A characteristic feature of the philosophy of mathematical practice is to attend to what people do when they do mathematics. But what does it mean to do mathematics? This question raises several issues regarding the nature of action, activity, and agency in mathematical practice. The present chapter reviews contributions in the field that have attempted to theorize about these notions. It begins with some motivations for taking agents seriously in the philosophical study of mathematical practice. The core (...) of the chapter discusses, in turn, what it means to carry out mathematical activities, do things with mathematical artifacts, engage with mathematical proofs, and perform mathematical actions prescribed by mathematical texts. Taken together, the various lines of work reported here provide an initial, but already sophisticated, picture of what it means to do mathematics. The chapter ends with some suggestions for future research on agency in mathematical practice. (shrink)

Mathematical proofs are not sequences of arbitrary deductive steps—each deductive step is, to some extent, rational. This paper aims to identify and characterize the particular form of rationality at play in mathematical proofs. The approach adopted consists in viewing mathematical proofs as reports of proof activities—that is, sequences of deductive inferences—and in characterizing the rationality of the former in terms of that of the latter. It is argued that proof activities are governed by specific norms of rational planning agency, (...) and that a deductive step in a mathematical proof qualifies as rational whenever the corresponding deductive inference in the associated proof activity figures in a plan that has been constructed rationally. It is then shown that mathematical proofs whose associated proof activities violate these norms are likely to be judged as defective by mathematical agents, thereby providing evidence that these norms are indeed present in mathematical practice. We conclude that, if mathematical proofs are not mere sequences of deductive steps, if they possess a rational structure, it is because they are the product of rational planning agents. (shrink)

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 theory of planning agency. It is argued that the proposed account can explain a significant range of distinctive phenomena commonly associated with proof understanding by mathematicians and philosophers. It is further argued, on the basis of a case study, that the account can yield precise diagnostics of understanding failures and can suggest ways to overcome them. Reflecting on the approach developed here, the essay concludes with some remarks on how to shape a general methodology common to the study of mathematical and scientific understanding and focused on human agency. (shrink)

In practice, mathematical proofs are most often the result of careful planning by the agents who produced them. As a consequence, each mathematical proof inherits a plan in virtue of the way it is produced, a plan which underlies its “architecture” or “unity”. This paper provides an account of plans and planning in the context of mathematical proofs. The approach adopted here consists in looking for these notions not in mathematical proofs themselves, but in the agents who produced them. The (...) starting point is to recognize that to each mathematical proof corresponds a proof activity which consists of a sequence of deductive inferences—i.e., a sequence of epistemic actions—and that any written mathematical proof is only a report of its corresponding proof activity. The main idea to be developed is that the plan of a mathematical proof is to be conceived and analyzed as the plan of the agent(s) who carried out the corresponding proof activity. The core of the paper is thus devoted to the development of an account of plans and planning in the context of proof activities. The account is based on the theory of planning agency developed by Michael Bratman in the philosophy of action. It is fleshed out by providing an analysis of the notions of intention—the elementary components of plans—and practical reasoning—the process by which plans are constructed—in the context of proof activities. These two notions are then used to offer a precise characterization of the desired notion of plan for proof activities. A fruitful connection can then be established between the resulting framework and the recent theme of modularity in mathematics introduced by Jeremy Avigad. This connection is exploited to yield the concept of modular presentations of mathematical proofs which has direct implications for how to write and present mathematical proofs so as to deliver various epistemic benefits. The account is finally compared to the technique of proof planning developed by Alan Bundy and colleagues in the field of automated theorem proving. The paper concludes with some remarks on how the framework can be used to provide an analysis of understanding and explanation in the context of mathematical proofs. (shrink)

In a recent paper, Negri and Pavlović (Studia Logica 1–35, 2020) have formulated a decidable sequent calculus for the logic of agency, specifically for a deliberative see-to-it-that modality, or dstit. In that paper the adequacy of the system is demonstrated by showing the derivability of the axiomatization of dstit from Belnap et al. (Facing the future: agents and choices in our indeterminist world. Oxford University Press, Oxford, 2001). And while the influence of the latter book on the study of (...) logics of agency cannot be overstated, we note that this is not the only axiomatization of that modality available. In fact, an earlier (and arguably purer) one was offered in Xu (J Philosophical Logic 27(5):505–552, 1998). In this article we fill this lacuna by proving that this alternative axiomatization is likewise readily derivable in the system of Negri and Pavlović (Studia Logica 1–35, 2020). (shrink)

The themes of connectedness and continuity, which are also mathematical properties, have run like a red thread through the last fifty years of History and Theory, notably in the theory of the narration of action in history. In this essay I review various answers to the question of the driving force that motivates action and that propels a sequence, continuous or discontinuous. These answers underpin narrative strategies intended to solve the problem of human agency and thereby to provide the (...) basis for historical narratives. I argue that both continuous and discontinuous conceptions of history have to do with the restrictive concept of trajectory. Most of our familiar concepts such as trajectory, equilibrium, optimum, probability, and sensitivity to initial conditions are taken from mathematics and physics, but how well adapted are they to dealing with the time of actors, whose actions are intermingled with uncertainty? I shall present alternative concepts of dynamics, ones that no longer lead toward just one particular future or that reflect a single past. On this basis I suggest reorganizing our view of historical time along the principles of maintenance, acquisition, and victory. Historical sources trace back not to one story or one process that is plausible or that appeals to common sense, but to a whole family of processes. From the past, we can obtain sets of constraints that circumscribe sets of stories rather than a single scenario. I shall then propose a topology of the time of action based on my alternative conception of dynamics, a topology made of what I call viability kernels, capture basins, and victory domains. (shrink)

