William Burnside was one of the three most important algebraists who were involved in the transformation of group theory from its nineteenth-century origins to a deeper twentieth-century subject. Building on work of earlier mathematicians, they were able to develop sophisticated tools for solving difficult problems. His works are of enormous historical importance; they remain also a source of inspiration and information. The works of his contemporaries, such as Klein, Frobenius, Schur, have been published as also have the works of his (...) immediate successors such as Phillip Hall. All of Burnside's papers are reproduced here, organized chronologically and with a detailed bibliography. Walter Feit has contributed a foreword, and a collection of introductory essays are included to provide a commentary on Burnside's work and set it in perspective along with a modern biography that draws on archive material. This is the first reference volume of Burnside's collected papers, enhanced by a series of critical essays on his work, and is important for group theorists and historians and philosophers of mathematics and fills the gap in this area of literature. (shrink)

Name der Zeitschrift: Deutsche Zeitschrift für Philosophie Jahrgang: 65 Heft: 1 Seiten: 16-30.

Anstatt die Herkunft von Leibniz' Monadenkonzept in rezeptionsgeschichtlicher Perspektive nachweisen zu wollen, erklärt die vorliegende Studie die offensichtliche Präsenz und Virulenz des Monadenbegriffs im 17. und 18. Jahrhundert selbst zu ihrem Untersuchungsgegenstand.Sie rekonstruiert den frühneuzeitlichen Bildungskanon zum Pythagoreismus, in dem der Monadenbegriff tradiert worden ist, und analysiert vor diesem Hintergrund die monadologischen Philosophien von Gottfried Wilhelm Leibniz, Christian Wolff und Andreas Clavius. An reichem Quellenmaterial zeigt sie, wie die ahistorisch argumentierenden Monadologien von Leibniz und Wolff von deren Zeitgenossen rehistorisiert bzw. (...) "repythagoreisiert", in das Raster des Antike-Moderne-Verhältnisses verortet und auf diese Weise evaluiert worden sind.Ein die Studie beschließender Ausblick fasst die Ergebnisse zusammen und weist selektiv auf die Wege der Monaden in die Moderne hin. (shrink)

Am Beispiel des lutherischen Erbauungsschriftstellers Johann Arndt (1555-1621) läßt sich ein naturtheologisches Frömmigkeitsverständnis aufzeigen, das vom Florentiner Neuplatonismus, von Paracelsus, vom Paracelsismus und von der Alchemie Heinrich Khunraths beeinflußt ist. Der Autor vorliegender Studie zeichnet die relevanten Traditionslinien quellennah nach und analysiert deren Einbindung und Interpretation in Arndts Schriften. Eine systematische Darstellung der Kohärenz von Naturphilosophie und Mystik in der frühen Neuzeit beschließt vorliegende Studie.

Die vorliegende Studie empfiehlt, Leistungsansprüche für Personen mit interventionsfordernden Risiken anhand einer neuen Rechtskategorie, der ‚risikoadaptieren Prävention‘, abzubilden. Spätestens seit dem bioinformatischen Innovationsschub kann eine risikoadaptierte Anwendung von prophylaktischen Maßnahmen umfassend gewährleistet werden. Jedoch können die gegebenen Rechtskategorien das medizinische Anwendungsfeld nicht adäquat steuern. Die Autoren Friedhelm Meier, Anke Harney, Kerstin Rhiem, Anja Neumann, Silke Neusser, Matthias Braun, Jürgen Wasem, Rita Schmutzler, Stefan Huster und Peter Dabrock haben zusammen im BMBF geförderten Projekt SYSKON. Re-Konfiguration von Gesundheit und Krankheit. (...) Ethische, psychosoziale, rechtliche und gesundheitsökonomische Herausforderungen der Systemmedizin die vorliegende Governance Perspective erarbeitet. This book is published open access under a CC BY 4.0 license. (shrink)

