Section I of Kant's Groundwork of the Metaphysics of Morals is meant to lead us from our everyday conception of morality to the supreme principle of all moral action, officially christened the ‘categorical imperative’ some twenty Academy pages further into the treatise. It is quite striking that in this first section Kant dispenses with the notorious technical language that pervades not just other parts of the Groundwork but also most of the remaining philosophical writings of the critical period. The mere (...) fact that Groundwork I is comparatively accessible does not, of course, make it straightforward or uncontroversial. Kant's readers are faced with, amongst other things, four unconvincing paragraphs on the natural purpose of practical reason (G IV 394–6), a crucial change of topic from good volition to acting from duty (G IV 397), an unstated ‘first proposition’ about moral value that has baffled generations of interpreters (presumably G IV 397–9), and a contentious shift from an allegedly unproblematic principle of practical universalizability to a substantive moral command (G IV 402). (shrink)

Packed with real-life examples of business decisions gone awry, the 8th Edition of BUSINESS ETHICS: CASE STUDIES AND SELECTED READINGS explores the complex issues of business ethics from the leaders' perspectives. This best-selling text offers a rare collection of readings which examines the business decision-making processes of many types of leaders, while revealing some of the common factors that push them over ethical lines they might not otherwise cross. A combination of short and long cases, readings, hypothetical situations, and current (...) ethical dilemmas, BUSINESS ETHICS: CASE STUDIES AND SELECTED READINGS provides a stimulating and thorough basis for evaluating business ethics, and encourages stronger values in future business leaders. Important Notice: Media content referenced within the product description or the product text may not be available in the ebook version. (shrink)

One of the most important challenges for the occupation of Iraq has been making decisions about the status of people who were either responsible for or who passively benefited from the regime’s past injustices.

Steffek advocates a return to a conception of public accountability as accountability to the wider public. He investigates the prospects for this beyond the state, which depends on the emergence of a transnational public sphere, consisting of media and organized civil society.

National Artificial Intelligence (AI) strategies articulate imaginaries of the integration of AI into society and envision the governing of AI research, development and applications accordingly. To integrate these central aspects of national AI strategies under one coherent perspective, this paper presented an analysis of Germany’s strategy ‘AI made in Germany’ through the conceptual lens of ordoliberal political rationality. The first part of the paper analyses how the guiding vision of a human-centric AI not only adheres to ethical and legal principles (...) consistent with Germany’s liberal democratic constitutional system but also addresses the risks and promises inherent to the ordoliberal problematization of freedom. Second, it is scrutinized how the strategy cultivates the fear of not achieving technological sovereignty in the AI sector. Thereby, it frames the global AI race as a race of competing (national) approaches to governing AI and articulates an ordoliberal approach to governing AI (the ‘third way’), according to which government has to operate between the twin dangers of governing too much and not governing enough. Third, the paper analyses how this ordoliberal proportionality of governing structures Germany’s Science Technology & Innovation Policy. It is shown that the corresponding risk-based approach of regulating AI constitutes a security apparatus as it produces an assessment of fears: weighting the fear of the failure to innovate with the fear of the ramifications of innovation. Finally, two lines of critical engagement based on this analysis are conducted. (shrink)

We argue that stereotypes associated with concepts like he-said–she-said, conspiracy theory, sexual harassment, and those expressed by paradigmatic slurs provide “normative inference tickets”: conceptual permissions to automatic, largely unreflective normative conclusions. These “mental shortcuts” are underwritten by associated stereotypes. Because stereotypes admit of exceptions, normative inference tickets are highly flexible and productive, but also liable to create serious epistemic and moral harms. Epistemically, many are unreliable, yielding false beliefs which resist counterexample; morally, many perpetuate bigotry and oppression. Still, some normative (...) inference tickets, like some activated by sexual harassment, constitute genuine moral and hermeneutical advances. For example, our framework helps explain Miranda Fricker’s notion of “hermeneutical lacunae”: what early victims of “sexual harassment” — as well as their harassers — lacked before the term was coined was a communal normative inference ticket — one that could take us, collectively, from “this is happening” to “this is wrong.”. (shrink)

