There is a long tradition, in the history and philosophy of science, of studying Kant’s philosophy of mathematics, but recently philosophers have begun to examine the way in which Kant’s reflections on mathematics play a role in his philosophy more generally, and in its development. For example, in the Critique of Pure Reason , Kant outlines the method of philosophy in general by contrasting it with the method of mathematics; in the Critique of Practical Reason , Kant compares the Formula (...) of Universal Law, central to his theory of moral judgement, to a mathematical postulate; in the Critique of Judgement , where he considers aesthetic judgment, Kant distinguishes the mathematical sublime from the dynamical sublime. This last point rests on the distinction that shapes the Transcendental Analytic of Concepts at the heart of Kant’s Critical philosophy, that between the mathematical and the dynamical categories. These examples make it clear that Kant's transcendental philosophy is strongly influenced by the importance and special status of mathematics. The contributions to this book explore this theme of the centrality of mathematics to Kant’s philosophy as a whole. This book was originally published as a special issue of the Canadian Journal of Philosophy. (shrink)

It's well-known that Kant believed that intuition was central to an account of mathematical knowledge. What that role is and how Kant argues for it are, however, still open to debate. There are, broadly speaking, two tendencies in interpreting Kant's account of intuition in mathematics, each emphasizing different aspects of Kant's general doctrine of intuition. On one view, most recently put forward by Michael Friedman, this central role for intuition is a direct result of the limitations of the syllogistic logic (...) available to Kant. On this view, Kant's reasons for introducing intuition are taken to be logical or mathematical, rather than philosophical. The other tendency, which I shall try to develop here, emphasizes an epistemological or phenomenological role for intuition in mathematics arising out of what may loosely be called Kant's ‘antiformalism.’This paper, which focuses specifically on the case of geometry, falls into two parts. First, I consider Kant's discussion of intuition in the Metaphysical Exposition of the concept of space. (shrink)

In lieu of an abstract, here is a brief excerpt of the content:Kant on the Method of MathematicsEmily Carson1. INTRODUCTIONThis paper will touch on three very general but closely related questions about Kant’s philosophy. First, on the role of mathematics as a paradigm of knowledge in the development of Kant’s Critical philosophy; second, on the nature of Kant’s opposition to his Leibnizean predecessors and its role in the development of the Critical philosophy; and finally, on the specific role of intuition (...) in Kant’s philosophy of mathematics. One of the points that I want to make is that recognizing the importance of these first two issues is essential to giving an adequate account of the third. That is, only by appreciating how Kant uses the example of mathematical knowledge, and in particular the objections he had to previous accounts of such knowledge, can we understand the philosophical role that he ascribes to intuition in his own account of mathematics.I don’t propose to explain the details of Kant’s philosophy of mathematics, but rather to compare his views on mathematics in the pre-Critical Prize Essay of 1764 to those of the Critique of Pure Reason, with the aim of showing how Kant’s doctrine of construction in pure intuition arises out of a combination of two factors: first, his attempt to ground the distinction between the respective methods of mathematics and philosophy, and second, his concern to defend the reality of mathematical knowledge against the views of those he called ‘the metaphysicians.’ The first factor demands an account of the certainty of mathematics, the second requires an account of its content. I shall argue that there is a possible conflict between Kant’s accounts of these features in the Prize Essay, a possibility which is finally ruled out only by means of the Critical doctrine of pure intuition. So I hope to show that there is a significant philosophical role for intuition in Kant’s account of mathematical knowledge (over and above the more logical role attributed to it on readings [End Page 629] such as those of Friedman, Beth, and Hintikka1) in reconciling the content of mathematics and its certainty.2. THE MATHEMATICIANS VS. THE METAPHYSICIANSThroughout his early writings, Kant appealed to the evidence and certainty of mathematics; his attitude towards metaphysics, however, underwent a dramatic shift. In the Physical Monadology of 1756, Kant asked how metaphysics and geometry can be united,[f] or the former peremptorily denies that space is infinitely divisible, while the latter, with its usual certainty, asserts that it is infinitely divisible. Geometry contends that empty space is necessary for free motion, while metaphysics hisses the idea off the stage. Geometry holds universal attraction or gravitation to be hardly explicable by mechanical causes but shows that it derives from the forces which are inherent in bodies at rest and which act at a distance, whereas metaphysics dismisses the notion as an empty delusion of the imagination [1:475–6].2He attempted in this work to reconcile the respective positions of metaphysics and geometry regarding infinite divisibility, thereby demonstrating that “it is neither the case that the geometer is mistaken nor that the opinion to be found among metaphysicians deviates from the truth” [1:480]. But in a series of works from 1762–3, Kant reveals a markedly different attitude towards metaphysics. For example, in “The only possible argument in support of a demonstration of the existence of God,” Kant says:the mania for method and the imitation of the mathematician, who advances with a sure step along a well-surfaced road, have occasioned a large number of such mishaps on the slippery ground of metaphysics. These mishaps are constantly before one’s eyes, but there is little hope that people will be warned by them, or that they will learn to be more circumspect as a result [2:71].In contrast, Kant describes the geometer as uncovering “with the greatest certainty” the most secret properties of that which is extended [2:70]. But the less conciliatory attitude to metaphysics comes out most clearly in Kant’s actual procedure in “The only possible argument.” In the Seventh Reflection, he presents an attempt to explain the origin of... (shrink)