Concerns a problem posed, but not solved, by Frege in part III of his Grundgesetze. As a preliminary to defining ‘real number’, Frege attempts to analyse the notion of a quantitative domain. He was unaware of the previous attempt of Otto Holder to do this; it is remarked how much weaker Frege's assumptions were in deriving theorems than Holder's. Frege deals with groups on which there is a right‐invariant semilinear ordering, although he does not use this terminology. He is uncertain (...) whether it can be deduced that the ordering is also left‐invariant, and proves as much as possible without invoking the assumption that it is. The independence proof, due to Dr Peter Neumann, establishes that it could not be deduced. (shrink)

Jacob Neumann provides a thoughtful reading of Paulo Freire in the 21st century: Education, dialogue, and transformation. His comments on the importance of contextualising Freire’s work and the value of openness in engaging Freirean ideas are insightful and helpful. His use of the term ‘apolitical’ is, however, rather more problematic. Drawing on points made in Paulo Freire in the 21st century, and with links to Freire’s wider philosophy and pedagogy, this article argues that education from a Freirean perspective is (...) always political. (shrink)

Paulo Freire’s work is often characterized and used in terms that seek to produce widespread political and economic changes across societies. Peter Roberts, however, in his book Paulo Freire in the twenty-first Century, offers readers a much different way of approaching Freire’s work. Throughout his book, Roberts presents Freire as recognizing the limitations of educational initiatives, as not seeking specific macro-political objectives, and as emphasizing openness to alternative discourses. These themes weave throughout each chapter of the book, in which (...) Roberts examines a wide range of topics, from Freire and Dostoevsky to reason and emotion to political correctness to Freire and the Tao Te Ching. In this review essay, I engage a number of purposes. I elucidate and trace these three themes as they weave throughout and support the various topics that Roberts examines in his book. I illustrate how Roberts’s treatment of these themes challenges many of the interpretations of Freire’s work found within the critical literature, and, through this critique, it offers readers new ways of thinking about Freire’s thinking. Lastly, I discuss how Roberts’s thoughts suggest new ways that Freire’s work, and critical education in general, might begin to make more meaningful and practical inroads into public education and might develop new avenues of scholarship on Freire’s work. (shrink)

In recent years there has been a robust but inconclusive debate over the existence and nature of indeterminacy in the world as described by quantum mechanics. I suggest that the inconclusive nature of the debate stems from starting from a metaphysical theory of indeterminacy. I propose instead framing the issue as a Carnapian explication project: start with the informal notion of indeterminacy used by physicists, and consider how best to make that concept precise. I defend a precisification based on von (...) Neumann’s interpretation of quantum states, and consider the nature of the indeterminacy that results. (shrink)

In lieu of an abstract, here is a brief excerpt of the content:Reviewed by:On Inception by Martin HeideggerDaniel NeumannHEIDEGGER, Martin. On Inception. Translated by Peter Hanley. Bloomington: Indiana University Press, 2023. xi + 171 pp. Cloth, $40.00This translation [End Page 548] of Heidegger's On Inception (written in 1941 and published in German in 2005 as Über den Anfang) is an important addition to the translated corpus of texts on the themes of Ereignis (event) and the history of beyng (Seynsgeschichte) (...) that occupied Heidegger's thinking from the mid-1930s to the mid-1940s, and that resulted in a series of writings that remained unpublished during his lifetime. Similar to those other volumes, On Inception does not follow a linear train of thought but offers short and often fragmentary notes and musings that, nonetheless, build on one another. There is a considerable thematic overlap with the other writings on the event. Many of the themes found here, such as the role of technology in exposing contemporary understanding of being, Hölderlin as the poet of the saying of beyng, or the notion of another beginning of the unconcealment of beyng, can be found in Contributions to Philosophy, Mindfulness, and The Event as well.What sets On Inception apart from these other volumes is the focus on the inceptual aspect of the thinking of beyng. In this regard, the first and longest of the six sections comprising the book (entitled "The Incipience of Inception") offers the most extended original contribution Heidegger makes here. It concerns the question of how one can think from out of the unconcealment of beyng. Exploring this topic throws more light on many of the questions that the reading of the other volumes raises, such as whether the event should be thought of as a one-time historical occurrence; how one can think from out of the event, that is, how it constitutes the possibility of thinking it; and the relationship between beings, being (referring to the truth of the presence of beings), and beyng (referring to the truth of the presencing of being). All of these issues concern the inceptual character of the event, whose understanding affords a better sense of paradigmatic change in thinking and dwelling associated with it. To understand the inceptual character of the event gives the reader a clue as to where to begin thinking (about) it. This does not remove the considerable and intentional obscurity surrounding these ideas, but it shows Heidegger as constantly altering and refining how to think of the history of the concealment and unconcealment of beyng. One of the biggest disagreements among interpreters has been whether to read this in transcendental or realist terms, that is, whether we should take the unconcealment of beyng as the proffering of a real, mind-independent totality or as a cipher for our transcendental ability to understand and make sense of the appearance of being. In this regard, the question of incipience goes toward elucidating who or what is thought to begin this unconcealment.What, then, does an inceptive thinking of beyng amount to? Put negatively, it can concern neither beyng as some sort of cause of beings, nor beings themselves as what appear as a consequence of beyng's unconcealment: "[I]nception is not the inception of something other than what it itself is; equally, inception is not the inception of itself, as if what were being thought of were a producing and causing." To think beyng as inception puts emphasis on the emergent nature of the opening of the clearing in which beings can come to presence for someone. That is, the [End Page 549] word "inception" names the very opening up of the possibility to consider the truth of beyng, that is, to think the event. What is at stake is therefore the incipient nature of inception—the fact that grasping what the term means cannot be based on any one incipient thing, but on incipience (Anfängnis). There is a processual (or, to use Daniela Vallega-Neu's more Heideggerian term, poietic) aspect to the way Heidegger thinks the event, and incipience in many ways expresses this poietic nature because it both suggests that there is something that begins and unfolds, but also conceals what... (shrink)

