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Although understanding is the object of a growing literature in epistemology and the philosophy of science, only few studies have concerned understanding in mathematics. This essay offers an account of a fundamental form of mathematical understanding: proof understanding. The account builds on a simple idea, namely that understanding a proof amounts to rationally reconstructing its underlying plan. This characterization is fleshed out by specifying the relevant notion of plan and the associated process of rational reconstruction, building in part on Bratman's (...) |
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When a train operator tells us that our train will be late ‘because of delays’, their attempt at explanation fails because there is insufficient distance between the explanans and the explanandum. In this paper, I motivate and defend an account of ‘explanatory distance’, based on the idea that explanations give information about dependence. I show that this account offers useful resources for addressing problem cases, including recent debates about grounding explanation, and the historical case of Molière’s dormitive virtue. |
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Facts about explanation are often taken as a guide to facts about metaphysics. Such inferences from explanation to metaphysics typically rely on two elements: explanatory realism, the view that it is a characteristic and necessary aspect of explanation to give information about metaphysical structure, and a backing model of explanation, according to which explanations are backed by supporting relations, such as causation. Combining explanatory realism with a backing model permits conclusions about metaphysics to follow straightforwardly from facts about explanation, and (...) |
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Metaphors are found all throughout science: in published papers, working hypotheses, policy documents, lecture slides, grant proposals, and press releases. They serve different functions, but perhaps most striking is the way they enable understanding, of a theory, phenomenon, or idea. In this paper, we leverage recent advances on the nature of metaphor and the nature of understanding to explore how they accomplish this feat. We attempt to shift the focus away from the epistemic value of the content of metaphors, to (...) |
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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 (...) |
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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, (...) |
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Starting with the slogan that understanding is a ‘knowledge of causes’, Stephen Grimm and John Greco have argued that understanding comes from a knowledge of dependence relations. Grounding is the trendiest dependence relation on the market, and if Grimm and Greco are correct, then instances of grounding should also give rise to understanding. In this paper, I will show that this prediction is correct – grounding does indeed generate understanding in just the way that Grimm and Greco anticipate. However, grounding (...) |
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By appealing to resources found in the scientific understanding literature, I identify in what senses idealisations afford understanding in the context of the (magnetic) Aharonov-Bohm effect. Three types of concepts of understanding are discussed: understanding-what, which has to do with understanding a phenomenon; understanding-with, which has to do with understanding a scientific theory; and understanding-why, which has to do with the reason some phenomenon occurs. Consequently, I outline an account of understanding-with that is suggested by the historical controversy surrounding the (...) |
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In making sense of the world, we typically cooperate, join forces, and draw on one another’s competence and expertise. A group or community in which there is a well-functioning division of cognitive-epistemic labor can achieve levels of understanding that a single agent who relies exclusively on her own capacities would probably never achieve. However, is understanding also collective? I.e., is understanding something that can be possessed by a group or community rather than by individuals? In this paper, I develop an (...) |
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It is widely acknowledged in the literature in social epistemology that knowledge has a social dimension: we are epistemically dependent upon one another for most of what we know. Our knowledge can be, and very often is, grounded on the epistemic achievement of somebody else. But what about epistemic aims other than knowledge? What about understanding? Prominent authors argue that understanding is not social in the same way in which knowledge is. Others can put us in the position to understand, (...) |
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Many have argued that the human sciences feature a unique form of understanding that is absent from the natural sciences. However, in the last decade or so, epistemologists and philosop... |
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What does it take to understand a phenomenon ideally, or to the highest conceivable extent? In this paper, we answer this question by arguing for five necessary conditions for ideal understanding: (i) representational accuracy, (ii) intelligibility, (iii) truth, (iv) reasonable endorsement, and (v) fitting. Even if one disagrees that there is some form of ideal understanding, these five conditions can be regarded as sufficient conditions for a particularly deep level of understanding. We then argue that grasping, novel predictions, and transparency (...) |
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InThere Are No Such Things As Theories(French 2020), the reification of theories is critically analysed and rejected. My aim here is to tease out some of the implications of this approach first of all, for how we, philosophers of science, should view the history of science; secondly, for how we should understand the devices that we use in our own philosophical practices; and thirdly, for how we might think about the relationship between the history of science and the philosophy of (...) |
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COVID-19 has substantially affected our lives during 2020. Since its beginning, several epidemiological models have been developed to investigate the specific dynamics of the disease. Early COVID-19 epidemiological models were purely statistical, based on a curve-fitting approach, and did not include causal knowledge about the disease. Yet, these models had predictive capacity; thus they were used to ground important political decisions, in virtue of the understanding of the dynamics of the pandemic that they offered. This raises a philosophical question about (...) |
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In recent years, several philosophers have argued that their discipline makes no progress (or not enough in comparison to the “hard sciences”). A key argument for this pessimistic position appeals to the purported fact that philosophers widely and systematically disagree on most major philosophical issues. In this paper, we take a step back from the debate about progress in philosophy specifically and consider the general question: How (if at all) would disagreement within a discipline undermine that discipline’s progress? We reject (...) |
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What is scientific progress? This paper advances an interpretation of this question, and an account that serves to answer it. Roughly, the question is here understood to concern what type of cognitive change with respect to a topic X constitutes a scientific improvement with respect to X. The answer explored in the paper is that the requisite type of cognitive change occurs when scientific results are made publicly available so as to make it possible for anyone to increase their understanding (...) |
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When science makes cognitive progress, who or what is it that improves in the requisite way? According to a widespread and unchallenged assumption, it is the cognitive attitudes of scientists themselves, i.e. the agents by whom scientific progress is made, that improve during progressive episodes. This paper argues against this assumption and explores a different approach. Scientific progress should be defined in terms of potential improvements to the cognitive attitudes of those for whom progress is made, i.e. the receivers rather (...) |
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This paper aims to flesh out the celebrated notion of reflective equilibrium within a probabilistic framework for epistemic rationality. On the account developed here, an agent's attitudes are in reflective equilibrium when there is a certain sort of harmony between the agent's credences, on the one hand, and what the agent accepts, on the other hand. Somewhat more precisely, reflective equilibrium is taken to consist in the agent accepting, or being prepared to accept, all and only claims that follow from (...) |
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To understand something involves some sort of commitment to a set of propositions comprising an account of the understood phenomenon. Some take this commitment to be a species of belief; others, such as Elgin and I, take it to be a kind of cognitive policy. This paper takes a step back from debates about the nature of understanding and asks when this commitment involved in understanding is epistemically appropriate, or ‘acceptable’ in Elgin’s terminology. In particular, appealing to lessons from the (...) |
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There is, among philosophers involved in the debate concerning the nature and epistemology of understanding, a general recognition that this state has a grasping component that accounts for some of its distinctive features. This paper defends the view that this component of understanding consists of a knowledge of how to use a particular explanation to account for a given phenomenon. The way in which a subject acquires this knowledge is examined and the result of this examination is shown to highlight (...) |
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The present paper examines a type of sceptical hypothesis put forward by Adam Carter that specifically targets understanding—the Confusion Hypothesis. After clarifying the nature and scope of that hypothesis, it discusses Carter’s favoured virtue perspectivist answer to the challenge it raises. It is argued that this answer is ultimately unsatisfying as it is unable to explain how a subject can obtain assurance that her grasp of a given body of information actually results from the competences she comes to appreciate as (...) |
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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. |
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