Interest in the computational aspects of modeling has been steadily growing in philosophy of science. This paper aims to advance the discussion by articulating the way in which modeling and computational errors are related and by explaining the significance of error management strategies for the rational reconstruction of scientific practice. To this end, we first characterize the role and nature of modeling error in relation to a recipe for model construction known as Euler’s recipe. We then describe a general model (...) that allows us to assess the quality of numerical solutions in terms of measures of computational errors that are completely interpretable in terms of modeling error. Finally, we emphasize that this type of error analysis involves forms of perturbation analysis that go beyond the basic model-theoretical and statistical/probabilistic tools typically used to characterize the scientific method; this demands that we revise and complement our reconstructive toolbox in a way that can affect our normative image of science. (shrink)

We argue that two powerful error-theoretic concepts provide a general framework that satisfactorily accounts for key aspects of the explanation of physical patterns. This method gives an objective criterion to determine which mathematical models in a class of neighboring models are just as good as the exact one. The method also emphasizes that abstraction is essential for explanation and provides a precise conceptual framework that determines whether a given abstraction is explanatorily relevant and justified. Hence, it increases our epistemological understanding (...) of how one should go about reconstructing scientific practices by making clear that, at a fundamental level, a key aspect of mathematical modeling consists in exactly solving nearby problems. (shrink)

Modern mathematical sciences are hard to imagine without appeal to efficient computational algorithms. We address several conceptual problems arising from this interaction by outlining rival but complementary perspectives on mathematical tractability. More specifically, we articulate three alternative characterizations of the complexity hierarchy of mathematical problems that are themselves based on different understandings of computational constraints. These distinctions resolve the tension between epistemic contexts in which exact solutions can be found and the ones in which they cannot; however, contrary to a (...) persistent myth, we conclude that having an exact solution is not generally more epistemologically beneficial than lacking one. (shrink)

ABSTRACT This paper examines consequences of the computer revolution in mathematics. By comparing its repercussions with those of conceptual developments that unfolded in the nineteenth century, I argue that the key epistemological lesson to draw from the two transformative periods is that effective and successful mathematical practices in science result from integrating the computational and conceptual styles of mathematics, and not that one of the two styles of mathematical reasoning is superior. Finally, I show that the methodology deployed by applied (...) mathematicians in modern scientific computing is a paradigmatic instance of this key lesson. (shrink)

The relatively recent increase in prominence of computer simulations in scientific inquiry gives us more reasons than ever before for asserting that mathematics is a wonderful tool. In fact, a practical knowledge of scientific computation has become essential for scientists working in all disciplines involving mathematics. Despite their incontestable success, it must be emphasized that the numerical methods subtending simulations provide at best approximate solutions and that they can also return very misleading results. Accordingly, epistemological sobriety demands that we clarify (...) the circumstances under which simulations can be relied upon. With this in mind, this paper articulates a general perspective to better understand and compare the strengths and weaknesses of various error-analysis methods. (shrink)

Despite being one of the most dependable methods used by applied mathematicians and engineers in handling complex systems, the finite element method commits variational crimes. This paper contextualizes the concept of variational crime within a broader account of mathematical practice by explaining the tradeoff between complexity and accuracy involved in the construction of numerical methods. We articulate two standards of accuracy used to determine whether inexact solutions are good enough and show that, despite violating the justificatory principles of one, the (...) finite element method nevertheless succeeds in obtaining its legitimacy from the other. (shrink)