The aim of this paper is to formulate and study two weak axiom systems for the conceptual framework of constructive set theory . Arithmetical CST is just strong enough to represent the class of von Neumann natural numbers and its arithmetic so as to interpret Heyting Arithmetic. Rudimentary CST is a very weak subsystem that is just strong enough to represent a constructive version of Jensenʼs rudimentary set theoretic functions and their theory. The paper is a contribution to the (...) study of formal systems for CST that capture significant stages in the development of constructive mathematics in CST. (shrink)

This chapter is offered as a contribution to the logic of down below. We attempt to demonstrate that the nature of human agency necessitates that there actually be such a logic. The ensuing sections develop the suggestion that cognition down below has a structure strikingly similar to the physical structure of quantum states. In its general form, this is not an idea that originates with the present authors. It is known that there exist mathematical models from the cognitive science of (...) cognition down below that have certain formal similarities to quantum mechanics. We want to take this idea seriously. We will propose that the subspaces of von Neumann-Birkhoff lattices are too crisp for modelling requisite cognitive aspects in relation to subsymbolic logic. Instead, we adopt an approach which relies on projections into nonorthogonal density states. The projection operator is motivated from cues which probe human memory. (shrink)

In 1936, G. Birkhoff and J. v. Neumann published an article with the title The logic of quantum mechanics'. In this paper, the authors demonstrated that in quantum mechanics the most simple observables which correspond to yes-no propositions about a quantum physical system constitute an algebraic structure, the most important proper ties of which are given by an orthocomplemented and quasimodular lattice Lq. Furthermore, this lattice of quantum mechanical proposi tions has, from a formal point of view, many similarities (...) with a Boolean lattice L8 which is known to be the lattice of classical propositional logic. Therefore, one could conjecture that due to the algebraic structure of quantum mechanical observables a logical calculus Q of quantum mechanical propositions is established, which is slightly different from the calculus L of classical propositional logic but which is applicable to all quantum mechanical propositions. This calculus has sometimes been called 'quan tum logic'. However, the statement that propositions about quantum physical systems are governed by the laws of quantum logic, which differ from ordinary classical logic and which are based on the empirically well-established quantum theory, is exposed to two serious objec tions: Logic is a theory which deals with those relationships between various propositions that are valid independent of the content of the respective propositions. Thus, the validity of logical relationships is not restricted to a special type of proposition, e. g. to propositions about classical physical systems. (shrink)