The primary aim of this article is to bring the work of Deleuze and Guattari to bear on the question ofcommunication in the classroom. I focus on the mathematics classroom, where agency and subjectivity are highly regulated by the rituals of the discipline, and where neoliberal psychological frameworks continue to dominate theories of teaching and learning. Moreover, the nature ofcommunication in mathematics classrooms remains highlyelusive and problematic, due in part to the distinct relationship the discipline has with (...) verbal language and thought. I first discuss current attempts to better address the embodied nature ofcommunication in mathematics classrooms, and argue that these remain overly logo-centric and language-centric in their conception of thinking. I then show how the work of Deleuze and Guattari on thought as a radical disruptive event can be used effectively to critique current pedagogical practices that privilege a narrow conception of communication in the classroom. I examine a set of exemplary classroom videos used in mathematics teacher education to argue that the current approach fails to honor the highly creative and disruptive nature ofthinking. (shrink)

This ambitious book by one of the most original and provocative thinkers in science studies offers a sophisticated new understanding of the nature of scientific, mathematical, and engineering practice and the production of scientific knowledge. Andrew Pickering offers a new approach to the unpredictable nature of change in science, taking into account the extraordinary number of factors—social, technological, conceptual, and natural—that interact to affect the creation of scientific knowledge. In his view, machines, instruments, facts, theories, conceptual and mathematical structures, disciplined (...) practices, and human beings are in constantly shifting relationships with one another—"mangled" together in unforeseeable ways that are shaped by the contingencies of culture, time, and place. Situating material as well as human agency in their larger cultural context, Pickering uses case studies to show how this picture of the open, changeable nature of science advances a richer understanding of scientific work both past and present. Pickering examines in detail the building of the bubble chamber in particle physics, the search for the quark, the construction of the quarternion system in mathematics, and the introduction of computer-controlled machine tools in industry. He uses these examples to address the most basic elements of scientific practice—the development of experimental apparatus, the production of facts, the development of theory, and the interrelation of machines and social organization. (shrink)

In this article, Kurt Stemhagen reconstructs mathematics education in light of Dewey's democratic theory and his ideas about mathematics and mathematics education. The resulting democratic philosophy and pedagogy of mathematics education emphasizes agency and the connections between mathematics and students' social experiences. Stemhagen considers questions about the disconnect between constructivist reformers and critical mathematics educators, and he positions Dewey's ideas as a way to draw on the best of both to create an active (...) and more democratic school math experience. (shrink)

This text looks at the construction of the Semantic Web, which will enable computers to automatically and independently consume Web-based information. With numerous programming examples, it is ideal for undergraduates and graduates in mathematics, computer science and logic and researchers interested in Multi-Agent Systems and the Semantic Web.

In this book, Binder shows that at the heart of the most prominent arguments in favour of value-neutral approaches to overall freedom lies the value freedom has for human agency and development. Far from leading to the adoption of a value-neutral approach, however, ascribing importance to freedom’s agency value requires one to adopt a refined value-based approach. Binder employs an axiomatic framework in order to develop such an approach. She shows that a focus on freedom’s agency value (...) has far reaching consequences for existing results in the freedom ranking literature: it requires one to move beyond a person’s given all-things-considered preferences to the values underlying a person’s preference formation. Furthermore, it requires, as Binder argues, one to account for those differences between choice options which really matter to people. Binder illustrates the implications of her analysis for the evaluation of public policy and human development with the capability approach: only if sufficient importance is ascribed to freedom’s agency value can the capability approach keep its promises. ​. (shrink)

The ArgumentWhen economists report on research using mathematical models, they use a literary form similar to the experimental report in the laboratory sciences. This form consists of a narrative of a series of events, with a clear temporal segregation of the agency of the author and the agency of the objects of study. Existing explanations of this literary form treat it as a rhetorical device that either conceals the agency of the author in constructing and interpreting the (...) findings, or simply appropriates the appearance of accepted scientific method. This article — based on analysis of a research program in economics, a single article that issued from that program, and in-depth interviews with the authors — proposes an alternate interpretation. Drawing on the praxeological “laboratory studies” tradition in science studies, we treat work with mathematical models as involving the interaction of economists with objects that act independently of the analyst's will. The clear separation of the economist's and the models agency, as depicted in the published report, is not the result of a rhetorical rewriting of actual events, but is a practical accomplishment. Every step in the analytical work that preceded the paper is devoted to developing a procedure in which the economists' agency will be completely accountable in terms of accepted practices, and the performance of the model will be distinct and compelling. (shrink)

This section aims to summarize and conclude Part I in the form of a taxonomy of legitimate and illegitimate corporate moral responsibility attributions. I believe we can categorise four types of corporate moral responsibility attributions two of which are legitimate and two which are illegitimate with regard to our concept of moral agency and our moral intuition of fairness.

If you have ever had to move house, you will know this: the worst part is the sofa. You cannot do it alone. Nor will it be enough for me to just lift one end waiting for you to lift the other. We will have to work together to get the job done. If spaces are tight, we will even have to find a practical solution to a tantalizing mathematical puzzle: the moving sofa problem.Joint actions like that are part and (...) parcel of everyday life. But what exactly is special about acting together? After all, the actions of two strangers also depend on one another when one exits and the other enters through a revolving door, when they happen to walk side-by-side along a forest path, or when they exchange blows in a pub brawl.The problem is that two patterns of social behavior might look identical, even though one is a case of joint action and the other is not. There need not be an observable difference between the movements of old friends taking their morning constitutional together, on the one hand, a .. (shrink)

The concept of event is one of the key notions of many theories dealing with causality or agency. In this paper we study different approaches to events that share the basic assumption that events can be analyzed fruitfully in branching-time structures. The terminological framework developed thereby may be helpful for further analyses in the fields of causality and agency and also in those fields of computational semantics, where similar concepts are considered.

