What is human understanding and why should we care about it? I propose a method of philosophical investigation called ‘function-first epistemology’ and use this method to investigate the nature and value of understanding-why. I argue that the concept of understanding-why serves the practical function of identifying good explainers, which is an important role in the general economy of our concepts. This hypothesis sheds light on a variety of issues in the epistemology of understanding including the role of explanation, the relationship (...) between understanding-why and knowledge, and the value of understanding-why. I conclude that understanding-why is valuable and yet knowledge plays more important roles in our epistemic life. (shrink)

What is understanding? My goal in this paper is to lay out a new approach to this question and clarify how that approach deals with certain issues. The claim is that understanding is a matter of compressing information about the understood so that it can be mentally useful. On this account, understanding amounts to having a representational kernel and the ability to use it to generate the information one needs regarding the target phenomenon. I argue that this ambitious new account (...) can accommodate much of the data that has motivated theories of understanding in philosophy of science, and can also be generally applicable in epistemology and daily life as well. (shrink)

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)

In this paper, I consider the relationship between coming to understand why something must be the case and coming to understand why it actually is the case in some particular instance. Peter Lipton uses the possibility of coming to understand a phenomenon via a necessity proof as an argument that there can be understanding with no explanation. Lipton’s argument has come under criticism, at least partially because one might think that understanding why something must be the case has a different (...) object from understanding the actual phenomenon. In this paper, I argue that that under certain circumstances it is fairly straightforward to come to understand an actual phenomenon on the basis of knowing why it had to be the case. Rather than relying on brute intuitions, my primary strategy will be to show that on least some modern accounts of understanding we can validate Lipton’s general point with respect to a variety of possible necessity relations. (shrink)

Analytic Philosophy, Volume 62, Issue 1, Page 33-56, March 2021.

Thought: A Journal of Philosophy, EarlyView.

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)

In this paper, we explore the link between understanding and transformative decisions. Paul (2014) suggests that one important aspect of making some decisions is that we make them not just on the basis of what data from other people tell us, but based on our own acquaintance with how the decision affects us. In this paper, we draw out a parallel between the sort of reasoning that Paul argues is required for authentic decision making and the sort of epistemic grasp (...) of a subject matter that is required for understanding. The central claim of this paper is that one’s ability to make a decision authentically is proportional to one’s ability to model what it is like to have the possible resultant experience. We endorse a broad notion according to which one can model something by thinking about relevantly similar things. (shrink)

Our goal in this paper is to experimentally investigate whether folk conceptions of explanation are psychologistic. In particular, are people more likely to classify speech acts as explanations when they cause understanding in their recipient? The empirical evidence that we present suggests this is so. Using the side-effect effect as a marker of mental state ascriptions, we argue that lay judgments of explanatory status are mediated by judgments of a speaker’s and/or audience’s mental states. First, we show that attributions of (...) both understanding and explanation exhibit a side-effect effect. Next, we show that when the speaker’s and audience’s level of understanding is stipulated, the explanation side-effect effect goes away entirely. These results not only extend the side-effect effect to attributions of understanding, they also suggest that attributions of explanation exhibit a side-effect effect because they depend upon attributions of understanding, supporting the idea that folk conceptions of explanation are psychologistic. (shrink)

Four experiments investigate the folk concept of “understanding,” in particular when and why it is deployed differently from the concept of knowledge. We argue for the positions that people have higher demands with respect to explanatory depth when it comes to attributing understanding, and that this is true, in part, because understanding attributions play a functional role in identifying experts who should be heeded with respect to the general field in question. These claims are supported by our findings that people (...) differentially withhold attributions of understanding when the object of attribution has minimal explanatory information. We also show that this tendency significantly correlates with people’s willingness to defer to others as potential experts. This work bears on a pressing issue in epistemology concerning the place and value of understanding. Our results also provide reason against positing a simple equation of knowledge and understanding. We contend that, because deference plays a crucial role in many aspects of everyday reasoning, the fact that we use understanding attributions to demarcate experts reveals a potential mechanism for achieving our epistemic aims in many domains. (shrink)

Dynamical models of cognition have played a central role in recent cognitive science. In this paper, we consider a common strategy by which dynamical models describe their target systems neither as purely static nor as purely dynamic, but rather using a hybrid approach. This hybridity reveals how dynamical models involve representational choices that are important for understanding the relationship between dynamical and non-dynamical representations of a system.