In this paper I argue that Kant's distinction in the Inaugural Dissertation between the sensible and the intelligible arises in part out of certain open questions left open by his comparison between mathematics and metaphysics in the Prize Essay. This distinction provides a philosophical justification for his distinction between the respective methods of mathematics and metaphysics and his claim that mathematics admits of a greater degree of certainty. More generally, this illustrates the importance of Kant's reflections on mathematics for the (...) development of his Critical philosophy. (shrink)

In her recent book, Realism in mathematics, Penelope Maddy attempts to reconcile a naturalistic epistemology with realism about set theory. The key to this reconciliation is an analogy between mathematics and the physical sciences based on the claim that we perceive the objects of set theory. In this paper I try to show that neither this claim nor the analogy can be sustained. But even if the claim that we perceive some sets is granted, I argue that Maddy's account fails (...) to explain the key issue faced by an epistemology for mathematics, namely the step from knowledge of the finite to knowledge of the infinite. (shrink)

By way of these investigations, we hope to understand better the rationale behind Kant's theory of intuition, as well as to grasp many facets of the relations ...

There is a long tradition, in the history and philosophy of science, of studying Kant’s philosophy of mathematics, but recently philosophers have begun to examine the way in which Kant’s reflections on mathematics play a role in his philosophy more generally, and in its development. For example, in the Critique of Pure Reason , Kant outlines the method of philosophy in general by contrasting it with the method of mathematics; in the Critique of Practical Reason , Kant compares the Formula (...) of Universal Law, central to his theory of moral judgement, to a mathematical postulate; in the Critique of Judgement , where he considers aesthetic judgment, Kant distinguishes the mathematical sublime from the dynamical sublime. This last point rests on the distinction that shapes the Transcendental Analytic of Concepts at the heart of Kant’s Critical philosophy, that between the mathematical and the dynamical categories. These examples make it clear that Kant's transcendental philosophy is strongly influenced by the importance and special status of mathematics. The contributions to this book explore this theme of the centrality of mathematics to Kant’s philosophy as a whole. This book was originally published as a special issue of the Canadian Journal of Philosophy. (shrink)

This paper is part of a larger project about the relation between mathematics and transcendental philosophy that I think is the most interesting feature of Kant’s philosophy of mathematics. This general view is that in the course of arguing independently of mathematical considerations for conditions of experience, Kant also establishes conditions of the possibility of mathematics. My broad aim in this paper is to clarify the sense in which this is an accurate description of Kant’s view of the relation between (...) mathematics and transcendental philosophy. (shrink)

StillwellJohn.* * _ A Concise History of Mathematics for Philosophers. _ Cambridge Elements in the Philosophy of Mathematics. Cambridge University Press, 2019. Pp. 69. ISBN: 978-1-108-45623-4, 978-1-108-61012-4. doi.org/10.1017/9781108610124.