Advanced AI systems are rapidly making their way into medical research and practice, and, arguably, it is only a matter of time before they will surpass human practitioners in terms of accuracy, reliability, and knowledge. If this is true, practitioners will have a prima facie epistemic and professional obligation to align their medical verdicts with those of advanced AI systems. However, in light of their complexity, these AI systems will often function as black boxes: the details of their contents, calculations, (...) and procedures cannot be meaningfully understood by human practitioners. When AI systems reach this level of complexity, we can also speak of black-box medicine. In this paper, we want to argue that black-box medicine conflicts with core ideals of patient-centered medicine. In particular, we claim, black-box medicine is not conducive for supporting informed decision-making based on shared information, shared deliberation, and shared mind between practitioner and patient. (shrink)

The Parmenides poses the question for what entities there are Forms, and the criticism of Forms it contains is commonly supposed to document an ontological reorientation in Plato. According to this reading, Forms no longer express the excellence of a given entity and a Socratic, ethical perspective on life, but come to resemble concepts, or what concepts designate, and are meant to explain nature as a whole. Plato’s conception of dialectic, it is further suggested, consequently changes into a value-neutral method (...) directed at tracing the interrelation of such Forms, an outlook supposedly documented in certain passages on method from the Sophist and the Statesman as well. -/- The article urges that this reading is untenable. For in the Parmenides the question for what entities one should posit Forms is left open, and the passages on method from the Sophist and Statesman neither encourage a non-normative ontology nor a value-neutral method of inquiry. What the three dialogues encourage us to do is rather to set common opinions about the relative worth and value of things aside when conducting ontological inquiries; and this attitude, the article concludes, demonstrates a close kinship, rather than a significant difference, between Plato’s Socrates and his Eleatic philosophers. (shrink)

This paper explores the possibility of moral conflict in Kant’s ethics. An analysis of the only explicit discussion of the topic in his published writings confirms that there is no room for genuine moral dilemmas. Conflict is limited to nonconclusive ‘grounds’ of obligation. They arise only in the sphere of ethical duty and, though defeasible, ought to be construed as the result of valid arguments an agent correctly judges to apply in the situation at hand. While it is difficult to (...) determine in theory what makes some of them stronger than others, these ‘grounds’ can account for practical residue in conflict cases and for a plausible form of agent regret. The principle that ‘ought implies can’ survives intact. (shrink)

What you believe about God actually changes your brain. Psychiatrist Tim Jennings unveils how our brains and bodies thrive when we have a healthy understanding of who God is. This expanded edition now includes a study guide to help you discover how neuroscience and Scripture come together to bring healing and transformation to our lives.

What is the relationship between the world and logic, between intuition and language, between objects and their quantitative determinations? Rationalists, on the one hand, hold that the world is structured in a rational way. Representationalists, on the other hand, assume that language, logic, and mathematics are only the means to order and describe the intuitively given world. In World and Logic, Jens Lemanski takes up three surprising arguments from Arthur Schopenhauer’s hitherto undiscovered Berlin Lectures, which concern the philosophy of (...) language, logic, and mathematics. Based on these arguments, Lemanski develops a new position entitled ‘rational representationalism’: the world is always structured by human beings according to linguistic, logical, and mathematical principles, but the basic vocabulary of these structural descriptions already contains metaphors taken from the world around us. (shrink)

This paper analyses a hitherto unknown technique of using logic diagrams to create argument maps in eristic dialectics. The method was invented in the 1810s and -20s by Arthur Schopenhauer, who is considered the originator of modern eristic. This technique of Schopenhauer could be interesting for several branches of research in the field of argumentation: Firstly, for the field of argument mapping, since here a hitherto unknown diagrammatic technique is shown in order to visualise possible situations of arguments in a (...) dialogical controversy. Secondly, the art of controversy or eristic, since the diagrams do not analyse the truth of judgements and the validity of inferences, but the persuasiveness of arguments in a dialogue. (shrink)

