Explanation and Understanding

The philosophy of mathematical practice (PMP) looks to evidence from working mathematics to help settle philosophical questions. One prominent program under the PMP banner is the study of explanation in mathematics, which aims to understand what sorts of proofs mathematicians consider explanatory and what role the pursuit of explanation plays in mathematical practice. In an effort to address worries about cherry-picked examples and file-drawer problems in PMP, a handful of authors have recently turned to corpus analysis methods as a promising (...) alternative to small-scale case studies. But this research has itself been criticized for attempting to draw philosophical conclusions from counts of ambiguous terms like ‘explain’. -/- What’s needed to propel such methods to greater success, it seems, is a language-processing tool capable of taking in large amounts of text and reasoning insightfully about the meanings it contains. The current generation of frontier language models is already adept at sophisticated text analysis. The main bottleneck, now on the verge of being overcome, has been the capability for researchers to feed such systems big-data-sized text corpora (and to receive reliably correct outputs in return). -/- This paper reports the results from such a corpus study facilitated by Google's Gemini 2.5 Pro, a model whose reasoning capabilities, advances in hallucination control and large context window allow for the accurate analysis of hundreds of pages of text per query. Based on a sample of 5000 arXiv mathematics papers, the experiments yielded a dataset of hundreds of useful annotated examples. Its aim was to gain insight on questions like the following: How often do mathematicians make claims about explanation in the relevant sense? Do mathematicians’ explanatory practices vary in any noticeable way by subject matter? Which philosophical theories of explanation are most consistent with a large body of non-cherry-picked examples? How might philosophers make further use of AI tools to gain insights from large datasets of this kind? As the first PMP study making extensive use of LLM methods, it also seeks to begin a conversation about these methods as research tools in practice-oriented philosophy and to evaluate the strengths and weaknesses of current models for such work. (shrink)

Philosophical theories of explanation characterize the difference between correct and incorrect explanations. While remaining neutral as to which of these ‘first-order’ theories is right, this paper asks the ‘meta-explanatory’ question: is the difference between correct and incorrect explanation real, i.e., objective or mind-independent? After offering a framework for distinguishing realist from anti-realist views, I sketch three distinct paths to explanatory anti-realism.

An account of scientific explanation is presented according to which (1) scientific explanation consists in solving “insight” problems (Metcalfe and Wiebe 1984) and (2) understanding is the result of solving such problems. The theory is pragmatic; it draws upon van Fraassen’s (1977, 1980) insights, avoids the objections to pragmatic accounts offered by Kitcher and Salmon (1987), and relates scientific explanation directly to understanding. The theory also accommodates cases of explanatory asymmetry and intuitively legitimate rejections of explanation requests.

We claim that scientists working with deep learning (DL) models exhibit a form of pragmatic understanding that is not reducible to or dependent on explanation. This pragmatic understanding comprises a set of learned methodological principles that underlie DL model design-choices and secure their reliability. We illustrate this action-oriented pragmatic understanding with a case study of AlphaFold2, highlighting the interplay between background knowledge of a problem and methodological choices involving techniques for constraining how a model learns from data. Building successful models (...) requires pragmatic understanding to apply modelling strategies that encourage the model to learn data patterns that will facilitate reliable generalisation. (shrink)

Recent discourse in the philosophy of scientific explanation involves an account known as the Kairetic account. I proposed implementing a complementarity view involving a mapping scheme to the Kairetic account and similar models. There are two natural concerns related to this mapping. The first concern is the treatment of multiple mappings required for an explanation: phenomena may involve two complementarity features. The second concern is regarding the acquisition of understanding and whether context-dependence facilitates understanding. This article aims to address the (...) first thought through an example involving interference and photon detectors in a telescope. I claim that context-dependent mapping is on a particle basis, accommodating the wave-particle duality for every single particle without generalization. I further introduce the implications of mathematical developments of a complementarity relation grounded in the uncertainty principle. In addition, I will offer the stance that context-dependence facilitates understanding because it ensures that explanations are logically consistent, precise, relevant, and comprehensive. (shrink)