What are the pillars on which the success of modern science rest? Although philosophers have much discussed what is behind science’s success, this paper argues that much of the discussion is misdirected. The extant literature rightly regards the semantic and inferential tools of formal logic and probability theory as pillars of scientific rationality, in the sense that they reveal the justificatory structure of important aspects of scientific practice. As key elements of our rational reconstruction toolbox, they make a fundamental contribution (...) to our understanding of the success of science.At the same time, any science, however exact, is dominated by approximation, error, and uncertainty, a fact that makes one wonder how science can be so successful. This paper articulates and illustrates general themes—e.g., that truth-preserving arguments often fail to preserve approximate truth—that highlight the need for additional semantic resources. Thus, our proposal is that persistent failures to unravel the reasons behind the success of science in the face of pervasive error and uncertainty should be attributed to an insufficiently rich way of rationally reconstructing scientific and mathematical knowledge. What is missing? This paper claims that there is a third formal method of reasoning that constitutes a distinct pillar on which rests the success of science, namely, perturbation theory. The paper outlines how the representational and inferential tools of perturbation theory differ from those of logic and probability theory, and how they enable us to understand the apparently elusive aspects of the success of science.However, compared to its peers, perturbative reasoning has not received the attention it deserves. As the paper explains, this partly results from the circumstances in which perturbation theory is taught, and partly from the fact that perturbation theory first appears to be a vaguely related collection of methods offering no systematic semantic insight. In an attempt to show that this first impression is wrong, this paper presents its contribution to the semantic dimension of scientific representation and inference in terms of what I call “semantic layering.”. (shrink)

This paper articulates an account of imperatives that sensibly supports the idea of a logic of imperative inferences. We rebuke common objections to the very possibility of such a logic, from a perspective based on recent linguistic work on the morphosyntax of imperatives. Specifically, we develop the notion that the content of an imperative sentence includes both a force operator alongside an imperational content to which the force applies. We further argue that this account of the content of imperatives constitutes (...) a plausible and flexible framework to develop a logic of imperative by examining a number of reconstructions of this idea using semantical analogs of widespread modal semantics. After studying the performance of those approaches, we conclude that progress in imperative logic has been hindered by the failure to adopt conflict-tolerant and resource-sensitive semantics, but suggest that such considerations can be incorporated in this flexible framework. Finally, we also propose a simple account of the difference between operators applying to the content of imperatives and imperative operators, in a way that sheds light on some of the issues underlying the usual antinomies. (shrink)

We demonstrate via several examples how the backward error viewpoint can be used in the analysis of solutions obtained by perturbation methods. We show that this viewpoint is quite general and offers several important advantages. Perhaps the most important is that backward error analysis can be used to demonstrate the validity of the solution, however obtained and by whichever method. This includes a nontrivial safeguard against slips, blunders, or bugs in the original computation. We also demonstrate its utility in deciding (...) when to truncate an asymptotic series, improving on the well-known rule of thumb indicating truncation just prior to the smallest term. We also give an example of elimination of spurious secular terms even when genuine secularity is present in the equation. We give short expositions of several well-known perturbation methods together with computer implementations. We also give a generic backward error based method that is equivalent to iteration for regular perturbation. (shrink)

Ethically permissible clinical trials must not expose subjects to risks that are unreasonable in relation to anticipated benefits. In the research ethics literature, this moral requirement is typically understood in one of two different ways: as requiring the existence of a state of clinical equipoise, meaning a state of honest, professional disagreement among the community of experts about the preferred treatment; or as requiring an equilibrium between individual and collective ethics. It has been maintained that this second interpretation makes it (...) mandatory to minimize the number of patients receiving the treatment that will eventually be shown to be inferior by the trial. This requirement has led to the development of adaptive trials, i.e., trials in which treatment allocation is determined by data accumulated during interim analysis. Many statisticians argue that in some circumstances—typically with potentially high benefits, as in the much discussed ECMO trial—adaptive design is the only ethically permissible experimental design. Nevertheless, some proponents of clinical equipoise argue that adaptive trials are neither ethically required nor permissible. More specifically, they argue that clinical trials using adaptive designs fail to meet the moral requirement of clinical equipoise, since these trials presuppose an epistemic state that is incompatible with a physician’s duty of care to her subjects. This paper emphasizes that the debate is to a large extent resting on an epistemological confusion. Specifically, I argue that this response conflates two different conceptions of statistical evidence, and that recognizing this distinction elucidates an epistemological framework in which adaptive trials are both consistent with and recommended by the moral requirement of clinical equipoise. (shrink)

