and advance a contextualist account of understanding attribution. Whereas other contextualist accounts make the degree in which the epistemic states of the relevant agents satisfy certain invariant conditions context-sensitive, the proposed account makes the conditions themselves context-sensitive.

The notion of a non-sensory mental state or event that plays a prominent role in coming to understand, an epistemic achievement distinct from mere knowledge, featured prominently in historical writings on philosophy, and philosophical methodology. It is, however, completely absent from contemporary discussions of the subject. This paper argues that intuition plays an epistemic role in understanding, including philosophical understanding, and offers an explanation of how intuition manages to play this role, if and when it does. It is argued, subsequently, (...) that this role is autonomous, in the sense that a source of understanding cannot be reduced to a source of justification, evidence, or reason. Finally, it is noted that such autonomy implies that popular forms of skepticism about intuition do not impugn intuition’s epistemic significance with respect to its status as a source of understanding. (shrink)

The paper argues that an account of understanding should take the form of a Carnapian explication and acknowledge that understanding comes in degrees. An explication of objectual understanding is defended, which helps to make sense of the cognitive achievements and goals of science. The explication combines a necessary condition with three evaluative dimensions: An epistemic agent understands a subject matter by means of a theory only if the agent commits herself sufficiently to the theory of the subject matter, and to (...) the degree that the agent grasps the theory (i.e., is able to make use of it), the theory answers to the facts and the agent’s commitment to the theory is justified. The threshold for outright attributions of understanding is determined contextually. The explication has descriptive as well as normative facets and allows for the possibility of understanding by means of non-explanatory (e.g., purely classificatory) theories. (shrink)

The paper argues that an account of understanding should take the form of a Carnapian explication and acknowledge that understanding comes in degrees. An explication of objectual understanding is defended, which helps to make sense of the cognitive achievements and goals of science. The explication combines a necessary condition with three evaluative dimensions: an epistemic agent understands a subject matter by means of a theory only if the agent commits herself sufficiently to the theory of the subject matter, and to (...) the degree that the agent grasps the theory (i.e., is able to make use of it), the theory answers to the facts and the agent’s commitment to the theory is justified. The threshold for outright attributions of understanding is determined contextually. The explication has descriptive as well as normative facets and allows for the possibility of understanding by means of non-explanatory (e.g., purely classificatory) theories. (shrink)

The articulation of an overarching account of scientific explanation has long been a central preoccupation for the philosophers of science. Although a while ago the literature was dominated by two approaches—a causal account and a unificationist account—today the consensus seems to be that the causal account has won. In this paper, I challenge this consensus and attempt to revive unificationism. More specifically, I aim to accomplish three goals. First, I add new criticisms to the standard anti-unificationist arguments, in order to (...) motivate the need for a revision of the doctrine. Second, and most importantly, I sketch such a revised version. Then I argue that, contrary to widespread belief, the causal account and this revised unificationist account of explanation are compatible. Moreover, I also maintain that the unificationist account has priority, since a most satisfactory theory of explanation can be obtained by incorporating the causal account, as a sub-component of the unificationist account. The driving force behind this reevaluation of the received view in the philosophy of explanation is a reconsideration of the role of scientific understanding. (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)

As the demand for explainable deep learning grows in the evaluation of language technologies, the value of a principled grounding for those explanations grows as well. Here we study the state-of-the-art in explanation for neural models for natural-language processing (NLP) tasks from the viewpoint of philosophy of science. We focus on recent evaluation work that finds brittleness in explanations obtained through attention mechanisms.We harness philosophical accounts of explanation to suggest broader conclusions from these studies. From this analysis, we assert the (...) impossibility of causal explanations from attention layers over text data. We then introduce NLP researchers to contemporary philosophy of science theories that allow robust yet non-causal reasoning in explanation, giving computer scientists a vocabulary for future research. (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)

We provide two programmatic frameworks for integrating philosophical research on understanding with complementary work in computer science, psychology, and neuroscience. First, philosophical theories of understanding have consequences about how agents should reason if they are to understand that can then be evaluated empirically by their concordance with findings in scientific studies of reasoning. Second, these studies use a multitude of explanations, and a philosophical theory of understanding is well suited to integrating these explanations in illuminating ways.

The paper provides a systematic overview of recent debates in epistemology and philosophy of science on the nature of understanding. We explain why philosophers have turned their attention to understanding and discuss conditions for “explanatory” understanding of why something is the case and for “objectual” understanding of a whole subject matter. The most debated conditions for these types of understanding roughly resemble the three traditional conditions for knowledge: truth, justification and belief. We discuss prominent views about how to construe these (...) conditions for understanding, whether understanding indeed requires conditions of all three types and whether additional conditions are needed. (shrink)