Book synopsis: The London School of Economics and Political Science has embraced the full range of the social sciences and its related disciplines. Contributors to this book were invited to write on the subject of freedom. The volume is an exemplary reflection of the variety, the individuality, the different interests, and the range of assumptions found in the scholars of the LSE. The authors come from varied backgrounds - linguistics, mathematics, computer science, sociology, geography, economics, industrial relations, anthropology, political (...) science. They provide a stimulating array of viewpoints on the universally discussed issue of freedom. (shrink)

In this paper we consider logical inference as an activity that results in proofs and hence produces knowledge. We suggest to merge the semantical analysis of deliberatively seeing-to-it-that from stit theory and the semantics of the epistemic logic with justification from. The general idea is to understand proving that A as seeing to it that a proof of A is available. We introduce a semantics of various notions of proving as an activity and present a number of valid principles that (...) relate the various notions of proving to each other and to notions of justified knowledge, implicit knowledge, and possibility. We also point out and comment upon certain principles our semantics fails to validate. (shrink)

For many, the two key thinkers about science in the twentieth century are Thomas Kuhn and Karl Popper, and one of the key questions in contemplating science is how to make sense of theory change. In Creatively Undecided, philosopher Menachem Fisch defends a new way to make sense of the rationality of scientific revolutions. He argues, loosely following Kuhn, for a strong notion of the framework dependency of all scientific practice, while at the same time he shows how such frameworks (...) can be deemed the possible outcomes of keen rational deliberation along Popperian lines. Fisch's innovation is to call attention to the importance of ambiguity and indecision in scientific change and advancement. Specifically, he backs the problem up, looking not at how we might communicate rationally across an already existing divide but at the rational incentive to create an alternative framework in the first place. Creatively Undecided will be essential reading for philosophers of science, and its vivid case study in Victorian mathematics will draw in historians. (shrink)

In this paper we show that the Hilbert system of agency and ability presented by Dag Elgesem is incomplete with respect to the intended semantics. We argue that completeness result may be easily regained. Finally, we shortly discuss some issues related to the philosophical intuition behind his approach. This is done by examining Elgesem's modal logic of agency and ability using semantics with different flavours.

A sense of agency (SoA) is the experience of subjective awareness regarding the control of one’s actions. Humans have a natural tendency to generate prediction models of the environment and adapt their models according to changes in the environment. The SoA is associated with the degree of the adaptation of the prediction models, e.g., insufficient adaptation causes low predictability and lowers the SoA over the environment. Thus, identifying the mechanisms behind the adaptation process of a prediction model related to (...) the SoA is essential for understanding the generative process of the SoA. In the first half of the current study, we constructed a mathematical model in which the SoA represents a likelihood value for a given observation (sensory feedback) in a prediction model of the environment and in which the prediction model is updated according to the likelihood value. From our mathematical model, we theoretically derived a testable hypothesis that the prediction model is updated according to a Bayesian rule or a stochastic gradient. In the second half of our study, we focused on the experimental examination of this hypothesis. In our experiment, human subjects were repeatedly asked to observe a moving square on a computer screen and press a button after a beep sound. The button press resulted in an abrupt jump of the moving square on the screen. Experiencing the various stochastic time intervals between the action execution button-press) and the consequent event square jumping caused gradual changes in the subjects' degree of their SoA. By comparing the above theoretical hypothesis with the experimental results, we concluded that the update (adaptation) rule of the prediction model based on the SoA is better described by a Bayesian update than by a stochastic gradient descent. (shrink)

Predictive policing has become a new panacea for crime prevention. However, we still know too little about the performance of computational methods in the context of predictive policing. The paper provides a detailed analysis of existing approaches to algorithmic crime forecasting. First, it is explained how predictive policing makes use of predictive models to generate crime forecasts. Afterwards, three epistemologies of predictive policing are distinguished: mathematical social science, social physics and machine learning. Finally, it is shown that these epistemologies have (...) significant implications for the constitution of predictive knowledge in terms of its genesis, scope, intelligibility and accessibility. It is the different ways future crimes are rendered knowledgeable in order to act upon them that reaffirm or reconfigure the status of criminological knowledge within the criminal justice system, direct the attention of law enforcement agencies to particular types of crimes and criminals and blank out others, satisfy the claim for the meaningfulness of predictions or break with it and allow professionals to understand the algorithmic systems they shall rely on or turn them into a black box. By distinguishing epistemologies and analysing their implications, this analysis provides insight into the techno-scientific foundations of predictive policing and enables us to critically engage with the socio-technical practices of algorithmic crime forecasting. (shrink)

This essay explores how mid-twentieth-century mathematicians at New York University envisioned their discipline, cultural identities and social roles, and how these self-constructed identities materialized in the planning of their new academic building, Warren Weaver Hall. These mathematicians considered their research to be a ‘living part of the stream of science’, requiring a mathematics research library which they equated to a scientific laboratory and a complex of computing rooms which served as an interdisciplinary research centre. Identifying as ‘scientists’, they understood (...) their societal value to be that of researchers, outputting mathematics research valuable to the natural sciences, the emerging field of computer science and the United States government and military, as well as educators. When the building opened in 1965, it was touted by the university administration as an ‘example of excellence’; it later, in 1970, became the site of heated negotiations when university student and faculty protestors staged a sit-in rebuking the Atomic Energy Commission's Computing Center housed on the second floor. A close study of the correspondence between the mathematicians and their peers in the university's administration, private foundations, government agencies and an architectural firm not only illuminates the day-to-day work practices of this eminent group of mathematicians, but also sheds light on their own self-constructed academic and social identities within their contemporaneous Cold War culture. (shrink)

Rational agents are important objects of study in several research communities, including economics, philosophy, cognitive science, and most recently computer science and artificial intelligence. Crudely, a rational agent is an entity that is capable of acting on its environment, and which chooses to act in such a way as to further its own best interests. There has recently been much interest in the use of mathematical logic for developing formal theories of such agents. Such theories view agents as practical reasoning (...) systems, deciding moment by moment which action to perform next, given the beliefs they have about the world and their desires with respect to how they would like the world to be. In this article, we survey the state of the art in developing logical theories of rational agency. Following a discussion on the dimensions along which such theories can vary, we briefly survey the logical tools available in order to construct such theories. We then review and critically assess three of the best known theories of rational agency: Cohen and Levesque's intention logic, Rao and Georgeff's BDI logics, and the KARO framework of Meyer et al. We then discuss the various roles that such logics can play in helping us to engineer rational agents, and conclude with a discussion of open problems. (shrink)