Although it is well-recognized that Max Weber was of central importance to many of the emigre social scientists who fled Hitler, commentators have overlooked both Weber’s attempt to found a new dynamic political science that would test partisan commitments and the endeavors of emigre political scientists to develop this project. This article lays out this new Weberian political science and assesses the fate of the various attempts on the part of the emigres to translate it into their new setting. It (...) shows that Weber forged a notion of political science that combined an existential notion of politics as inexorable power struggle with a sociology of the business of politics that provided the setting in which that struggle was to take place. It also shows that the central purpose of this political science was to aid political partisans in clarifying the meaning of their political commitments by forcing them to view these commitments as they are shaped in the socio-political context that determines the struggle for power. I then show that Mannheim sought to radicalize this approach to political science by seeking to construct the political backdrop for the testing of political ideas out of a political field not out of parties, politicians, and state institutions but out of competing ideologies, each of which could be shown to have some insight into the dynamics of political conflict. For Mannheim we could now test political ideas against political reality by playing them off against each other. I call this project of testing political ideas against existential and sociological notions of the political field the Weber–Mannheim project. I then show how three emigre political scientists – Arnold Brecht, Hans Morgenthau, and Franz Neumann – sought to carry on the Weber–Mannheim project in their new setting. I argue that, of the three, Franz Neumann in his great work Behemoth, was most successful in staying true to that project. For he was able to find in his analysis of the Weimar Republic and the fascist regime a way of demonstrating the dynamics under which democracy and dictatorship fail or succeed while still maintaining openings for political will. Both Brecht and Morgenthau seem to have flattened the dynamic aspect of the Weberian and Mannheimian notions of a prudential political science – though it was Morgenthau who had the most successful reception in political science. (shrink)

Just as Bell proposed that we excise the word “measurement” from physics, so I propose that we should excise the word “experience”: “experience” and its cognates should not appear in the formulation of any physical theory, including quantum mechanics and its various interpretations. The reasons are more or less the same as Bell gives for “measurement”: “experience” is a vague term, and experiencing systems are made out of atoms obeying quantum mechanics. Bell’s exhortation concerning “measurement” has largely been taken on (...) board in the foundations of quantum mechanics. But appeals to “experience” remain—in part, I will argue, because of a bad argument that can be traced back to von Neumann, and in part because of mistaken impressions about the fundamentality of experience. (shrink)

Most models of risky decision making assume that all relevant information is taken into account (e.g., Kahneman & Tversky, 1979; von Neumann & Morgenstern, 1944). However, there are also some models supposing that only part of the information is considered (e.g., Brandstätter, Gigerenzer, & Hertwig, 2006; Gigerenzer & Gaissmaier, 2011). To further investigate the amount of information that is usually used for decision making, and how the use depends on feedback, we conducted a series of three experiments in which (...) participants choose between two lotteries and where no feedback, outcome feedback, and error feedback was provided, respectively. The result show that without feedback participants mostly chose the lottery with the higher winning probability, and largely ignored the potential gains. The same result occurred when the outcome of each decision was fed back. Only after presenting error feedback (i.e., signaling whether a choice was optimal or not), participants considered probabilities as well as gains, resulting in more optimal choices. We propose that outcome feedback was ineffective, because of its probabilistic and ambiguous nature. Participants improve information integration only if provided with a consistent and deterministic signal such as error feedback. (shrink)

Usually, quantum mechanics is considered as the prototype of a probabilistic theory. In contrast to statistical mechanics, dice throwing, and roulette game, quantum mechanical probability statements cannot be reduced to causally determined individual events, whose explicit calculation is, however, too complicated for all practical purposes. Even hypothetically, one must not assume that quantum mechanical events were determined in principle and merely computationally intractable, since that assumption would lead to probabilistic predictions which contradict quantum mechanics. Hence, the title of this article (...) seems somewhat surprising at first glance, and in particular it seems difficult to connect a probability free quantum mechanics with the work of John von Neumann. (shrink)

In single-person decision theory, Bayesian rationality requires the agent first to attach subjective probabilities to each uncertain event, and then to maximize the expected value of a von Neumann—Morgenstern utility function that is unique up to a cardinal equivalence class. When the agent receives new information, it also requires subjective probabilities to be revised according to Bayes’ rule.