One of the most unsettling problems in the history of philosophy examines how mathematics can be used to adequately represent the world. An influential thesis, stated by Eugene Wigner in his paper entitled "The Unreasonable Effectiveness of Mathematics in the Natural Sciences," claims that "the miracle of the appropriateness of the language of mathematics for the formulation of the laws of physics is a wonderful gift which we neither understand nor deserve." Contrary to this view, this thesis delineates and implements (...) a strategy to show that the applicability of mathematics is very reasonable indeed. I distinguish three forms of the problem of the applicability of mathematics, and focus on one I call the problem of uncanny accuracy: Given that the construction and manipulation of mathematical representations is pervaded by uncertainty, error, approximation, and idealization, how can their apparently uncanny accuracy be explained? I argue that this question has found no satisfactory answer because our rational reconstruction of scientific practice has not involved tools rich enough to capture the logic of mathematical modelling. Thus, I characterize a general schema of mathematical analysis of real systems, focusing on the selection of modelling assumptions, on the construction of model equations, and on the extraction of information, in order to address contextually determinate questions on some behaviour of interest. A concept of selective accuracy is developed to explain the way in which qualitative and quantitative solutions should be utilized to understand systems. The qualitative methods rely on asymptotic methods and on sensitivity analysis, whereas the quantitative methods are best understood using backward error analysis. The basic underpinning of this perspective is readily understandable across scientific fields, and it thereby provides a view of mathematical tractability readily interpretable in the broader context of mathematical modelling. In addition, this perspective is used to discuss the nature of theories, the role of scaling, and the epistemological and semantic aspects of experimentation. In conclusion, we argue for a method of local and global conceptual analysis that goes beyond the reach of the tools standardly used to capture the logic of science; on their basis, the applicability of mathematics finds itself demystified. (shrink)

ACMES is a multidisciplinary conference series that focuses on epistemological and mathematical issues relating to computation in modern science. This volume includes a selection of papers presented at the 2015 and 2016 conferences held at Western University that provide an interdisciplinary outlook on modern applied mathematics that draws from theory and practice, and situates it in proper context. These papers come from leading mathematicians, computational scientists, and philosophers of science, and cover a broad collection of mathematical and philosophical topics, including (...) numerical analysis and its underlying philosophy, computer algebra, reliability and uncertainty quantification, computation and complexity theory, combinatorics, error analysis, perturbation theory, experimental mathematics, scientific epistemology, and foundations of mathematics. By bringing together contributions from researchers who approach the mathematical sciences from different perspectives, the volume will further readers' understanding of the multifaceted role of mathematics in modern science, informed by the state of the art in mathematics, scientific computing, and current modeling techniques. (shrink)

(No abstract is available for this citation).

Foucault’s work is rich enough to sustain multiple readings. I argue in this paper for the continued construction and maintenance of what I have called the ‘American Foucault’, whose principal preoccupation is with the question of how to be free within our contemporary political constraints and possibilities. (Such a Foucault can be found in the works of American writers such as W. E. Connolly, Todd May, and Thomas Dumm.) Appreciation of Foucault’s contribution to an understanding of freedom is too often (...) hampered, however, by the insistence on the part of many of the most influential of Foucault’s critics (and some of his defenders) that his particular mode of thinking is ultimately too irresponsible. It is thought that Foucault’s refusal to account for the grounds of his work vitiates his overall project. I argue that, if we distinguish between the ‘account-ability’ demanded by his critics and the ‘response-ability’ that his work permits, we will be in a better position to appreciate the timeliness of his conception of freedom. (shrink)

A work that underscores the need to examine history from a philosophical perspective.

This book discusses the relevance of philosophy courses within the undergraduate curriculum as integral to the self-formation that is at the heart of a liberal education. The objective is to provide a historically layered view of what it can still mean to study for its own sake. The elective university classroom is important because the course of study is chosen out of personal interest and enthusiasm, as opposed to being primarily governed by predetermined disciplinary objectives. It engages the student's mind (...) directly and freely, and counters the overly specialized minds favoured by the contemporary university as well as the commodification of its degrees. The discussion builds on the distinction put forward by Raymond Williams between a dominant culture (in this case, university study as contributing to research and/or marketable degrees) and alternative and/or oppositional cultures that have both residual and emergent dimensions. The elective stream of university study is treated as alternative and oppositional to the dominant culture. The elective university classroom is examined as a combination of a classroom, students, texts, and professors. Each element is explored in terms of its alternative/residual significance as illustrated through the history of philosophy: the classroom and students through the life and death of Socrates; texts through the origins of the university in medieval scholasticism; the professor in the Humboldtian reform of the university at the beginning of the nineteenth century in Berlin. (shrink)