Scientific anomalies are observations and facts that contradict current scientific theories and they are instrumental in scientific theory change. Philosophers of science have approached scientific theory change from different perspectives as Darden (Theory change in science: Strategies from Mendelian genetics, 1991) observes: Lakatos (In: Lakatos, Musgrave (eds) Criticism and the growth of knowledge, 1970) approaches it as a progressive “research programmes” consisting of incremental improvements (“monster barring” in Lakatos, Proofs and refutations: The logic of mathematical discovery, 1976), Kuhn (The structure (...) of scientific revolutions, 1996) observes that changes in “paradigms” are instigated by a crisis from some anomaly, and Hanson (In: Feigl, Maxwell (eds) Current issues in the philosophy of science, 1961) proposes that discovery does not begin with hypothesis but with some “problematic phenomena requiring explanation”. Even though anomalies are important in all of these approaches to scientific theory change, there have been only few investigations into the specific role anomalies play in scientific theory change. Furthermore, much of these approaches focus on the theories themselves and not on how the scientists and their experiments bring about scientific change (Gooding, Experiment and the making of meaning: Human agency in scientific observation and experiment, 1990). To address these issues, this paper approaches scientific anomaly resolution from a meaning construction point of view. Conceptual integration theory (Fauconnier and Turner, Cogn Sci 22:133–187, 1996; The way we think: Conceptual blending and mind’s hidden complexities, 2002) from cognitive linguistics describes how one constructs meaning from various stimuli, such as text and diagrams, through conceptual integration or blending. The conceptual integration networks that describe the conceptual integration process characterize cognition that occurs unconsciously during meaning construction. These same networks are used to describe some of the cognition while resolving an anomaly in molecular genetics called RNA interference (RNAi) in a case study. The RNAi case study is a cognitive-historical reconstruction (Nersessian, In: Giere (ed) Cognitive models of science, 1992) that reconstructs how the RNAi anomaly was resolved. This reconstruction traces four relevant molecular genetics publications in describing the cognition necessary in accounting for how RNAi was resolved through strategies (Darden 1991), abductive reasoning (Peirce, In: Hartshorne, Weiss (eds) Collected papers, 1958), and experimental reasoning (Gooding 1990). The results of the case study show that experiments play a crucial role in formulating an explanation of the RNAi anomaly and the integration networks describe the experiments’ role. Furthermore, these results suggest that RNAi anomaly resolution is embodied. It is embodied in a sense that cognition described in the cognitive-historical reconstruction is experientially based. (shrink)

Responding to widespread interest within cultural studies and social inquiry, this book addresses the question 'what is a mathematical concept?' using a variety of vanguard theories in the humanities and posthumanities. Tapping historical, philosophical, sociological and psychological perspectives, each chapter explores the question of how mathematics comes to matter. Of interest to scholars across the usual disciplinary divides, this book tracks mathematics as a cultural activity, drawing connections with empirical practice. Unlike other books in this area, it is (...) highly interdisciplinary, devoted to exploring the ontology of mathematics as it plays out in different contexts. This book will appeal to scholars who are interested in particular mathematical habits - creative diagramming, structural mappings, material agency, interdisciplinary coverings - that shed light on both mathematics and other disciplines. Chapters are also relevant to social sciences and humanities scholars, as each offers philosophical insight into mathematics and how we might live mathematically. (shrink)

This article traces the different classifications of diesel emissions either as “safe” or as “hazardous” in the US and in West Germany between 1977 and 1995. It argues that the environmental regulation of diesel emissions was a political threshold. It contributes to our general understanding of how politicians, environmental lobbyists, scientists, and engineers constructed the standards and norms that defined the “safe” limit of environmental pollutants. After discussing how diesel emissions came under review as a potential carcinogen, I will show (...) that the coding as “safe” or as “hazardous” resulted from negotiations that were entirely dependent on the temporal, geographical, and intellectual contexts in which diesel technology, scientific research on their emissions, and political regulation were embedded. In particular, I trace the differences in German and US regulatory policy. While US regulation relied more on epidemiology that provided only weak data on the carcinogenicity of diesel particulates in the early 1980s, German government agencies tended to base their policy around the mid-1980s more on the results of animal tests and shortly afterwards also on epidemiology. Furthermore, the article reveals how US and German automakers tried to foster doubt on the carcinogenicity of diesel emissions and how their approaches differed and shifted. Thereby, it sheds light on the triangular relationship between technology, science, and politics in regulatory processes by analyzing the different roles of the state, automakers, scientists, and environmental agencies in Germany and in the United States. (shrink)

The paper presents an infinite hierarchy of sound and complete axiomatic systems for Two-Dimensional Modal Tense Logic with Historical Necessity, Agents and Acts. A main novelty of these logics is their capacity to represent formally (i) basic action-sentences asserting that such and such an act is performed/omitted by an agent, as well as (ii) causative action-sentences asserting that by performing/omitting a certain act, an agent causes that such and such a state-of-affairs is realized (e.g. comes about/ceases/remains/remains absent). We illustrate how (...) the formal machinery of our systems can be used to reconstruct a number of interesting ideas in the Logic of Agency and Action that have been proposed by authors like von Wright, von Kutschera, Belnap and Segerberg. (shrink)