This thesis attempts to argue against an influential interpretation of Kant's philosophy of mathematics according to which the role of pure intuition is primarily logical. Kant's appeal to pure intuition, and consequently his belief in the synthetic character of mathematics, is, on this view, a result of the limitations of the logical resources available in his time. In contrast to this, a reading is presented of the development of Kant's philosophy of mathematics which emphasises a much richer philosophical role for (...) intuition, beyond that of filling in deductive gaps in mathematical arguments. This role is largely determined by two factors: on the one hand, the epistemological gap in a traditional account of mathematical certainty, and on the other hand, the metaphysical worry raised by the followers of Leibniz and Wolff regarding the status of mathematics as a science consisting of truths. ;By appreciating how Kant's philosophy of mathematics developed against the background of what he saw as a conflict between the 'metaphysicians' and the 'mathematicians', we can see how the doctrine of pure intuition was required to fill the gaps in the account of the method and certainty of mathematics which Kant presents in the Prize Essay of 1764. This conflict takes its sharpest form between the monadists who uphold the metaphysical necessity of simple elements, and the geometers who uphold the infinite divisibility of space. In the Prize Essay Kant indirectly addresses this conflict by comparing the two disciplines. He asserts that the method of attaining certainty in mathematics is different from the method of metaphysics, and that as a result of this difference--primarily the different roles of definitions in each--mathematics is capable of a higher degree of certainty than metaphysics. He does not, however, explain this difference. Such an explanation seems particularly important in light of Kant's wish to secure geometry against the challenge of metaphysics. This thesis attempts to show that it is to provide such an explanation, to provide a philosophical grounding for the Prize Essay account, that Kant invokes the doctrine of pure intuition in his later account of mathematical knowledge. (shrink)

The broadly-stated aim of this rich collection is to reevaluate and reconceptualize the mathematization thesis, which the editors take to signify “above all the transformation of scientific concepts and methods, especially those concerning the nature of matter, space, and time, through the introduction of mathematical techniques and ideas”. As a historiographical thesis, it is the thesis that “the scientific revolution, and by implication modern science as a whole, is guided by the project of mathematization”.In the introduction to the volume, the (...) editors acknowledge the virtues of the historiographical thesis, which explain its persistence. For example, it highlights a constitutive feature... (shrink)

This is a book of wide-ranging scope, as the title suggests. First, it canvasses a broad selection of topics—from electromagnetism and quantum mechanics to Husserl’s phenomological constitution of logic, from Russell and Wittgenstein to Hartry Field. Second, its aims are broad. The author describes the book both as a “rational reconstruction of Poincaré’s position” and as a “treatise on modern epistemology”. The former description is somewhat misleading in that, together with Zahar’s stated aim of both “clarifying and of then reconciling (...) Poincaré’s various theses about the foundations of mathematics and the natural sciences”, it might give the reader hope that all of these theses might be shown to be part of one unified position. In fact, though, Poincaré’s philosophy of physics and his philosophy of mathematics turn out to be fundamentally different. Zahar attributes to Poincaré a “structural realist” view of physics and a “quasi-Kantian” constructivist view of mathematics. It’s not entirely clear, though, why the considerations adduced in favor of structural realism in physics can’t be carried over to the case of mathematics. More might have been said to explain this divergence, perhaps for example by developing the contrast in the introduction between the empirical testability of scientific hypotheses and the intuitive self-evidence of mathematical theorems. (shrink)