Taste as Experience puts the pleasure of food at the center of human experience. It shows how the sense of taste informs our preferences for and relationship to nature, pushes us toward ethical practices of consumption, and impresses upon us the importance of aesthetics. Eating is often dismissed as a necessary aspect of survival, and our personal enjoyment of food is considered a quirk. Nicola Perullo sees food as the only portion of the world we take in on a daily (...) basis, constituting our first and most significant encounter with the earth. Perullo has long observed people's food practices and has listened to their food experiences. He draws on years of research to explain the complex meanings behind our food choices and the thinking that accompanies our gustatory actions. He also considers our indifference toward food as a force influencing us as much as engagement. For Perullo, taste is value and wisdom. It cannot be reduced to mere chemical or cultural factors but embodies the quality and quantity of our earthly experience. (shrink)

This book is the first extensive treatment of Husserl's phenomenology of time-consciousness. Nicolas de Warren uses detailed analysis of texts by Husserl, some only recently published in German, to examine Husserl's treatment of time-consciousness and its significance for his conception of subjectivity. He traces the development of Husserl's thinking on the problem of time from Franz Brentano's descriptive psychology, and situates it in the framework of his transcendental project as a whole. Particular discussions include the significance of time-consciousness for (...) other phenomenological themes: perceptual experience, the imagination, remembrance, self-consciousness, embodiment, and the consciousness of others. The result is an illuminating exploration of how and why Husserl considered the question of time-consciousness to be the most difficult, yet also the most central, of all the challenges facing his unique philosophical enterprise"--Provided by publisher. (shrink)

In the historical context of a crisis in biological psychiatry, psychedelic drugs paired with psychotherapy are globally re-emerging in research clinics as a potential transdiagnostic therapy for treating mood disorders, addictions, and other forms of psychological distress. The treatments are poised to soon shift from clinical trials to widespread service delivery in places like Australia, North America, and Europe, which has prompted ethical questions by social scientists and bioethicists. Taking a broader view, we argue that the ethics of psychedelic therapy (...) concerns not simply how psychotherapies are different when paired with psychedelic drugs, but how psychedelic therapies shape and are shaped by different values, norms, and metaphysical commitments. Drawing from the published literature and interviews with seven psychedelic therapists working in clinical trials in the United States, Germany, Switzerland, and Australia, this article opens the black box of the treatments to consider the values and informal debates currently animating the therapies. Considering questions of patient autonomy, mechanisms of therapeutic action, and which therapies are best suited to pair with psychedelic substances, we examine the ethics of psychedelic therapy as an emergent form of life. To bring this form of life out in fuller relief, we conclude by comparing and contrasting it with ayahuasca use in Amazonian shamanism. (shrink)

Methexiology is not a particular theory, but rather a general philosophical orientation. Therefore, in Methexiology: Philosophical Theology and Theological Philosophy for the Deification of Humanity, Nicolas Laos elucidates the significance of methexiology for the study of ontology, epistemology, ethics, philosophical psychology, theory of justice, philosophy of history, and philosophy of religion. Laos argues that, faced with the modern and the postmodern crises of meaning, we need a new myth, a new spiritual formula, for the resacralization of humanity and the (...) cosmos, without restoring defunct totems, without using tales as "cheap" substitutes for the lack of a life-giving myth, and without negating history. In his Methexiology, Laos studies the "genealogy" of the modern and the postmodern crises of meaning, and, based on his new interpretation of classical Greek philosophy and Hesychasm, proposes methexiology as a way of overcoming the crises of meaning and as a way of resacralizing humanity and the cosmos through a new metaphysically grounded humanism. (shrink)