Computational systems biologists create and manipulate computational models of biological systems, but they do not always have straightforward epistemic access to the content and behavioural profile of such models because of their length, coding idiosyncrasies, and formal complexity. This creates difficulties both for modellers in their research groups and for their bioscience collaborators who rely on these models. In this paper we introduce a new kind of visualization that was developed to address just this sort of epistemic opacity. The visualization (...) is unusual in that it depicts the dynamics and structure of a computer model instead of that model’s target system, and because it is generated algorithmically. Using considerations from epistemology and aesthetics, we explore how this new kind of visualization increases scientific understanding of the content and function of computer models in systems biology to reduce epistemic opacity. (shrink)

Is understanding subject to a factivity constraint? That is, must the agent’s representation of some subject matter be accurate in order for her to understand that subject matter? ‘No’, I argue in this paper. As an alternative, I formulate a novel manipulationist account of understanding. Rather than correctly representing, understanding, on this account, is a matter of being able to manipulate a representation of the world to satisfy contextually salient interests. This account of understanding is preferable to factivism, I argue, (...) mainly for simplicity reasons. While it explains the intuitive data about understanding as successfully as factivist accounts, it is simpler by virtue of reducing the value truth bestows on understanding to that of usability. (shrink)

Explainable artificial intelligence (XAI) is an emerging, multidisciplinary field of research that seeks to develop methods and tools for making AI systems more explainable or interpretable. XAI researchers increasingly recognise explainability as a context-, audience- and purpose-sensitive phenomenon, rather than a single well-defined property that can be directly measured and optimised. However, since there is currently no overarching definition of explainability, this poses a risk of miscommunication between the many different researchers within this multidisciplinary space. This is the problem we (...) seek to address in this paper. We outline a framework, called Explanatory Pragmatism, which we argue has two attractive features. First, it allows us to conceptualise explainability in explicitly context-, audience- and purpose-relative terms, while retaining a unified underlying definition of explainability. Second, it makes visible any normative disagreements that may underpin conflicting claims about explainability regarding the purposes for which explanations are sought. Third, it allows us to distinguish several dimensions of AI explainability. We illustrate this framework by applying it to a case study involving a machine learning model for predicting whether patients suffering disorders of consciousness were likely to recover consciousness. (shrink)

Explaining phenomena is a primary goal of science. Consequently, it is unsurprising that gaining a proper understanding of the nature of explanation is an important goal of science education. In order to properly understand explanation, however, it is not enough to simply consider theories of the nature of explanation. Properly understanding explanation requires grasping the relation between explanation and understanding, as well as how explanations can lead to scientific knowledge. This article examines the nature of explanation, its relation to understanding, (...) and how explanations are used to generate scientific knowledge via inferences to the best explanation. Studying these features and applications of explanation not only provides insight into a concept that is important for science education in its own right, but also sheds light on an aspect of recent debates concerning the so-called consensus view of nature of science (NOS). Once the relation between explanation, understanding, and knowledge is clear, it becomes apparent that science is unified in important ways. Seeing this unification provides some support for thinking that there are general features of NOS of the sort proposed by the consensus view and that teaching about these general features of NOS should be a goal of science education. (shrink)

In pedagogical contexts and in everyday life, we often come to believe something because it would best explain the data. What is it about the explanatory endeavor that makes it essential to everyday learning and to scientific progress? There are at least two plausible answers. On one view, there is something special about having true explanations. This view is highly intuitive: it’s clear why true explanations might improve one’s epistemic position. However, there is another possibility—it could be that the process (...) of seeking, generating, or evaluating explanations itself puts one in a better epistemic position, even when the outcome of the process is not a true explanation. In other words, it could be that accurate explanations are beneficial, or it could be that high-quality explaining is beneficial, where there is something about the activity of looking for an explanation that improves our epistemic standing. The main goal of this paper is to tease apart these two possibilities, both theoretically and empirically, which we align with “Inference to the Best Explanation” and “Explaining for the Best Inference”, respectively. We also provide some initial support for EBI and identify promising directions for future research. (shrink)