This book is a welcome contribution to the literature on Kant's philosophy of mathematics in two particular respects. First, the author systematically traces the development of Kant's thought on mathematics from the very early pre-Critical writings through to the Critical philosophy. Secondly, it puts forward a challenge to contemporary Anglo-Saxon commentators on Kant's philosophy of mathematics which merits consideration.A central theme of the book is that an adequate understanding of Kant's pronouncements on mathematics must begin with the recognition that mathematics (...) in Kant's time was poised at the beginning of what Pierobon calls the ‘algebraic revolution’ of the nineteenth century. For Kant, Euclidean geometry, with its heavy reliance on the geometric image, was the paradigm of certainty. The algebraic revolution of the nineteenth century replaced that paradigm with an algebraic formalism, thereby freeing mathematics from any connection to the geometric image, and also severing the link to intuition. Pierobon describes this as the ‘divergence between the image and writing [l'écriture]’. So great was the shift, Pierobon suggests, that, after the developments of the nineteenth century, it became difficult to find any sense in Kant's conception of mathematics as sensible knowledge. This, certainly, was the view of Russell, who notoriously claimed in Mysticism and Logic that modern developments in logic dealt a ‘fatal blow to the Kantian philosophy’ and that ‘the whole doctrine of a priori intuitions, by which Kant explained the possibility of pure mathematics, is wholly inapplicable to mathematics in its present form’.1 Pierobon claims, though, that much of Anglo-Saxon commentary on Kant's philosophy of mathematics begins from this ‘rationalist and logicist’ position, reading Kant's philosophy of mathematics from a post-algebraic-revolution perspective. This book attempts to offer a corrective to that position by offering a Kantian conception of mathematics …. (shrink)

Play is a vital component of the social life and well-being of both children and adults. This book examines the concept of play and considers a variety of the related philosophical issues. It also includes meta-analyses from a range of philosophers and theorists, as well as an exploration of some key applied ethical considerations. The main objective of The Philosophy of Play is to provide a richer understanding of the concept and nature of play and its relation to human life (...) and values, and to build disciplinary and paradigmatic bridges between scholars of philosophy and scholars of play. Including specific chapters dedicated to children and play, and exploring the work of key thinkers such as Plato, Sartre, Wittgenstein, Gadamer, Deleuze and Nietzsche, this book is invaluable reading for any advanced student, researcher or practitioner with an interest in education, playwork, leisure studies, applied ethics or the philosophy of sport. (shrink)

How should we distinguish between ethical and unethical ways of pursuing profit in a market? The market failures approach (MFA) to business ethics purports to provide an answer to this question. I argue that it fails to do so. The source of this failure is the MFA’s reliance on Pareto efficiency as a core ethical principle. Many ethically “preferred” tactics for seeking profit cannot be justified by appeal to Pareto efficiency. One important reason for this is that Pareto efficiency, as (...) understood by the theory of welfare economics upon which the MFA relies, assumes a static conception of efficiency. This is a problem because many ethically “preferred” tactics can only be justified by appeal to dynamic efficiency considerations. I argue that, instead of Pareto efficiency, we should look to the value of wealth creation to understand the ethical constraints on how market actors may pursue profit. (shrink)

The role and value of science within sport increases with ever greater professionalization and commercialization. Scientific and technological innovations are devised to increase performance, ensure greater accuracy of measurement and officiating, reduce risks of harm, enhance spectatorship and raise revenues. However, such innovations inevitably come up against epistemological and metaphysical problems related to the nature of sport and physical competition. This special issue identifies and explores key and contemporary philosophical issues in relation to the science of sport and exercise. The (...) opening four chapters focus on the nature of scientific evidence, and causation in sport; the middle four chapters on the influence of science and technology and its relationship to sport officiating; whilst the final three chapters consider the way in which science affects the construction of sport. It brings together scholars working on philosophical problems in sport to examine issues related to the values and assumptions behind sport and exercise science, key problems that result, and provide recommendations for improving its practice. (shrink)

