This volume contains thirteen papers that were presented at the 2017 Annual Meeting of the Canadian Society for History and Philosophy of Mathematics/Société canadienne d’histoire et de philosophie des mathématiques, which was held at Ryerson University in Toronto. It showcases rigorously reviewed modern scholarship on an interesting variety of topics in the history and philosophy of mathematics from Ancient Greece to the twentieth century. -/- A series of chapters all set in the eighteenth century consider topics such as John Marsh’s (...) techniques for the computation of decimal fractions, Euler’s efforts to compute the surface area of scalene cones, a little-known work by John Playfair on the practical aspects of mathematics, and Monge’s use of descriptive geometry. -/- After a brief stop in the nineteenth century to consider the culture of research mathematics in 1860s Prussia, the book moves into the twentieth century with an examination of the historical context within which the Axiom of Choice was developed and a paper discussing Anatoly Vlasov’s adaptation of the Boltzmann equation to ionized gases. The remaining chapters deal with the philosophy of twentieth-century mathematics through topics such as an historically informed discussion of finitism and its limits; a reexamination of Mary Leng’s defenses of mathematical fictionalism through an alternative, anti-realist approach to mathematics; and a look at the reasons that mathematicians select specific problems to pursue. -/- Written by leading scholars in the field, these papers are accessible to not only mathematicians and students of the history and philosophy of mathematics, but also anyone with a general interest in mathematics. (shrink)

The concept of the self in Western psychology derives primarily from the work of Freud, Jung, and Rogers. To some extent Western formulations of the self evidence a homunculus-like quality lacking in some Eastern conceptions, especially those derived from the Vijnanavada and Zen Buddhist traditions. The Buddhist notion of self circumvents reification, being an impermanent gestalt formed by the interaction of five skandhas or aggregates . Each skandha is in turn a transient pattern formed by the interaction of the other (...) four. The fifth skandha includes eight consciousnesses, one of which results in the experience of the ego or self as homunculus, which Buddhist psychology rejects as delusion. Implications for psychotherapy and everyday life are discussed. 2012 APA, all rights reserved). (shrink)

The related fields of fractal image encoding and fractal image analysis have blossomed in recent years. This book, originating from a NATO Advanced Study Institute held in 1995, presents work by leading researchers. It is developing the subjects at an introductory level, but it also has some recent and exciting results in both fields. The book contains a thorough discussion of fractal image compression and decompression, including both continuous and discrete formulations, vector space and hierarchical methods, and algorithmic optimizations. The (...) book also discusses multifractal approaches to image analysis, segmentation, and recognition, including medical applications. (shrink)

Places the development of Anaximander's thought within social, political, cosmological, astronomical, and technological contexts.

This dissertation is about the nature of perspectival thoughts and the context-sensitivity of the language used to express them. It focuses on two kinds of perspectival thoughts: ‘subjective’ evaluative thoughts about matters of personal taste, such as 'Beetroot is delicious' or 'Skydiving is fun', and first-personal or de se thoughts about oneself, such as 'I am hungry' or 'I have been fooled.' The dissertation defends of a novel form of relativism about truth - the idea that the truth of some (...) perspectival thought and talk is relative to the perspective of an evaluating subject or group. In Part I, I argue that the realm of ‘subjective’ evaluative thought and talk whose truth is perspective-relative includes attributions of knowledge of the form ’S knows that p.’ Following a brief introduction, chapter 2 presents a new, error-theoretic objection against relativism about knowledge attributions. The case for relativism regarding knowledge attributions rests on the claim that relativism is the only view that explains all of the empirical data from speakers' use of the word "know" without recourse to an error theory. In chapter 2, I show that the relativist can only account for sceptical paradoxes and ordinary epistemic closure puzzles if she attributes a problematic form of semantic blindness to speakers. However, in 3 I show that all major competitor theories - forms of invariantism and contextualism - are subject to equally serious error-theoretic objections. This raises the following fundamental question for empirical theorising about the meaning of natural language expressions: If error attributions are ubiquitous, by which criteria do we evaluate and compare the force of error-theoretic objections and the plausibility of error attributions? I provide a number of criteria and argue that they give us reason to think that relativism's error attributions are more plausible than those of its competitors. In Part II, I develop a novel unified account of the content and communication of perspectival thoughts. Many relativists regarding ‘subjective’ thoughts and Lewisians about de se thoughts endorse a view of belief as self-location. In chapter 4, I argue that the self-location view of belief is in conflict with the received picture of linguistic communication, which understands communication as the transmission of information from speaker's head to hearer's head. I argue that understanding mental content and speech act content in terms of sequenced worlds allows a reconciliation of these views. On the view I advocate, content is modelled as a set of sequenced worlds - possible worlds ‘centred’ on a group of individuals inhabiting the world at some time. Intuitively, a sequenced world is a way a group of people may be. I develop a Stalnakerian model of communication based on sequenced worlds content, and I provide a suitable semantics for personal pronouns and predicates of personal taste. In chapter 5, I show that one of the advantages of this model is its compatibility with both nonindexical contextualism and truth relativism about taste. I argue in chapters 5 and 6 that the empirical data from eavesdropping, retraction, and disagreement cases supports a relativist completion of the model, and I show in detail how to account for these phenomena on the sequenced worlds view. (shrink)