How can we develop an adequate scientific understanding of the minds of nonhuman animals? We argue for a methodology based on multi-dimensional profile accounts. Such accounts are already used for the comparative study of norm cognition, consciousness, empathy and causal cognition, among others. This methodology demands that a cognitive capacity is characterized by a set of independent dimensions where each dimension is connected to operationalizable empirical indicators. Based on the level of realization for each indicator the level of implementation of (...) a dimension is determined for a species, resulting in a multi-dimensional profile for each species. We analyze what this methodology is committed to. Then, we argue that this methodology has several benefits over competing unidimensional methodologies, by overcoming intractable disagreements, capturing the evolutionary continuity of cognition, alleviating anthropocentrism, and delivering more informative accounts of animal cognition. By demonstrating how this multidimensional methodology can be fruitfully combined with a methodology which focuses on the search for natural kinds in comparative cognition, we address the most important objection to the multidimensional profile methodology. We conclude that multidimensional profile accounts of all complex cognitive capacities should be developed and then used to facilitate scientific understanding of animal minds. (shrink)

Throughout science and mathematics, expert inquirers often reformulate existing problem-solving procedures and theories. But what value is there to reformulating, particularly when one already knows how to solve a given problem? Is reformulating merely instrumentally valuable for other practical or epistemic aims, or does it constitute a distinctive kind of epistemic achievement? I argue that by changing what we need to know to solve a problem, significant reformulations constitute a kind of intellectual value. Whereas some reformulations are trivial notational variants, (...) a significant reformulation provides an inferentially distinct problem-solving plan. I situate my preferred position as a middle ground between deflationary and metaphysically-substantial alternatives. (shrink)

Scientific understanding typically involves multiple specialists performing interdependent tasks. According to several social–epistemological accounts, this suggests that scientific communities are collective epistemic subjects. We argue instead that the data does not warrant the postulation of a collective subject. Our position, rather, is fictionalist: we argue that the use of sentences attributing understanding to scientific communities amounts to loose talk which is best construed as indicating how social environments associated with a scientific community promote individual scientists' understanding.

This paper examines cases in which an individual’s misunderstanding improves the scientific community’s understanding through “corrective” processes that produce understanding from poor epistemic inputs. To highlight the unique features of valuable misunderstandings and corrective processes, we contrast them with other social-epistemological phenomena including testimonial understanding, collective understanding, Longino’s critical contextual empiricism, and knowledge from falsehoods.

Many varieties of understanding subsist in a thinker’s having the right kind of mental connection to a certain body of fact (or putative fact), a connection often called “grasp”. The use of a single term suggests a single connection that does the job in every kind of understanding. Then again, “grasp” might be an umbrella term covering a diverse plurality of understanding-granting mind-world relations. This paper argues for the former, unified view of grasp in two ways. First, it advances a (...) broad, ability-based construal of grasp, along with a test for lack of grasp, that suggests that a certain specific connection plays an essential role in many varieties of understanding. Second, the paper considers a number of challenges to the thesis of unity that arise in a range of different kinds of understanding (scientific, moral, objectual, humanistic), and seeks to disarm them. (shrink)

Feynman diagrams are used to calculate scattering amplitudes in quantum field theory, where they simplify the derivation of individual terms in the corresponding perturbation series. Considered mathematical tools with an approximative character, the received view in the philosophy of physics denies that individual diagrams can represent physical processes. A different story, however, can be observed in physics practice. From education to high-profile research publications, Feynman diagrams are used in connection with particle phenomena without any reference to perturbative calculations. In the (...) first part of the paper, I argue that this illuminates an additional use of Feynman diagrams that is not calculatory but representational. It is not a possible translation into mathematical terms that prompts this practice but rather the epistemic insights into the target phenomenon that the diagrams provide. Based on this practical use, I intend to push back against the received view. In the second part of the paper, I conceptualize the representative use of Feynman diagrams as models that provide modal understanding of their associated target phenomena. The set of Feynman diagrams corresponding to an interaction is taken as a possibility space whose dependency relations can be analysed, allowing an agent to grasp possible target behaviour, leading to understanding. In clearly separating the diagrams from perturbative calculations for their use as a model, the concerns that hinder a representative reading can be resolved. (shrink)