Blaise Pascal est le penseur radical des limites et des contradictions de l'homme, ni ange ni bête. Contrairement à ce qu'en prétend l'orgueil de toute une modernité, la raison ne peut pas tout ; mais contrairement au désespoir du fanatisme, la raison n'est pas sans force. Jusqu'où alors peut-elle s'exercer? Pour Pascal, la philosophie ne saurait faire l'économie de la question de Dieu, Elle doit donc croiser la théologie. Mais comment vont se nouer l'ordre de l'esprit et celui de la (...) charité? Pascal produit ainsi une analyse critique de la philosophie comme telle, de ses capacités et de ses limites, que le présent ouvrage se donne pour tâche de clarifier. Que peut la philosophie? Mais qui décide de ce qu'elle peut, et surtout de ce qu'elle ne peut pas? Comment s'établissent alors ses rapports avec la théologie? Ce que Pascal nous invite ainsi à penser, c'est toujours à la fois la misère et la grandeur de la philosophie. (shrink)

Dans son dernier cours au Collège de France, Michel Foucault nous parle d'un oubli, plus fondamental à ses yeux que le fameux "oubli de l'être", ou plus précisément d'une négligence ; une négligence dont la philosophie est responsable, ce qui est d'autant plus paradoxal qu'il concerne précisément la vie philosophique. "Je voudrais, en tout cas, suggérer simplement que s'il est vrai que la question de l'être a bien été ce que la philosophie occidentale a oublié et dont l'oubli a rendu (...) possible la métaphysique, peut-être aussi la question de la vie philosophique n'a-t-elle pas cessé d'être, je ne dirais pas oubliée, mais négligée ; elle n'a pas cessé d'apparaître comme en trop par rapport à la philosophie, à la pratique philosophique, à un discours de plus en plus indexé au modèle scientifique" Cette négligence a une histoire. Car le problème de la vie philosophique a été posé dans toute sa radicalité dans l'Antiquité ; il n'était pas complètement oublié à l'époque moderne, comme en témoigne l'oeuvre de Spinoza ; mais à partir du moment "où la philosophie est devenue un métier de professeur, c'est-à-dire au début du XIXème siècle", elle a évacué du champ des problèmes pertinents, des problèmes "sérieux", cela même qui pourtant lui avait donné son horizon et sa raison d'être : la possibilité de définir une vie philosophique, c'est-à-dire une vie juste, une vie bonne, une "vraie vie". (shrink)

Die Utopien sind tot, es leben die Utopien. In diesem Buch wird die Utopie sozialer Gerechtigkeit entwickelt. INhaltlich besteht es in dem Dreischritt, (1) aus im Alltag von jedermann hin und wieder geauSSerten situativen Urteilen das gemeinsame Grundverstandnis von Gerechtigkeit zu destillieren, (2) anhand dieses Gelanders die bedeutendsten zeitgenossischen Theoretiker sozialer Gerechtigkeit akribisch zu lesen und in konstruktiver Absicht zu kritisieren, um (3) in ersten Ansatzen eine gerechtere Zukunftsgesellschaft zu skizzieren, deren quer zu tradierten Ideologien liegendes System sich ethischer Sozialismus (...) nennen lieSSe. (shrink)

This book advances a new interpretation of Hart's penal philosophy. Positioning itself in opposition to current interpretations, the book argues that Hart does not defend a mixed theory of punishment, nor a rule-utilitarian theory of punishment, nor a liberal form of utilitarianism, nor a goal and constraint approach. Rather, it is argued, his penal philosophy is based on his moral pluralism, which comprises two aspects: value pluralism and pluralism with respect to forms of moral reason. It is held that this (...) means, on the one hand, that criminal law has an irreducible complexity due to the compromises it makes to accommodate competing values, and on the other hand, that there need not be one single justification of punishment. This original interpretation is not based only on Hart's key volume on the subject Punishment and Responsibility, but on a careful reading of his complete works. The book will be a valuable resource for academics and researchers interested in Hart's philosophy, the philosophy of law and criminal law. (shrink)