Our epistemic access to mathematical objects, like numbers, is mediated through our external representations of them, like numerals. Nevertheless, the role of formal notations and, in particular, of the internal structure of these notations has not received much attention in philosophy of mathematics and cognitive science. While systems of number words and of numerals are often treated alike, I argue that they have crucial structural differences, and that one has to understand how the external representation works in order to form (...) an advanced conception of numbers. The relation between external representations and mathematical cognition will be discussed by drawing on experimental results from cognitive science and mathematics education, and I argue for the constitutive role of external representations for the development of an advanced conception of numbers. (shrink)

Dirk Paul Bogner widmet sich der Frage, welche Relevanz Kurt Lewins Feldtheorie im Bereich der pädagogischen Diagnostik haben könnte. Er untermauert die These, dass die Lewin’sche Feldtheorie eine völlig neue Sicht auf Lern-, Entwicklungs- und Erziehungsprozesse eröffnen würde, und legt dar, inwiefern die Einbeziehung der Dimension des Raumes die Analyse dieser erziehungswissenschaftlich relevanten Topoi verfeinern könnte. Er erörtert mittels hermeneutischer Textauslegung und vergleichender Dokumentenanalyse, warum Lewin keine erziehungswissenschaftliche Resonanz erzeugen konnte, obwohl in der Erziehungswissenschaft auch heute noch intensiv Begriffe, (...) die entweder direkt aus der Feldtheorie stammen oder aber von dieser konsequent definiert wurden, verwendet werden. (shrink)

There has recently been a wave of attempts to make sense of the role of de se thoughts in linguistic communication. A majority of the attempts assume a Perryan or a Lewisian view of de se thought. Views with these assumptions, I suggest, come in four varieties: uncentering (Egan 2007, Kölbel 2013, Moss 2012), recentering (Heim 2004, Weber 2012), multicentering (Kindermann 2014, Ninan 2010, Torre 2009), and no centering (Kaplan 1989, Perry 1979). I argue first that all four varieties of (...) centering are committed to what I call a shifting operation on the hearer's part. I argue second that, against common assumption, there is no real choice to make between the views. By showing that attempts to establish an advantage for some view over the others fail across the board, I make the case for neutralism regarding the varieties of centering – the claim that coverage of the empirical data is exactly the same for each view, and that the views are broadly equal in simplicity and elegance. (shrink)

In the study of human thought there could hardly be a more fundamental con cern than language and reasoning. In the tradition of Western philosophy, humans are distinguished by their ability to speak and to think rationally. And language is often considered a prerequisite for rational thought. If psycholoQists, then, are ever to discover what is truly human about their species, they will have to discover how language is produced and understood, and how it plays a role in reasoning and (...) other forms of rational thought. Within psychology there has been an imperative to study language and rea soning together. Since Wundt, psychologists have succeeded in building a the oretical foundation for both language and reasoning. What has become clear from these beginnings is that the two are inextricably bound to each other. Like the two players ina chess game, take away one of them and the game no longer exists. On the one hand, producing and understanding speech re quires an intricate process of reasoning. Speakers must rationally choose sentences that will affect their listeners in ways they intend, and listen ers must infer what speakers could conceivably have meant in selecting the sentences they did. Reasoning, inference, and rational thought lie at the very center of speaking and listening. On the other hand, logical reasoning begins with, and is influenced by, the language in which a problem is stated. (shrink)

We show that the Bohmian approach in terms of persisting particles that move on continuous trajectories following a deterministic law can be literally applied to QFT. By means of the Dirac sea model – exemplified in the electron sector of the standard model neglecting radiation – we explain how starting from persisting particles, one is led to standard QFT employing creation and annihilation operators when tracking the dynamics with respect to a reference state, the so-called vacuum. Since on the level (...) of wave functions, both formalisms are mathematically equivalent, this proposal provides for an ontology of QFT that includes a dynamics of individual processes, solves the measurement problem and explains the appearance of creation and annihilation events. (shrink)

In Miletus, about 550 B.C., together with our world-picture cosmology was born. This book tells the story. In Part One the reader is introduced in the archaic world-picture of a flat earth with the cupola of the celestial vault onto which the celestial bodies are attached. One of the subjects treated in that context is the riddle of the tilted celestial axis. This part also contains an extensive chapter on archaic astronomical instruments. Part Two shows how Anaximander (610-547 B.C.) blew (...) up this archaic world-picture and replaced it by a new one that is essentially still ours. He taught that the celestial bodies orbit at different distances and that the earth floats unsupported in space. This makes him the founding father of cosmology. Part Three discusses topics that completed the new picture described by Anaximander. Special attention is paid to the confrontation between Anaxagoras and Aristotle on the question whether the earth is flat or spherical, and on the battle between Aristotle and Heraclides Ponticus on the question whether the universe is finite or infinite. (shrink)

Jonathan Wolff is Professor of Philosophy at University College London. He is the author of Robert Nozick (1991), An Introduction to Political Philosophy (1996) and Why Read Marx Today (2002). He is currently working on a number of topics at the intersection of political philosophy and public policy.