The apparent downsides of opaque algorithms has led to a demand for explainable AI (XAI) methods by which a user might come to understand why an algorithm produced the particular output it did, given its inputs. Patients, for example, might find that the lack of explanation of the process underlying the algorithmic recommendations for diagnosis and treatment hinders their ability to provide informed consent. This paper examines the impact of two factors on user perceptions of explanations for AI systems in (...) medical contexts. The factors considered were the stakes of the decision—high versus low—and the decision source—human versus AI. 484 participants were presented with vignettes in which medical diagnosis and treatment plan recommendations were made by humans or by AI. Separate vignettes were used for high stakes scenarios involving life-threatening diseases, and low stakes scenarios involving mild diseases. In each vignette, an explanation for the decision was given. Four explanation types were tested across separate vignettes: no explanation, counterfactual, causal and a novel ‘narrative-based’ explanation, not previously considered. This yielded a total of 16 conditions, of which each participant saw only one. Individuals were asked to evaluate the explanations they received based on helpfulness, understanding, consent, reliability, trust, interests and likelihood of undergoing treatment. We observed a main effect for stakes on all factors and a main effect for decision source on all factors except for helpfulness and likelihood to undergo treatment. While we observed effects for explanation on helpfulness, understanding, consent, reliability, trust and interests, we by and large did not see any differences between the effects of explanation types. This suggests that the effectiveness of explanations may not depend on type of explanation but instead, on the stakes and decision source. (shrink)

Recent works in the philosophy of mathematical practice and mathematical education have challenged orthodox views of mathematical explanation by developing Understanding-first accounts according to which mathematical explanation should be cashed out in terms of understanding. In this article, we explore two arguments that might have motivated this move, (i) the context-sensitivity argument and (ii) the inadequacy of knowing why argument. We show that although these arguments are derived from compelling observations, they ultimately rest on a misunderstanding of what Explanation-first accounts (...) are committed to and an underestimation of the resources available to them. By clarifying the terms at play in the debate and distinguishing different objects of evaluation, we show that the insightful observations about practice and education made by challengers to the orthodoxy are in fact best accounted for within the traditional Explanation-first framework. (shrink)

Philosophers of science have variously tried to characterize how-possibly explanations (HPEs) and distinguish them from how-actually explanations (HAEs). I argue that existing contributions to this debate have failed to pay attention to the different, but complementary, functions possibilities play in scientific explanations. To bring these functions to the fore, I introduce a distinction between what I call elucidating and embedding HPEs. While elucidating HPEs specify and demonstrate possible processes for a given research target, embedding HPEs demonstrate how the research target (...) fits into a space of suitably constrained possibilities. I specify both functions of HPE with reference to two case studies from origins-of-life research. I contrast my distinction with an alternative proposal by Wirling and Grüne-Yanoff (2024) to highlight that focusing on the functions, rather than types, of possibilities in explanation is better suited to account for key scientific practices. (shrink)

The Measurement problem and Non-locality are classical problems in Quantum Mechanics and still unsolved in spite of the many proposed solutions. A new interpretation is proposed here, based on the idea that they are closely related problems. But it requires that we consider space and time not as objective mediums but as features of our representation of reality, as Kant explained more than two centuries ago.

Metaphysical proposals are strongly influenced by epistemic considerations. Our capacity to know, explain or perceive influences theories about what is fundamental, exists or is true. These kinds of connections are pervasive as, for example, Fine (2012) and Schaffer (2009) base their metaphysics on explanation, Benacerraf (1973) and Peacocke (1999) base their metaphysics on our ability to know metaphysical truths, and Lewis (1986) and Jackson (1994) base their metaphysics on compatibility with contemporary physics. In each case, pertinent epistemic factors are used (...) to motivate – provide reasons to accept or reject – particular metaphysical theories. This thesis examines significant epistemic factors, their connected metaphysical theories and the nature of the motivating connection exhibited between them to develop a novel approach to metaphysics: called ‘Epistemic Metaphysics’. To do this, in four papers, arguments are constructed in specific areas of metaphysics where epistemic considerations play central roles. Among others, topics covered include explanation, realism, normativity, laws, chance, dependence, empirical adequacy, and ontology. Then, by drawing inspiration from this wide array of philosophical arguments, a fine-grained account of the epistemic constraints on metaphysical inquiry can be composed; one that properly respects the intricacies of functional philosophical debate and provides general guidelines that are appropriate in any piecemeal application. Identifying the epistemic factors already employed in metaphysical arguments makes it possible to systematise the motivating connections into a set of general metaphysical maxims that constrain metaphysical theory choice: a framework for an explicitly epistemic approach to metaphysics. (shrink)