Die Suche nach historischen Quellen für die Leibniz’sche Philosophie scheint zunächst unerschöpflich. Durch alle in diesem Band versammelten Arbeiten wird der Einfluss der Philosophie des Aristoteles auf das Leibniz’sche Denken näher umrissen. Ein wesentliches Ziel ist es hierbei, einen Beitrag zur Analyse dieser philosophischen Beziehung zu leisten und zu zeigen, dass auch Aristoteles’ Philosophie nach Ansicht unserer Autoren entscheidend zum Verständnis des Leibniz’schen Denkens beiträgt. Die Texte befassen sich mit wesentlichen Themen der Leibniz’schen Logik und Metaphysik, z. B. mit den (...) Grundbegriffen „Monade“ (und deren „Körperhaftigkeit“), „Entelechie“, „Nous“, mit dem Problem der Individuation (Individuum, Atomismus, Einheit), mit den substanziellen Formen, mit der Wissenschaft im Allgemeinen und der Technik, mit der Transformation der Logik, mit den Prinzipien (nämlich denjenigen des zureichenden Grundes, der Individuation und der Notwendigkeit), mit Zukunft und Kontingenz sowie Vergänglichkeit, mit der Theorie der syllogistischen Folgerung, usw. Diese Themen werden stets in der Gegenüberstellung von Leibniz und Aristoteles behandelt – sie zeigen daher, wie Leibniz aristotelische Thesen übernahm, veränderte oder kritisierte. The search for the historical sources of Leibniz’s philosphy initially seems to be unending. All the essays in this volume outline more clearly the influence of Aristotle’s philosophy on Leibniz’s thought. In this context a fundamental aim is to contribute to the analysis of this philosophical relationship and to demonstrate that Aristotle’s philosophy, in the opinion of our authors, plays a decisive role in the understanding of Leibniz’s thought. The texts address fundamental themes of Leibniz’s logic and metaphysics, e.g. the basic concepts of ‘monads’ (and their ‘corporality’), ‘entelechy’ and ‘nous; the problem of individuation (individual, atomism, unity); substantial forms; knowledge in general, and technology; the transformation of logic; principles (namely those of sufficient grounds, of individuation and of necesssity); future and contingency and transientness; the theory of syllogistic deduction, etc. These themes are regularly considered in the comparison between Leibniz and Aristotle – they demonstrate how Leibniz took over, treated or criticised Aristotelian theses. (shrink)

This chapter deals with one of the common fallacies in Western philosophy, inappropriate appeal to authority (IAA). IAA has many different facets. At its core, it is a fallacy that assumes that because someone is an authority, we should listen to that person. The problem with IAA is that it ignores content in favor of credentials and power. There are a few different ways in which IAA can occur. IAA seems to be the result of a flaw in human thinking. (...) Social cognitive theory, a theory that helps explain human action, notes that humans tend to act like each other. The tendency to listen to authorities who are not authorities explains why celebrities are able to sell us stuff. The important thing to remember about IAA is that it is not just a fallacy that comes up in arguments that do not matter. (shrink)

For decades, liberal democracy has been extolled as the best system of governance to have emerged out of the long experience of history. Today, such a confident assertion is far from self-evident. Democracy, in crisis across the West, must prove itself. This highly timely volume is both a conceptual and practical guide of impressive scope to the challenges of good governance as the world continues to undergo profound transformation in the coming decades.

The empirical study of belief is emerging at a rapid clip, uniting work from all corners of cognitive science. Reliance on belief in understanding and predicting behavior is widespread. Examples can be found, inter alia, in the placebo, attribution theory, theory of mind, and comparative psychological literatures. Research on belief also provides evidence for robust generalizations, including about how we fix, store, and change our beliefs. Evidence supports the existence of a Spinozan system of belief fixation: one that is automatic (...) and independent of belief rejection. Independent research supports the existence of a system of fragmented belief storage: one that relies on large numbers of causally isolated, context-sensitive stores of belief in memory. Finally, empirical and observational data support at least two systems of belief change. One system adheres, mostly, to epistemological norms of updating; the other, the psychological immune system, functions to guard our most centrally held beliefs from potential inconsistency with newly formed beliefs. Refining our under- standing of these systems can shed light on pressing real-world issues, such as how fake news, propaganda, and brainwashing exploit our psychology of belief, and how best to construct our modern informational world. (shrink)