In lieu of an abstract, here is a brief excerpt of the content:Matter and Spirit in the Age of Animal MagnetismEric G. WilsonDuring the Romantic period, writers on both sides of the Atlantic explored the sleepwalker as a merger of holiness and horror. Emerging when scientific thinkers for the first time were connecting spirit to electricity and magnetism, the somnambulist became to certain Romantics a disclosure of the difficulty of harmonizing unseen and seen, agency and necessity. This problem prominently (...) arose in Anton Mesmer's late eighteenth-century experiments in animal magnetism, in which the sleepwalker proved a paradox: an opaque revelation of transparent currents and an unconscious vehicle of sophisticated thought. Romantics such as Coleridge embraced the somnambulist as an embodiment of these troubles involved in relating motion and meaning. Coleridge and those who responded to him saw in the hypnotized human this sobering possibility: the invisible requires the visible to make itself manifest while the visible needs the invisible to become significant. 1 This is sublime and sinister: to elevate a material form to spiritual power is transcendence; to sink the boundless into a body is grotesque.Here I explore the philosophical implications of animal magnetism, the place of the sleepwalker in the history of ideas, and the role of the hypnotized human in Romantic writers, especially Coleridge. I also meditate on relationships between matter and spirit, machine and human, word and thing. Along the way, I place the history of ideas and the works of Romantic writers in mutually illuminating dialogues. The literary texts shed fresh light on philosophical problems while the ideas reveal hidden literary elements.The somnambulistic trance had been around long before Mesmer's magnetic sleeps. For centuries, shamans had used auto-hypnosis to sound [End Page 329] their souls and other-hypnosis to cure their tribe-members' ailments. However, somnambulism could not become a scientific phenomenon until Europeans in laboratories began to study electricity and magnetism. In the early modern period, Paracelsus argued that a vital fluid courses through the cosmos. The human being draws this flow like a magnet attracts force. When the body pulls to itself evil effluvia, it falls ill. To return patients to health, Paracelsus placed magnets on painful areas. He hoped to extract the unwanted current and return it to the cosmic swirl. 2 In "magnetizing" spirit, Paracelsus opened a door for empirical inquiry into the invisible world. In 1600, William Gilbert claimed that magnets correspond to the earth: both are animated by universal attraction and repulsion. 3 By the end of the seventeenth-century, Newton proposed that things are impelled by a force that draws and repels. Newton's theory of gravity inspired natural philosophers of the next centuries to search for a principle of which the magnet and the spark are manifestations. 4During the second half of the eighteenth century and the early part of the nineteenth, natural philosophers explored electricity and magnetism with unprecedented precision. In 1752, Benjamin Franklin revealed the mystery of lightning and perhaps the spark of life. 5 Inspired by Franklin, F. C. Oetinger, J. L. Fricker, and Prokop Divisch developed a theology of electricity, based on the belief that God is the electrical current. 6 Later in the century, Luigi Galvani and Alessandro Volta debated over whether the galvanic flow might be the origin and principle of life itself. 7 A few years before Franklin harvested lightning, John Michell argued that the magnetic force is not constrained to lodestones but is possibly pervasive. Some years later, Franz Aepinus suggested that magnetism and electricity manifest a deep energy. Soon after, C. A. de Coulomb discovered the mathematical law by which electrical and magnetic forces operate (Whittaker, pp. 50–59).These findings led to the breakthroughs of the nineteenth century. 8 In 1807, Humphry Davy hypothesized that chemical elements interact through electromagnetic affinity or repulsion. 9 In 1820, H. C. Oersted demonstrated the correspondence between electricity and magnetism. The same year, A. M. Ampere formulated the laws by which electrical and magnetic currents interact (Whittaker, pp. 81–86). Michael Faraday in 1831 revealed electromagnetic induction and thus inaugurated a second Copernican revolution: he showed that matter is not solid and discrete but a field of electromagnetic energy. 10 The dreams of [End... (shrink)

Drawing on sources such as home furnishing manuals, hygiene and household guidebooks, as well as literary texts, this article examines how the nineteenth-century domestic interior can be regarded as a functional environment regulated by textiles. In the debate about the correct usage of furnishing textiles in line with contemporary aesthetic and sanitary standards, women were held responsible for regulating these textile environments. While on the one hand this led to a supposedly natural and mechanical conflation of women and domestic space (...) which has often been interpreted as restrictive and encapsulating, my aim is to identify a specific feminine agency that has its origin in the home but is not limited to it. By tracing the negotiations of this gendered textile expertise in different fields of knowledge and forms of representation, this article reevaluates the relationship between textiles, domesticity and femininity in the nineteenth century. (shrink)

This volume examines the limitations of mathematical logic and proposes a new approach to logic intended to overcome them. To this end, the book compares mathematical logic with earlier views of logic, both in the ancient and in the modern age, including those of Plato, Aristotle, Bacon, Descartes, Leibniz, and Kant. From the comparison it is apparent that a basic limitation of mathematical logic is that it narrows down the scope of logic confining it to the study of deduction, without (...) providing tools for discovering anything new. As a result, mathematical logic has had little impact on scientific practice. Therefore, this volume proposes a view of logic according to which logic is intended, first of all, to provide rules of discovery, that is, non-deductive rules for finding hypotheses to solve problems. This is essential if logic is to play any relevant role in mathematics, science and even philosophy. To comply with this view of logic, this volume formulates several rules of discovery, such as induction, analogy, generalization, specialization, metaphor, metonymy, definition, and diagrams. A logic based on such rules is basically a logic of discovery, and involves a new view of the relation of logic to evolution, language, reason, method and knowledge, particularly mathematical knowledge. It also involves a new view of the relation of philosophy to knowledge. This book puts forward such new views, trying to open again many doors that the founding fathers of mathematical logic had closed historically. (shrink)

The massive industrialization of World War I resulted in a previously unimaginable number of casualties. The military and civil agencies in Germany that managed the welfare systems for veterans collaborated with companies, engineers and physicians to produce prosthetic arms, hands and legs that would allow disabled former soldiers to re-enter the factory as productive workers. This article focuses on the one of the best known arm prosthesis, the Siemens-Schuckert-Arm. While other historians have argued that the military command “recycled” disabled soldiers (...) effectively, this article argues instead that this “recycling” was incomplete due to three factors: not all offices and individuals worked together effectively; the price of the arm was too high; and employers thought the disabled would be less productive then female or elderly workers. In other words, while military and civil welfare agencies attempted to re-purpose disabled soldiers using advanced prosthetic technology, their efforts fell far short of fully reintegrating these soldiers into the war effort. (shrink)