Mathematicians often describe the importance of well-developed intuition to productive research and successful learning. But neither education researchers nor philosophers interested in epistemic dimensions of mathematical practice have yet given the topic the sustained attention it deserves. The trouble is partly that intuition in the relevant sense lacks a usefully clear characterization, so we begin by offering one: mature intuition, we say, is the capacity for fast, fluent, reliable and insightful inference with respect to some subject matter. We illustrate the (...) role of mature intuition in mathematical practice with an assortment of examples, including data from a sequence of clinical interviews in which a student improves upon initially misleading covariational intuitions. Finally, we show how the study of intuition can yield insights for philosophers and education theorists. First, it contributes to a longstanding debate in epistemology by undermining epistemicism, the view that an agent’s degree of objectual understanding is determined exclusively by their knowledge, beliefs and credences. We argue on the contrary that intuition can contribute directly and independently to understanding. Second, we identify potential pedagogical avenues towards the development of mature intuition, highlighting strategies including adding imagery, developing associations, establishing confidence and generalizing concepts. (shrink)

This paper attempts to revive the epistemological discussion of scientific articles. What are their epistemic aims, and how are they achieved? We argue that scientific experimental articles are best understood as a particular kind of narrative: i.e., modernist narratives (think: Woolf, Joyce), at least in the sense that they employ many of the same techniques, including colligation and the juxtaposition of multiple perspectives. We suggest that this way of writing is necessary given the nature of modern science, but it also (...) has specific epistemic benefits: it provides readers with an effective way to grasp the content of scientific articles which increases their understanding. On the other hand, modernist writing is vulnerable to certain kinds of epistemic abuses, which can be found instantiated in modern scientific writing as well. (shrink)

To understand why a phenomenon occurs, it is not enough to possess a correct explanation of the phenomenon: you must grasp the explanation. In this formulation, “grasp” is a placeholder, standing for the psychological or epistemic relation that connects a mind to the explanatory facts in such a way as to produce understanding. This paper proposes and defends an account of the “grasping” relation according to which grasp of a property (to take one example of the sort of entity that (...) turns up in explanations) is a matter of recognitional ability: roughly, a property is grasped to the extent to which the would-be understander is capable of recognizing instances of the property. (shrink)

Dasgupta poses a serious challenge to realism about natural properties. He argues that there is no acceptable explanation of why natural properties deserve the value realists assign to them and are consequently absent of value. In response, this paper defines and defends an alternative non-explanatory account of normativity compatible with realism. Unlike Lewis and Sider, who believe it is sufficient to defend realism solely on realist terms, I engage with the challenge on unfriendly grounds by revealing a tu quoque. Dasgupta (...) and anti-realists face a similar challenge to that directed against realism: one that not only undermines the objection to realism by legitimising non-explanatory normativity but leaves them facing a significant dilemma. (shrink)

Models are indispensable tools of scientific inquiry, and one of their main uses is to improve our understanding of the phenomena they represent. How do models accomplish this? And what does this tell us about the nature of understanding? While much recent work has aimed at answering these questions, philosophers' focus has been squarely on models in empirical science. I aim to show that pure mathematics also deserves a seat at the table. I begin by presenting two cases: Cramér’s random (...) model of the prime numbers and the function field model of the integers. These cases show that mathematicians, like empirical scientists, rely on unrealistic models to gain understanding of complex phenomena. They also have important implications for some much-discussed theses about scientific understanding. First, modeling practices in mathematics confirm that one can gain understanding without obtaining an explanation. Second, these cases undermine the popular thesis that unrealistic models confer understanding by imparting counterfactual knowledge. (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)