Nash is famous for many inventions, but it is less known that he, simultaneously with Marschak, also was the first to axiomatize expected utility for risk. In particular, these authors were the first to state the independence condition, a condition that should have been but was not stated by von Neumann and Morgenstern. Marschak’s paper resulted from interactions with several people at the Cowles Commission. We document unique letters and personal communications with Nash, Samuelson, Arrow, Dalkey, and others, making (...) plausible that Nash made his discovery independently from the others. (shrink)

Berkeley’s likeness principle is the claim that “an idea can be like nothing but an idea”. The likeness principle is intended to undermine representationalism: the view (that Berkeley attributes to thinkers like Descartes and Locke) that all human knowledge is mediated by ideas in the mind which represent material objects. Yet, Berkeley appears to leave the likeness principle unargued for. This has led to several attempts to explain why Berkeley accepts it. In contrast to ‘metaphysical’ and ‘epistemological’ interpretations available in (...) the literature, in this paper I defend a ‘conceptual’ interpretation. I argue that Berkeley accepts the likeness principle on the basis of (i) his commitment to the transparency of ideas, and (ii) his account of resemblance which he sets out in his works on vision. Thus, I provide an explanation for Berkeley’s reasons for accepting the likeness principle which, appropriately, focuses on his views concerning ideas and likeness. (shrink)

This is the classic work upon which modern-day game theory is based. What began as a modest proposal that a mathematician and an economist write a short paper together blossomed, when Princeton University Press published Theory of Games and Economic Behavior. In it, John von Neumann and Oskar Morgenstern conceived a groundbreaking mathematical theory of economic and social organization, based on a theory of games of strategy. Not only would this revolutionize economics, but the entirely new field of scientific (...) inquiry it yielded--game theory--has since been widely used to analyze a host of real-world phenomena from arms races to optimal policy choices of presidential candidates, from vaccination policy to major league baseball salary negotiations. And it is today established throughout both the social sciences and a wide range of other sciences. (shrink)

In this important new book in the IPPP series, a group of leading thinkers in psychiatry, psychology, and philosophy offer alternative perspectives that address both the scientific and clinical aspects of psychiatric validation, emphasizing throughout their philosophical and historical considerations.

Margaret Macdonald was at the institutional heart of analytic philosophy in Britain in the mid-twentieth century. Yet, her views on the nature of philosophical theories diverge quite considerably from those of many of her contemporaries. In this paper, I focus on her 1953 article ‘Linguistic Philosophy and Perception’, a provocative paper in which Macdonald argues that the value of philosophical theories is more akin to that of poetry or art than science or mathematics. I do so for two reasons. First, (...) because it reveals just how far Macdonald’s meta- philosophical views diverged from those of many of her contemporaries. Second, because the discussion in LPP pre-empts recent literature on the nature of philosophical inquiry and the efficacy of philosophical arguments. Indeed, Macdonald’s paper is just as likely to provoke discussion today as it was in the 1950s. (shrink)

It is argued that causal understanding originates in experiences of acting on objects. Such experiences have consistent features that can be used as clues to causal identification and judgment. These are singular clues, meaning that they can be detected in single instances. A catalog of 14 singular clues is proposed. The clues function as heuristics for generating causal judgments under uncertainty and are a pervasive source of bias in causal judgment. More sophisticated clues such as mechanism clues and repeated interventions (...) are derived from the 14. Research on the use of empirical information and conditional probabilities to identify causes has used scenarios in which several of the clues are present, and the use of empirical association information for causal judgment depends on the presence of singular clues. It is the singular clues and their origin that are basic to causal understanding, not multiple instance clues such as empirical association, contingency, and conditional probabilities. (shrink)

This book represents the views of one of the greatest mathematicians of the twentieth century on the analogies between computing machines and the living human brain.

This paper provides a philosophical evaluation of the concept of handedness prevalent but largely unspoken in the scientific literature. This literature defines handedness as the preference or ability to use one hand rather than the other across a range of common activities. Using the philosophical discipline of phenomenology, I articulate and critique this conceptualization of handedness. Phenomenology shows defining a concept of handedness by focusing on hand use leads to a right hand biased concept. I argue further that a phenomenological (...) model based in spatial orientation rather than hand use provides a more inclusive concept of handedness. (shrink)