In lieu of an abstract, here is a brief excerpt of the content:“Listening to Reason”:The Role of Persuasion in Aristotle’s Account of Praise, Blame, and the VoluntaryAllen SpeightAristotle connects praise and blame closely to the voluntary, but the question of how his discussion of these terms should be construed more broadly in the context of a theory of responsibility has been much disputed. There are some well-known difficulties with the coherence of Aristotle's views in this regard: animals and children, for (...) example, are said to be voluntary agents, but are not held to be responsible;1 moreover, praise and blame seem to be important for what might be thought to be incompatible purposes—on the one hand, for behavioral improvement and correction (a usually prospective concern) and, on the other hand, for assessment of moral responsibility in terms of what an agent merits or deserves for what he or she has done (a retrospective concern).2One of Aristotle's first examples of the use of praise and blame in the Nicomachean Ethics captures some of the difficulty commentators have found in trying to understand his position. In drawing an analogy to illustrate the difference between parts of the soul, Aristotle comments that "in morally strong and morally weak men we praise (epainoumen) the reason that guides them and the rational element of the soul, because it exhorts them to follow the right path and to do what is best" (NE 1102b13-15). There is, he thus claims, an appetitive part of the soul thatpartakes of reason insofar as it complies with reason and accepts its leadership (hē(i) katēkoon estin autou kai peitharchikon); it possesses reason in the sense that we say it is "reasonable" to accept the advice of a father and of friends, not in the sense that we have a "rational" understanding of mathematical propositions. That the irrational element can be persuaded (peithetai) by the rational is shown by the fact that admonition (nouthetēsis) and all manner of rebuke (epitimēsis) and exhortation (paraklēsis) are possible. If it is correct to say that the appetitive part, too, has reason, it follows that the rational element of the soul has two subdivisions: the one possesses reason in the [End Page 213] strict sense, contained within itself, and the other possesses reason in the sense that it listens to reason as one would listen to a father.(NE 1102b31-1103a)I will argue that this image of listening and persuasion is more significant for Aristotle's conceptions of voluntariness and responsibility than is often thought. The image suggests not only that Aristotle is interested in both prospective moral education and retrospective assessments of responsibility, but that a crucial (and, in the literature to this point, quite neglected) term that he offers as a gloss for understanding his conception of the voluntary—the notion of peithō or persuasion—is in fact central to his employment of the categories of praise and blame in both prospective and retrospective senses. Aristotle's use of the concept of persuasion is not merely a casual gloss, but gives him instead an unusually helpful category for understanding the range of types of action within his philosophy of agency and how they fit within the larger scheme of parts of the soul in the Ethics and the distinctions among actions that stem from virtue, vice, moral weakness, and moral strength.In what follows, I will first examine how Aristotle uses peithō to explain the related notions of the voluntary (as to hekousion is usually translated) and the noncompulsory in the Nicomachean Ethics, III.5, and the Eudemian Ethics, II.8. I will then explore how Aristotle appeals to peithō and its cognates to address one of the most vexing problems his theory of voluntary agency must work out—the problem of akrasia and enkrateia (moral weakness and moral strength)—and, next, more widely how these related concepts become relevant for his account of the parts of the soul and gradations of action.I. Persuasion and the Voluntary (EE II.8 and NE III.5)Aristotle appears to link closely the notions of voluntariness (to hekousion)and persuasion (hē peithō).Bonitz's Index takes the two terms straightforwardly... (shrink)

How far should our realism extend? For many years philosophers of mathematics and philosophers of ethics have worked independently to address the question of how best to understand the entities apparently referred to by mathematical and ethical talk. But the similarities between their endeavours are not often emphasised. This book provides that emphasis. In particular, it focuses on two types of argumentative strategies that have been deployed in both areas. The first—debunking arguments—aims to put pressure on realism by emphasising (...) the seeming redundancy of mathematical or moral entities when it comes to explaining our judgements. In the moral realm this challenge has been made by Gilbert Harman and Sharon Street; in the mathematical realm it is known as the 'Benacerraf-Field' problem. The second strategy—indispensability arguments—aims to provide support for realism by emphasising the seeming intellectual indispensability of mathematical or moral entities, for example when constructing good explanatory theories. This strategy is associated with Quine and Putnam in mathematics and with Nicholas Sturgeon and David Enoch in ethics. Explanation in Ethics and Mathematics addresses these issues through an explicitly comparative methodology which we call the 'companions in illumination' approach. By considering how argumentative strategies in the philosophy of mathematics might apply to the philosophy of ethics, and vice versa, the papers collected here break new ground in both areas. For good measure, two further companions for illumination are also broached: the philosophy of chance and the philosophy of religion. Collectively, these comparisons light up new questions, arguments, and problems of interest to scholars interested in realism in any area. (shrink)

Here the author of How to Solve It explains how to become a "good guesser." Marked by G. Polya's simple, energetic prose and use of clever examples from a wide range of human activities, this two-volume work explores techniques of guessing, inductive reasoning, and reasoning by analogy, and the role they play in the most rigorous of deductive disciplines.

Public deliberation, highly valued by many African societies, becomes the cornerstone of a new system of African political philosophy in this brilliant, highly original study. In Deliberative Agency, philosopher Uchenna Okeja offers a way to construct a new political center by building it around the ubiquitous African practice of public deliberation, a widely accepted means to resolve legal matters, reconcile feuding groups, and reestablish harmony. In cities, hometown associations and voluntary organizations carry out the task of fostering deliberation among (...) African groups for different reasons. In some instances, the deliberation aims to settle disputes. In others, the aim is to decide the best action to take to address unfortunate incidents such as death. Through a measured, comparative analysis, Deliberative Agency argues that the best way to reimagine and harness the idea of public deliberation, based on current experiences in Africa, is to see it as performance of agency. Building a new political center around the practice places agency at the core of a new political life in Africa. (shrink)

We find that agency problems are embedded in firm's excess and abnormal equity investments that are mainly dictated by controlling shareholder's motives and ethical choices manifested in ownership and board structure. The excess equity investment is gauged with respect to industry average. The abnormal equity investment is specifically referred to the number of nominal investment companies that are fully controlled by the controlling owners while subject to little governance. Our empirical evidences of 345 Taiwanese non-financial listed firms show that (...) firm's excess and abnormal equity investments are negatively correlated with controlling shareholder's cash flow rights while are positively correlated with the control-cash flow deviation, and board affiliation. The results are supportive of the positive incentive hypothesis and the negative entrenchment hypothesis put forth by La Porta et al. and Claessen et al.. The negative relation between equity investment and firm's value further supports the agency postulation that corporate excess and abnormal equity investments represent a leeway for controlling shareholder to exploit wealth of minority shareholders. This study potentially contributes to the literature of business ethics by portraying an empirically testable linkage from controlling owner's ethical choices to his actions and therefore firm's value. (shrink)