Science frequently gives us multiple, compatible ways of solving the same problem or formulating the same theory. These compatible formulations change our understanding of the world, despite providing the same explanations. According to what I call "conceptualism," reformulations change our understanding by clarifying the epistemic structure of theories. I illustrate conceptualism by analyzing a typical example of symmetry-based reformulation in chemical physics. This case study poses a problem for "explanationism," the rival thesis that differences in understanding require ontic explanatory differences. (...) To defend conceptualism, I consider how prominent accounts of explanation might accommodate this case study. I argue that either they do not succeed, or they generate a skeptical challenge. (shrink)

This paper aims, first, to argue against using opaque AI technologies in decision making processes, and second to suggest that we need to possess a qualitative form of understanding about them. It first argues that opaque artificially intelligent technologies are suitable for users who remain indifferent to the understanding of decisions made by means of these technologies. According to virtue ethics, this implies that these technologies are not well-suited for those who care about realizing their moral capacity. The paper then (...) draws on discussions on scientific understanding to suggest that an AI technology becomes understandable to its users when they are provided with a qualitative account of the consequences of using it. As a result, explainable AI methods can render an AI technology understandable to its users by presenting the qualitative implications of employing the technology for their lives. (shrink)

Those who wish to defend the role of aesthetic values in science face a dilemma: Either aesthetic language is used metaphorically for what are ultimately epistemic features, or aesthetic language is used literally but it is difficult to see the importance of such values in science. I introduce a new account that gets around this problem by looking to an overlooked source of aesthetic value in science: the relation between form and content. I argue that a fit between the content (...) of a thought experiment, and the way in which that content is formulated, can have important epistemic pay offs through contributing to scientific understanding. (shrink)

The paper introduces a special issue of the journal Philosophical Problems in Science (ZFN) on the topic of the nature and norms of scientific explanation.

We present the negative phenomena of understanding in relation to scientific explanations. We begin by formulating the distinction between genuine understanding and lack of understanding, to define the epistemic category of misunderstanding. We illustrate misunderstanding with a short meta-philosophical study on the current debates about distinctively mathematical explanations.

Bas van Fraassen has argued that explanatory reasoning does not provide confirmation for explanatory hypotheses because explanatory reasoning increases information and increasing information does not provide confirmation. We compare this argument with a skeptical argument that one should never add any beliefs because adding beliefs increases information and increasing information does not provide confirmation. We discuss the similarities between these two arguments and identify several problems with van Fraassen’s argument.

Models are the coin of the realm in current philosophy of science, as they are in science itself, having replaced laws and theories as the primary strategy. Logical Positivism tried to erase the older neo-Kantian distinction between ideal constructions and reality. It returns in the case of models. Nowak’s concept of idealization pro- vided an alternative account of this issue. It construed model application as concretizations of hypotheses which improve by accounting for exceptions. This appears to account for physical law. (...) But it raises the problem of uniqueness: is the result unique, as physical law should be? Neo-Kantianism failed this test. Its solutions were circular justifications for claims of uniqueness. Nowak inherited the problem without resolving it. (shrink)

Scientists strive to understand the world. Traditionally, philosophers of science have thought that this is a matter of constructing explanations, based on theories and laws, thereby gaining understanding of phenomena by explaining them. This thesis takes a radically different approach, instead relating the notion of understanding to the activities that scientists perform. Scientific understanding is not just a matter of representing or explaining the world, but a matter of practical and intelligent doing. Philosophers of science have continued to sell short (...) the project of making sense of scientific understanding, limiting their views to the articulated and well-formed products of inquiry, like theory and explanation. In taking a pragmatist approach to the epistemology of understanding, I reorientate our theorising about understanding from products to processes, and from explanations to methods and concepts. I thereby provide an ecumenical account of scientific understanding that can accommodate the dynamics and heterogeneity of scientific practice. In Chapter 1, I argue against the dominant focus on explanatory understanding in philosophy of science, thereby making room for my own account of operational understanding. Chapter 2 provides an account of how concepts are essential constituents of understanding. Concepts frame entities so that scientists can think and talk about and interact with them intelligently. Chapter 3 gives an account of understanding-how, through my notion of operational understanding, which relates to the methods that structure and guide successful performances of activities. In Chapter 4, I take up the task of describing the psychology of understanding, the kind of state that understanding is, which I argue is accounted for in terms of skill. In Chapter 5, I develop an account of how cognitive devices — tools for thinking, like models and thought-experiments — facilitate and produce understanding. (shrink)