After a crisis, broad and sweeping reforms are enacted to restore trust. Following the 2007-2008 Great Financial Crisis, the European Union has engaged in an ambitious overhaul of banking regulation. One of its centerpieces, the 2013 Fourth Capital Requirements Directive, tackles, amongst other things, the perceived pre-crisis failings in the governance of banks. We focus on the provisions that are aimed at reshaping bank boards’ composition, functioning, and their members’ liabilities, and argue that they are unlikely to improve bank boards’ (...) effectiveness or prevent excessive risk-taking. We criticize some of them for mandating solutions, like board diversity and the separation of chairman and CEO, that may be good for some banks but are bad for others, in the absence of any convincing argument that their overall effect is positive. We also criticize enhanced board liability by showing that it may increase the risk of herd behavior and lead to more serious harm in the event of managerial mistakes. We also highlight that the push towards unfriendly boards will negatively affect board dynamics and make boards as dysfunctional as when the CEO dominates them. We further argue that limits on directorships and diversity requirements will worsen the shortage of bank directors, while requirements for induction and training and board evaluation exercises will more likely lead to tick-the-box exercises than under the current situation in which they are just best practices. We conclude that European policymakers and supervisors should avoid using a heavy hand, respectively, when issuing rules implementing CRD IV provisions with regard to bank boards and when enforcing them. (shrink)

In recent years, neuroscience has been a particularly prolific discipline stimulating many innovative treatment approaches in medicine. However, when it comes to the brain, new techniques of intervention do not always meet with a positive public response, in spite of promising therapeutic benefits. The reason for this caution clearly is the brain’s special importance as “organ of the mind”. As such it is widely held to be the origin of mankind’s unique position among living beings. Likewise, on the level of (...) the individual human being, the brain is considered the material substrate of those traits that in combination render each person unique. In view of this preeminent significance of the brain, it is understandable that, in general, interventions into the brain are considered a delicate issue and that new techniques of intervention are scrutinised with particular care. However, in doing so it is important not to go to the opposite extreme and shy away from promising new therapeutic approaches for debilitating disorders of the brain. With respect to the new techniques of brain intervention a broad interdisciplinary perspective is required to discern irrational fear from justified concern. Hence, the Europäische Akademie established a project group consisting, on the one hand, of experts from different fields of medicine who have got first-hand experience of applying the techniques at issue and, on the other hand, of philosophers and a legal expert. The task of this team was to review the state of the art with respect to each single technique of intervening in the brain, to indicate future developments, and to address the ethical and legal issues common to all of them. The project’s outcome is the book at hand. (shrink)

Dieses Buch hat sich die Aufgabe gestellt, den Beitrag der allgemeinen Wissenschaftstheorie der Naturwissenschaften zur Forschungsmethodik des naturwissenschaftlich arbeitenden Zweiges der Psychologie zu erbringen. Im Anschluss an die Ausarbeitung der Programmatik einer Protopsychologie – der Wissenschaftstheorie der Psychologie – werden traditionelle wissenschaftstheoretische Probleme erörtert, welche für die naturwissenschaftliche Psychologie – aber auch für andere Naturwissenschaften – von Relevanz sind. Die Themenpalette reicht hierbei von der Frage nach den wesentlichen Merkmalen von Naturgesetzen bis hin zur Planung, Durchführung und Evaluation von Experimenten. (...) Spezifische Probleme der Psychologie – etwa die Frage nach der methodischen Rolle der Instruktion im psychologischen Experiment – werden dabei jeweils besonders berücksichtigt. (shrink)

To this day, there persists a widespread assumption that Adorno's references to Marx - and especially to Marx's critique of political economy - represent a relic from an early and short-lived stage of Adorno's theoretical development. On the basis of relevant and largely unpublished textual sources, this book refutes this thesis while showing that the centre of Adorno's critical theory of society is occupied by a critique not only of political economy, but of economy in general.

Volume II deals with philosophy of mathematics and general philosophy of science. In discussing theoretical entities, the notion of antirealism formulated in Volume I is further elaborated: Contrary to what is usually attributed to antirealism or idealism, the author does not claim that theoretical entities do not really exist, but rather that their existence is not independent of the possibility to know about them.

Drawing on letters, orations and disputations, this book argues that during the seventeenth century, the Amsterdam Athenaeum, despite the revolutionary debates of the time, and despite the intellectual liberalism characteristic of Amsterdam, remained traditional in its teaching.