The paper asks whether diagrams in mathematics are particularly fruitful compared to other types of representations. In order to respond to this question a number of examples of propositions and their proofs are considered. In addition I use part of Peirce’s semiotics to characterise different types of signs used in mathematical reasoning, distinguishing between symbolic expressions and 2-dimensional diagrams. As a starting point I examine a proposal by Macbeth. Macbeth explains how it can be that objects “pop up”, e.g., (...) as a consequence of the constructions made in the diagrams of Euclid, that is, why they are fruitful. It turns out, however, that diagrams are not exclusively fruitful in this sense. By analysing the proofs given in the paper I introduce the notion of a ‘faithful representation’. A faithful representation represents as either an image or as a metaphor. Secondly it represents certain relevant relations. Thirdly manipulations on the representations respect manipulations on the objects they represent, so that new relations may be found. The examples given in the paper illustrate how such representations can be fruitful. These examples include proofs based on both symbolic expressions as well as diagrams and so it seems diagrams are not special when it comes to fruitfulness. Having said this, I do present two features of diagrams that seem to be unique. One consists of the possibility of exhibiting the type of relation in a diagram—or simply showing that a relation exists—as a contrast to stating in words that it exists. The second is the spatial configurations possible when using diagrams, e.g., allowing to show multiple relations in a single diagram. (shrink)

In this chapter we will argue, firstly, that Bacon’s engages in a pecu-liar form of mathematization of nature that develops a quali-quantitative methodology of measurement. Secondly, we will show that medicine is one of the disciplines where that dual way of measurement is practiced. In the first section of the chapter, we will expose the ontology involved in the Baconian proposal of measurement of nature. The second section will address the place that mixed mathematics occupies in Bacon’s scheme of (...) scientific branches and will suggest that a proper advancement of medicine can generate a new branch of mixed mathematics. The next section will reconstruct Bacon’s approach to measurement and expose its quali-quantitative import. In the last section, we will show some examples of medicine in which this quali-quantitative measurement is applied. (shrink)

Although there is a consensus among philosophers of mathematics and mathematicians that mathematical explanations exist, only a few authors have proposed accounts of explanation in mathematics. These accounts fit into the unificationist or top-down approach to explanation. We argue that these models can be complemented by a bottom-up approach to explanation in mathematics. We introduce the mechanistic model of explanation in science and discuss the possibility of using this model in mathematics, arguing that using it does (...) not presuppose a Platonist view of mathematics and allows one to gain insight into why a theorem is true by answering what-if-things-had-been-different questions. (shrink)

With democracy in mind, promoting students’ cognitive, personal, and social development can inform and shape the mathematics curriculum and classroom practice with the goal of their becoming more capable, self-reflective, and socially aware human beings. Toward that realization, their mathematics experience could include: heuristics, as it provides a natural language for problem solving; habits of mind, so students can think and act with a more developed “reflective intelligence”; and multiple-centers investigations, where collaborations based on shared mathematical interest can (...) be pursued. In this way, their education would be “a fostering, a nurturing, a cultivating process” that supports the development of democratic society. (shrink)

This paper draws attention to the role of the IAEA in shaping radiation dosimetry practices, instrumentation, and standards in the late 1950s and 1960s. It traces the beginnings of the IAEA’s radiation dose intercomparison program which targeted all member states and involved the WHO so as to standardize dosimetry on a global level. To standardize dosimetric measurement methods, techniques, and instruments, however, one had to devise a method of comparing absorbed dose measurements in one laboratory with those performed in others (...) with a high degree of accuracy. In 1964 the IAEA thus started to build up what I call the “global experiment,” an intercomparison of radiation doses with participating laboratories from many of its member states. To carry out the process of worldwide standardization in radiation dosimetry, I argue, an organization with the diplomatic power and global reach of the IAEA was absolutely necessary. Thus, “global experiment” indicates a novel understanding of the experimental process. What counts as an experiment became governed by a process that was designed and strictly regulated by an international organization; it took place simultaneously in several laboratories across the globe, while experimental data became centrally owned and alienated from those that produced it. (shrink)

Some mathematical proofs explain why the theorems they prove hold. This paper identifies several challenges for any counterfactual account of explanation in mathematics (that is, any account according to which an explanatory proof reveals how the explanandum would have been different, had facts in the explanans been different). The paper presumes that countermathematicals can be nontrivial. It argues that nevertheless, a counterfactual account portrays explanatory power as too easy to achieve, does not capture explanatory asymmetry, and fails to specify (...) why certain proofs are explanatory and others are not. Greater informativeness about counterfactual dependence can even yield less explanatory power. (shrink)

Agency often consists in performing actions and engaging in activities that are successful. We pour glasses, catch objects, carry things, recite poems, and play instruments. It has therefore seemed tempting in recent philosophical thinking to conceptualise the relationship between our agentive abilities and our successes as follows: (Success) S is exercising their ability to ϕ only if S successfully ϕ-s. This paper argues that (Success) is false based on the observation that agency also often consists in making mistakes. (...) We bungle things. We spill water, we miss objects thrown at us, we drop things, misremember lines, and mess up songs. I argue that these mistakes, doings that fall short of being a φ-ing, can only be understood as subpar exercises of the ability to φ. Since this understanding is incompatible with (Success), the thesis should be given up. (shrink)

The philosophical problem that stems from the successful application of mathematics in the empirical sciences has recently attracted growing interest within philosophers of mathematics and philosophers of science. Nevertheless, little attention has been devoted to the converse applicability issue of how physical considerations find successful application in mathematics. In this article, focusing on some case studies, I address the latter issue and argue that some successful applications of physics to mathematics essentially depend on the use of (...) conservation principles. I conclude with a short discussion of how the successful interplay between conservation principles and mathematics can be accounted for. (shrink)

ABSTRACT Our goal in this paper is to extend counterfactual accounts of scientific explanation to mathematics. Our focus, in particular, is on intra-mathematical explanations: explanations of one mathematical fact in terms of another. We offer a basic counterfactual theory of intra-mathematical explanations, before modelling the explanatory structure of a test case using counterfactual machinery. We finish by considering the application of counterpossibles to mathematical explanation, and explore a second test case along these lines.