In the course of developing an account of scientific progress, C. D. McCoy (2022) appeals centrally to understanding as well as to problem-solving. On the face of it, McCoy’s account could thus be described as a kind of hybrid of the understanding-based account that I favor (Dellsén 2016, 2021) and the functional (a.k.a. problem-solving) account developed most prominently by Laudan (1977; see also Kuhn 1970; Shan 2019). In this commentary, I offer two possible interpretations of McCoy’s account and explain why (...) I do not find it entirely compelling on either interpretation. (shrink)

Roughly, the noetic account characterizes scientific progress in terms of increased understanding. This chapter outlines a version of the noetic account according to which scientific progress on some phenomenon consists in making scientific information publicly available so as to enable relevant members of society to increase their understanding of that phenomenon. This version of the noetic account is briefly compared with four rival accounts of scientific progress, viz. the truthlikeness account, the problem-solving account, the new functional account, and the epistemic (...) account. In addition, the chapter seeks to precisify the question that accounts of scientific progress are (or should be) aiming to answer, viz. “What type of cognitive change with respect to a given topic or phenomenon X constitutes a (greater or lesser degree of) scientific improvement with respect to X?”. (shrink)

This book presents fresh insights into analogue quantum simulation. It argues that these simulations are a new instrument of science. They require a bespoke philosophical analysis, sensitive to both the similarities to and the differences with conventional scientific practices such as analogical argument, experimentation, and classical simulation. -/- The analysis situates the various forms of analogue quantum simulation on the methodological map of modern science. In doing so, it clarifies the functions that analogue quantum simulation serves in scientific practice. To (...) this end, the authors introduce a number of important terminological distinctions. They establish that analogue quantum ‘computation' and ‘emulation' are distinct scientific practices and lead to distinct forms of scientific understanding. The authors also demonstrate the normative value of the computation vs. emulation distinction at both an epistemic and a pragmatic level. -/- The volume features a range of detailed case studies focusing on: i) cold atom computation of many-body localisation and the Higgs mode; ii) photonic emulation of quantum effects in biological systems; and iii) emulation of Hawking radiation in dispersive optical media. Overall, readers will discover a normative framework to isolate and support the goals of scientists undertaking analogue quantum simulation and emulation. This framework will prove useful to both working scientists and philosophers of science interested in cutting-edge scientific practice. (shrink)

I reply to Henk de Regt's "Can Scientific Understanding be Reduced to Knowledge?," which appears in the same volume.

In earlier work, I criticized de Regt’s contextual theory of understanding, and advertised the advantages of my own, knowledge-based account. Using the early history of the standard model in particle physics as an illustration, I instead consider the benefits of unifying these two accounts of understanding. I argue that de Regt’s account substantially improves my own account of explanatory consideration, and that my account of explanatory comparison substantially improves upon his account of explanatory evaluation. De Regt and my apparent disagreement (...) about the so-called factivity of understanding is defused through a voluntaristic approach to the scientific realism 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.