On the Horizon of World Literature compares literary texts from asynchronous periods of incipient literary modernity in different parts of the world: Romantic England and Republican China. These moments were oriented alike by "world literature" as a discursive framework of classifications that connected and re-organized local articulations of literary histories and literary modernities. World literature thus provided-and continues to provide-a condition of possibility for conversation between cultures as well as for their mutual provincialization. The book offers readings of a selection (...) of literary forms that serve also as textual sites for the enactment of new socio-political forms of life. The literary manifesto, the tale collection, the familiar essay, and the domestic novel function as testing grounds for questions of both literary-aesthetic and socio-political importance: What does it mean to attain a voice? What is a common reader? How does one dwell in the ordinary? What is a woman? In different languages and activating heterogeneous literary and philosophical traditions, works by Percy Bysshe Shelley, Lu Xun, Charles and Mary Lamb, Lin Shu, Zhou Zuoren, Jane Austen, and Eileen Chang explore the far-from-settled problem of what it means to be modern in different lifeworlds. Sun's book brings to light the disciplinary-historical impact world literature has had in shaping literary traditions and practices around the world. The book renews the practice of close reading by offering the model of a deprovincialized close reading loosened from confinement within monocultural hermeneutic circles. By means of its own focus on England and China, the book provides methods useful for comparatists working between other Western and non-Western languages. It establishes the critical significance of Romanticism for the discipline of literary studies and opens up new paths of research in global Romanticism and global nineteenth-century studies. And it offers a new approach to analyzing the cosmopolitan character of the literary and cultural transformations of early twentieth-century China. (shrink)

Many business ethicists assume that if a type of conduct is illegal, then it is also unethical. This article scrutinizes that assumption, using the rideshare company Uber’s illegal operation in the city of Philadelphia as a case study. I argue that Uber’s unlawful conduct was permissible. I also argue that this position is not an extreme one: it is consistent with a variety of theoretical commitments in the analytic philosophical tradition regarding political obligation. I conclude by showing why business ethicists (...) would have a better rejoinder to the “dominant view” of business ethics associated with Milton Friedman if they dispensed with the assumption that illegal implies unethical. (shrink)

Interpreters are less univocal than one might think in assessing Søren Kierkegaard's attitude toward eudaimonism. Through an analysis of several key texts from across Kierkegaard's authorship, I argue that existing interpretations do not convincingly address the relationship between Kierkegaard's critique of eudaimonism and his mid-nineteenth-century context, which was dominated by post-Kantian idealists. While I am sympathetic to aspects of deontological and aretaic interpretations, a contextual reading shows that his critique centers on what he diagnoses as the enclosure of the modern (...) self. This puts his critique of eudaimonism in the purview of his moral psychology and in continuity with his critique of romanticism. (shrink)

Thomas Carson offers the most comprehensive and up-to-date investigation of moral and conceptual questions about lying and deception. Part I addresses conceptual questions and offers definitions of lying, deception, and related concepts such as withholding information, "keeping someone in the dark," and "half truths." Part II deals with questions in ethical theory. Carson argues that standard debates about lying and deception between act-utilitarians and their critics are inconclusive because they rest on appeals to disputed moral intuitions. He defends (...) a version of the golden rule and a theory of moral reasoning. His theory implies that there is a moral presumption against lying and deception that causes harm — a presumption at least as strong as that endorsed by act-utilitarianism. He uses this theory to justify his claims about the issues he addresses in Part III: deception and withholding information in sales, deception in advertising, bluffing in negotiations, the duties of professionals to inform clients, lying and deception by leaders as a pretext for fighting wars, and lying and deception about history, and cases of distorting the historical record by telling half-truths. The book concludes with a qualified defence of the view that honesty is a virtue.Readership: Scholars and advanced students of philosophy, as well as historians and students of history. (shrink)