The connection between understanding and explanation has recently been of interest to philosophers. Inglis and Mejía-Ramos (Synthese, 2019) propose that within mathematics, we should accept a functional account of explanation that characterizes explanations as those things that produce understanding. In this paper, I start with the assumption that this view of mathematical explanation is correct and consider what we can consequently learn about mathematical explanation. I argue that this view of explanation suggests that we should shift the question of explanation (...) away from why-questions and towards a “what’s going on here” question. Additionally, I argue that when we recognize the connection between understanding and explanation we naturally see how more than just proof can be explanatory. I expand this point by detailing how definitions and diagrams can be explanatory. In all, we see that when we take seriously the connection between understanding and explanation, we get a better sense of how explanation arises within mathematics. (shrink)

Previous research in Explainable Artificial Intelligence (XAI) suggests that a main aim of explainability approaches is to satisfy specific interests, goals, expectations, needs, and demands regarding artificial systems (we call these “stakeholders' desiderata”) in a variety of contexts. However, the literature on XAI is vast, spreads out across multiple largely disconnected disciplines, and it often remains unclear how explainability approaches are supposed to achieve the goal of satisfying stakeholders' desiderata. This paper discusses the main classes of stakeholders calling for explainability (...) of artificial systems and reviews their desiderata. We provide a model that explicitly spells out the main concepts and relations necessary to consider and investigate when evaluating, adjusting, choosing, and developing explainability approaches that aim to satisfy stakeholders' desiderata. This model can serve researchers from the variety of different disciplines involved in XAI as a common ground. It emphasizes where there is interdisciplinary potential in the evaluation and the development of explainability approaches. (shrink)

Mathematical explanations are poorly understood. Although mathematicians seem to regularly suggest that some proofs are explanatory whereas others are not, none of the philosophical accounts of what such claims mean has become widely accepted. In this paper we explore Wilkenfeld’s suggestion that explanations are those sorts of things that generate understanding. By considering a basic model of human cognitive architecture, we suggest that existing accounts of mathematical explanation are all derivable consequences of Wilkenfeld’s ‘functional explanation’ proposal. We therefore argue that (...) the explanatory criteria offered by earlier accounts can all be thought of as features that make it more likely that a mathematical proof will generate understanding. On the functional account, features such as characterising properties, unification, and salience correlate with explanatoriness, but they do not define explanatoriness. (shrink)

This paper offers a normative account of the speech act of explanation with understanding as its norm. The previous accounts of the speech act of explanation rely on the factive notion of understanding and maintain that proper explanations require knowledge. I argue, however, that such accounts are too demanding and do not reflect the everyday practice of explanation and the attribution of understanding. Instead, I argue that the non-factive, objectual attitude of understanding is sufficient for a proper explanation. On the (...) normative level, explanations are governed by an audience-centred norm, i.e., they are sensitive to the epistemic position of the audience. According to the proposed account, an explanation is a communicative act in which one puts the audience in a position to understand the explained phenomenon. This proposal fits into the recent wave of applications of the normative account and makes space for the pluralism of illocutionary acts. (shrink)

The way in which one understands information and concepts, and the way a student works to develop this, is an individual aspect of learning that cannot be universally defined as (at least manifested) the same for everyone. ‘Understanding’ is a broad term, and the way one achieves understanding is dependent on the way that material is presented. In this article, we argue that the philosophy of science can be important to nursing education—in particular, by showing that the way we imbue (...) understanding might depend on the meaning of ‘understanding’. Diagrams and concept maps are meant to guide newly formed knowledge and connections to develop proper thinking (e.g., the order in which nursing students must prioritize data) that a student requires in the field. We argue that whether or not an image/diagram/concept map confers understanding will depend on both what the object is and what we mean by ‘understanding’. (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)

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 counterfactual approach to explainable AI (XAI) seeks to provide understanding of AI systems through the provision of counterfactual explanations. In a recent systematic review, Chou et al. (Inform Fus 81:59–83, 2022) argue that the counterfactual approach does not clearly provide causal understanding. They diagnose the problem in terms of the underlying framework within which the counterfactual approach has been developed. To date, the counterfactual approach has not been developed in concert with the approach for specifying causes developed by Pearl (...) (Causality: Models, reasoning, and inference. Cambridge University Press, 2000) and Woodward (Making things happen: A theory of causal explanation. Oxford University Press, 2003). In this paper, I build on Chou et al.’s work by applying the Pearl-Woodward approach. I argue that the standard counterfactual approach to XAI is capable of delivering causal understanding, but that there are limitations on its capacity to do so. I suggest a way to overcome these limitations. (shrink)