En el presente artículo me ocupo de la discusión acerca de cuán exigentes son nuestras obligaciones de contribuir con dinero y tiempo a las agencias humanitarias que asisten a personas en situación de pobreza extrema en el mundo. Defiendo una posición intermedia, moderada, frente a la posición extrema formulada por Peter Singer y frente a la posición según la cual nuestras obligaciones son mínimas. La objeción principal contra esas dos posiciones es que, cuando analizan la situación en que los potenciales (...) donantes se encuentran frente a las personas en situación de pobreza extrema, omiten el carácter iterativo que es propio de esa situación. La posición moderada, en cambio, tiene en cuenta ese carácter, gracias a que entiende a nuestras obligaciones hacia los pobres globales como obligaciones imperfectas. In this article I engage in the debate about the demandingness of our duties to contribute with money and time to humanitarian agencies that assist people who live in extreme poverty around the world. I defend an intermediate, moderate, view against Peter Singer's extreme view, and also against the view according to which our duties are minimal. The main objection regarding those two views is that, when they analyze the situation in which potential donors are vis-à-vis people who live in extreme poverty, they miss its distinctive iterative character. The moderate view, on the contrary, pays heed to that character, thanks to its account of our duties towards the global poor as imperfect duties. (shrink)

This chapter begins by sketching an account of morally responsible agency and the general conditions under which it may fail. We discuss how far individuals with psychiatric diagnoses may be exempt from morally responsible agency in the way that infants are, with examples drawn from a sample of diagnoses intended to make dierent issues salient. We further discuss a recent proposal that clinicians may hold patients responsible without blaming them for their acts. We also consider cognitively impaired subjects (...) in the light of related issues in moral and political theory, asking whether they have been unjustly excluded from liberal conceptions of political community due to their presumed lack of agency. (shrink)

This paper contains a defense against anti-realism in mathematics in the light both of incompleteness and of the fact that mathematics is a ‘cultural artifact.’. Anti-realism (here) is the view that theorems, say, of aritltmetic cannot be taken at face value to express true propositions about the system of numbers but must be reconstrued to be about somctliiiig else or about nothing at all. A ‘bite-the-bullet’ aspect of the defease is that, adopting new axioms, liitherto independent, is not. (...) a matter of recognizing trutlis wliich had previoasly been unrecognized, but of extending the domain of what is true. (shrink)

In lieu of an abstract, here is a brief excerpt of the content:Reviewed by:Advances in Peircean Mathematics: The Colombian School ed. by Fernando ZalameaGianluca CaterinaFernando Zalamea (Ed.) Advances in Peircean Mathematics: The Colombian School Berlin, Boston: De Gruyter, 2022. 212 pp. (incl. index).The volume Advances in Peircean Mathematics is an important, very much needed contribution towards a deeper understanding of the impact of Peirce's work especially in the fields of mathematics, logic, and semiotic. It fills a (...) gap in the current literature by recasting some of [End Page 373] Peirce's profound mathematical insights into a formal framework. This is a finely edited editorial project, which summarizes the work of more than two decades done by a group of scholars—the Colombian School—lead by Fernando Zalamea, a pioneer of Peirce studies, and pragmatism in general, in Latin America.The structure of the volume unfolds in three dense chapters, each corresponding to a specific mathematical context connected to various aspects of Peirce's work. Broadly speaking, in the first chapter, Gustavo Arengas proposes the theory of higher category theory as a natural framework to represent the main traits of Peirce's semiotic; in the second chapter, Francisco Vargas develops a thorough set-theoretical model of Peirce's continuum; in the third chapter, Arnold Oostra, in a truly Peircean spirit, formalizes the notion of Intuitionistic Existential Graphs, emphasizing the idea that intuitionistic logic is the most natural context to represent and understand Peirce's diagrammatic logic. The fourth and last chapter, penned by Zalamea, provides the reader with a solid summary of the main results presented in the volume along with a robust road map to navigate through the technical details of the text.Mathematics, as implied by the title of the volume, is at the core of this project, and the authors do not shy away from the complexity, details, and depth of it in order to shed light on some of the most fundamental and groundbreaking nature of Peirce's ideas. That level of rigor and formal soundness is certainly one of the strengths of the volume, although readers who may not be acquainted with at least some basic notions of category theory or with the mathematics of Peirce's work, may find some of the text a bit terse—this is not a casual reading and it does require a certain level of commitment in order to appreciate the depth of the provided insights. On the other hand, all the background material is clearly laid out, making the volume a self-contained work which can be thoroughly enjoyed by a general audience.The real upshot of recasting some of Peirce's intuitions within the fabric of formal mathematics is not only that of providing the instruments to clarify those ideas, but also that of highlighting the role that Peirce's work has been playing in the development of modern mathematics in many relevant aspects, from the very genesis of category theory—which today is widely regarded as a necessary and unifying language in several fields of the mathematical and physical sciences—to the development of non-standard analysis, just to mention a few of them.An elegant instance of such perspective is offered by Gustavo Arengas in the first chapter, where it is argued that ∞-categories can be used to model the natural order of hierarchies implicit in Peirce's conception of the basic triadic relation between sign, object, and interpreter. What, at first glance, may seem just a simple analogy, unfolds onto a methodical and enlightening analysis of Peirce's semiotic, as the author builds [End Page 374] the connections with the relevant categorical constructions in a precise manner. Most of the rest of the chapter focuses on Peirce's notions of the pragmatic and pragmaticist maxim, and the use of basic structures such as monads, limits, presheaves and sheaves as the natural environment to better convey their meaning, both from a mathematical and a philosophical perspective. The reader will find it interesting to realize that, by delving deeper into the understanding of the relational nature of category theory, a great chunk of Peirce's work can be seen as fundamentally intertwined with the apparatus and the language of modern mathematics... (shrink)