In this contribution we will approach language and images in different modalities: speech and face, anticipated and imagined movements, illusions on the sound by the image. It will be the opportunity for us to revisit the Gestalt concepts which were considered obsolete since structuralism in Humanities. As instantiated by Gilbert Durand in The Anthropological Structures of the Imaginary (1999, French 1st ed. 1960), we shall recall that Gestalt is not—even implicitly—an exclusively static approach to cognition. On the contrary we will (...) emphasize that forms can emerge from movements and stabilize in memory, thence morphology. And for speech, we will consider phonology as the stabilized outcome from audible and visible gestures of the mouth—caught in the time-course of a flow of some four in six syllables by second—via the perception of motor coordinations: which is necessary to master the most common expression of language between humans. We will adopt here also for the perceptual flows of spoken language, Multimodal Scene Analysis, the ongoing legacy of Gestalt Theory, including one of our main research topics: the gestural expression of the face and the hand for Deaf people, who practise as an augment French LPC (Langue française Parlée Complétée), adapted in 1967 from Cued Speech by its originator Dr Richard Cornett. (shrink)

This wise, stirring book argues that the search for meaning can immeasurably deepen our lives and is far more fulfilling than the pursuit of personal happiness. There is a myth in our culture that the search for meaning is some esoteric pursuit--that you have to travel to a distant monastery or page through dusty volumes to figure out life's great secret. The truth is, there are untapped sources of meaning all around us--right here, right now. Drawing on the latest research (...) in positive psychology; on insights from George Eliot, Viktor Frankl, Aristotle, the Buddha, and other great minds; and on interviews with seekers of meaning, Emily Esfahani Smith lays out the four pillars upon which meaning rests. Belonging: We all need to find our tribe and forge relationships in which we feel understood, recognized, and valued--to know we matter to others. Purpose: We all need a far-reaching goal that motivates us, serves as the organizing principle of our lives, and drives us to make a contribution to the world. Storytelling: We are all storytellers, taking our disparate experiences and assembling them into a coherent narrative that allows us to make sense of ourselves and the world. Transcendence: During a transcendent or mystical experience, we feel we have risen above the everyday world and are connected to something vast and meaningful. To bring those concepts to life, Smith visits a tight-knit fishing village on the Chesapeake Bay, stargazes in West Texas, attends a dinner where young people gather to share their experiences of untimely loss, and more. And she explores how we might begin to build a culture of meaning in our schools, our workplaces, and our communities. Inspiring and story-driven, The Power of Meaning will strike a profound chord in anyone seeking a richer, more satisfying life. (shrink)

Buying local is a prominent form of ethical consumption. We commonly assume that products that are local are in some respect ethically superior to ones that are not. This article contributes to research on local food by scrutinizing this assumption in light of some central values of the locavore movement. It identifies four central ethical causes from prior literature on locavorism: protecting the environment, promoting community, promoting small business, and contributing to the prosperity of one’s local economy. It then analyzes (...) whether the contribution of buying local to these causes can justify the general perception that buying local is a good way to be an ethical consumer. Its main finding is that these justifications fail to provide a strong positive ethical reason for consumers in general to adopt the practice of buying local. (shrink)

This article briefly considers current positions about whether the inclusion of the perspectives and interests of marginalised groups in the construction of knowledge is of epistemic value. It is then argued that applied social epistemology is the proper epistemic stance to take in evaluating this question. Theorists who have held that diversity makes an epistemic contribution are interpreted as attempting to reform social pathways to knowledge in ways that make true belief more likely. Thus, the demand for diversity challenges the (...) individualistic and a priori nature of traditional epistemology. This stance has consequences for education. It supports greater attention to helping students examine the testimonial bases for their beliefs. And it prepares students for their role as citizens in supporting policies that maintain credible inclusive institutions of public knowledge. (shrink)

Name der Zeitschrift: Kierkegaard Studies Yearbook Jahrgang: 19 Heft: 1 Seiten: 231-252.

This paper examines the use of case studies in ethics education. While not dismissing their value for specific purposes, the paper shows the limits of their use. While agreeing that case studies are narratives, although rather thin stories, the paper argues that the claim that case studies could represent reality is difficult to sustain. Instead, the paper suggests a way of using stories in ethics teaching that could be more real for students, while also giving them a way of thinking (...) about their own professional practices. The paper shows how the method can be used to develop a more critical and reflective practice for students in the health care professions. Some immediate problems with the method are discussed. (shrink)