While discussions of the imagination have been limited in philosophy of science, this is beginning to change. In recent years, a vast literature on imagination in science has emerged. This paper surveys the current field, including the changing attitudes towards the scientific imagination, the fiction view of models, how the imagination can lead to knowledge and understanding, and the value of different types of imagination. It ends with a discussion of the gaps in the current literature, indicating avenues for future (...) research. (shrink)

The framework of the modern Western analysis of culture, in terms of the socio-historical situation of the subject and the reciprocal influence of one on the other, has its roots in nineteenth century discussions. This paper will examine two traditions: the hermeneutic approach of Wilhelm Dilthey, and the Völkerpsychologie of Moses Lazarus and Chajim Steinthal. The account will focus on two elements. First, Lazarus and Steinthal attempted to motivate an account based on collective structures, or forms, of rationality made manifest (...) by a people or Volk; the paper will explore their account of how collective structures can be employed in sociohistorical analysis. Second, Dilthey rejected Lazarus’s and Steinthal’s argument that it was possible to identify the norms of action governing social phenomena. Dilthey rejected any account of psychology that took it to be law-governed, even retrospectively, because he argued that the ‘nexus of life’ that is the ultimate basis of the human sciences cannot be reduced to any law-governed or explanatory relationship between the self, society, and nature. However, there is a deep tension in Dilthey’s position here, which is evident in the development of his work over time. The account below will explore this tension and its significance for the understanding of the subject and the role of psychology in the human sciences. (shrink)

Under what conditions does machine learning (ML) model opacity inhibit the possibility of explaining and understanding phenomena? In this article, I argue that nonepistemic values give shape to the ML opacity problem even if we keep researcher interests fixed. Treating ML models as an instance of doing model-based science to explain and understand phenomena reveals that there is (i) an external opacity problem, where the presence of inductive risk imposes higher standards on externally validating models, and (ii) an internal opacity (...) problem, where greater inductive risk demands a higher level of transparency regarding the inferences the model makes. (shrink)

Simple idealized models seem to provide more understanding than opaque, complex, and hyper-realistic models. However, an increasing number of scientists are going in the opposite direction by utilizing opaque machine learning models to make predictions and draw inferences, suggesting that scientists are opting for models that have less potential for understanding. Are scientists trading understanding for some other epistemic or pragmatic good when they choose a machine learning model? Or are the assumptions behind why minimal models provide understanding misguided? In (...) this paper, using the case of deep neural networks, I argue that it is not the complexity or black box nature of a model that limits how much understanding the model provides. Instead, it is a lack of scientific and empirical evidence supporting the link that connects a model to the target phenomenon that primarily prohibits understanding. (shrink)

Deep neural networks have become increasingly successful in applications from biology to cosmology to social science. Trained DNNs, moreover, correspond to models that ideally allow the prediction of new phenomena. Building in part on the literature on ‘eXplainable AI’, I here argue that these models are instrumental in a sense that makes them non-explanatory, and that their automated generation is opaque in a unique way. This combination implies the possibility of an unprecedented gap between discovery and explanation: When unsupervised models (...) are successfully used in exploratory contexts, scientists face a whole new challenge in forming the concepts required for understanding underlying mechanisms. (shrink)

In this paper, I offer an analysis of the radical disagreement over the adequacy of string theory. The prominence of string theory despite its notorious lack of empirical support is sometimes explained as a troubling case of science gone awry, driven largely by sociological mechanisms such as groupthink (e.g. Smolin 2006). Others, such as Dawid (2013), explain the controversy by positing a methodological revolution of sorts, according to which string theorists have quietly turned to nonempirical methods of theory assessment given (...) the technological inability to directly test the theory. The appropriate response, according to Dawid, is to acknowledge this development and widen the canons of acceptable scientific methods. As I’ll argue, however, the current situation in fundamental physics does not require either of these responses. Rather, as I’ll suggest, much of the controversy stems from a failure to properly distinguish the “context of justification” from the “context of pursuit”. Both those who accuse string theorists of betraying the scientific method and those who advocate an enlarged conception of scientific methodology objectionably conflate epistemic justification with judgements of pursuit-worthiness. Once we get clear about this distinction and about the different norms governing the two contexts, the current situation in fundamental physics becomes much less puzzling. After defending this diagnosis of the controversy, I’ll show how the argument patterns that have been posited by Dawid as constituting an emergent methodological revolution in science are better off if reworked as arguments belonging to the context of pursuit. (shrink)

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 (...) of X. This account is briefly compared to two rival accounts of scientific progress, based respectively on increasing truthlikeness and accumulating knowledge, and is argued to be preferable to both. (shrink)

Hempel seems to hold the following three views: (H1) Understanding is pragmatic/relativistic: Whether one understands why X happened in terms of Explanation E depends on one's beliefs and cognitive abilities; (H2) Whether a scientific explanation is good, just like whether a mathematical proof is good, is a nonpragmatic and objective issue independent of the beliefs or cognitive abilities of individuals; (H3) The goal of scientific explanation is understanding: A good scientific explanation is the one that provides understanding. Apparently, H1, H2, (...) and H3 cannot be all true. Some philosophers think that Hempel is inconsistent, while some others claim that Hempel does not actually hold H3. I argue that Hempel does hold H3 and that he can consistently hold all of H1, H2, and H3 if he endorses what I call the “understanding argument.” I also show how attributing the understanding argument to Hempel can make more sense of his D-N model and his philosophical analysis of the pragmatic aspects of scientific explanation. (shrink)

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)

Science is replete with falsehoods that epistemically facilitate understanding by virtue of being the very falsehoods they are. In view of this puzzling fact, some have relaxed the truth requirement on understanding. I offer a factive view of understanding that fully accommodates the puzzling fact in four steps: (i) I argue that the question how these falsehoods are related to the phenomenon to be understood and the question how they figure into the content of understanding it are independent. (ii) I (...) argue that the falsehoods do not figure into the understanding’s content by being elements of its periphery or core. (iii) Drawing lessons from case studies, I argue that the falsehoods merely enable understanding. When working with such falsehoods, only the truths we extract from them are elements of the content of our understanding. (iv) I argue that the extraction view is compatible with the thesis that falsehoods can have an epistemic value by virtue of being the very falsehoods they are. (shrink)

Elgin offers an influential and far-reaching challenge to veritism. She takes scientific understanding to be non-factive and maintains that there are epistemically useful falsehoods that figure ineliminably in scientific understanding and whose falsehood is no epistemic defect. Veritism, she argues, cannot account for these facts. This paper argues that while Elgin rightly draws attention to several features of epistemic practices frequently neglected by veritists, veritists have numerous plausible ways of responding to her arguments. In particular, it is not clear that (...) false propositional commitments figure ineliminably in understanding in the manner supposed by Elgin. Moreover, even if scientific understanding were non-factive and false propositional commitments did figure ineliminably in understanding, the veritist can account for this in several ways without thereby abandoning veritism. (shrink)

The notion of understanding occupies an increasingly prominent place in contemporary epistemology, philosophy of science, and moral theory. A central and ongoing debate about the nature of understanding is how it relates to the truth. In a series of influential contributions, Catherine Elgin has used a variety of familiar motivations for antirealism in philosophy of science to defend a non- factive theory of understanding. Key to her position are: (i) the fact that false theories can contribute to the upwards trajectory (...) of scientific understanding, and (ii) the essential role of inaccurate idealisations in scientific research. Using Elgin’s arguments as a foil, I show that a strictly factive theory of understanding has resources with which to offer a unified response to both the problem of idealisations and the role of false theories in the upwards trajectory of scientific understanding. Hence, strictly factive theories of understanding are viable notwithstanding these forceful criticisms. (shrink)

What exactly do we need in order to enjoy the cognitive benefit that is supposed to be provided by an explanation? Some philosophers :15–37, 2012, Episteme 10:1–17, 2013, Eur J Philos Sci 5:377–385, 2015, Understanding, explanation, and scientific knowledge, Cambridge University Press, Cambridge, 2017) would say that all that we need is to know the explanation. Others :1–26, 2012; Strevens in Stud Hist Philos Sci Part A 44:510–515, 2013) would say that achieving understanding with the help of an explanation requires (...) more than that, that it requires a grasping or an understanding of the explanation. My aim in this paper is to come up with a new answer to this problem by exploring the shortcomings of the received view of understanding. In my view, besides having testimonial knowledge of an explanation, obtaining explanatory understanding requires full cognitive access to the explanation. (shrink)