Possible-worlds accounts of mental or linguistic content are often criticized for being too coarse-grained. To make room for more fine-grained distinctions among contents, several authors have recently proposed extending the space of possible worlds by "impossible worlds". We argue that this strategy comes with serious costs: we would effectively have to abandon most of the features that make the possible-worlds framework attractive. More generally, we argue that while there are intuitive and theoretical considerations against overly coarse-grained notions of content, the (...) same kinds of considerations also prohibit an overly fine-grained individuation of content. An adequate notion of content, it seems, should have intermediate granularity. However, it is hard to construe a notion of content that meets these demands. Any notion of content, we suggest, must be either implausibly coarse-grained or implausibly fine-grained (or both). (shrink)

Is Kant’s ethical theory too demanding? Do its commands ask too much of us, either by calling for self-sacrifice on particular occasions, or by pervading our lives to the extent that there is no room for permissible action? In this article, I argue that Kant’s ethics is very demanding, but not excessively so. The notion of ‘latitude’ does not help. But we need to bear in mind that moral laws are self-imposed and cannot be externally enforced; that ‘right action’ is (...) not a category of Kantian ethics – there is a more and a less, and lack of perfection does not entail vice; and that only practice makes perfect, i.e. how much virtue can realistically be expected can vary from agent to agent. The principle that ‘ought’ is limited by ‘can’ is firmly entrenched in Kant’s ethical thought. (shrink)

Slurs have been standardly assumed to bear a very direct, very distinctive semantic relationship to what philosophers have called “neutral counterpart” terms. I argue that this is mistaken: the general relationship between paradigmatic slurs and their “neutral counterparts” should be assumed to be the same one that obtains between ‘chick flick’ and ‘romantic comedy’, as well a huge number of other more prosaic pairs of derogatory and “less derogatory” expressions. The most plausible general relationship between these latter expressions — and (...) thus, I argue, between paradigmatic slurs and “neutral counterpart” terms — is one of overlap in presumed extension, grounded in overlap in associated stereotypes. The resulting framework has the advantages of being simple, unified, and, unlike its orthodox rivals, neatly accommodating of a much wider range of data than has previously been considered. More importantly, it positions us to better understand, identify, and confront the insidious mechanisms of ordinary bigotry. (shrink)

The traditional Lewis–Stalnaker semantics treats all counterfactuals with an impossible antecedent as trivially or vacuously true. Many have regarded this as a serious defect of the semantics. For intuitively, it seems, counterfactuals with impossible antecedents—counterpossibles—can be non-trivially true and non-trivially false. Whereas the counterpossible "If Hobbes had squared the circle, then the mathematical community at the time would have been surprised" seems true, "If Hobbes had squared the circle, then sick children in the mountains of Afghanistan at the time would (...) have been thrilled" seems false. Many have proposed to extend the Lewis–Stalnaker semantics with impossible worlds to make room for a non-trivial or non-vacuous treatment of counterpossibles. Roughly, on the extended Lewis–Stalnaker semantics, we evaluate a counterfactual of the form "If A had been true, then C would have been true" by going to closest world—whether possible or impossible—in which A is true and check whether C is also true in that world. If the answer is "yes", the counterfactual is true; otherwise it is false. Since there are impossible worlds in which the mathematically impossible happens, there are impossible worlds in which Hobbes manages to square the circle. And intuitively, in the closest such impossible worlds, sick children in the mountains of Afghanistan are not thrilled—they remain sick and unmoved by the mathematical developments in Europe. If so, the counterpossible "If Hobbes had squared the circle, then sick children in the mountains of Afghanistan at the time would have been thrilled" comes out false, as desired. In this paper, I will critically investigate the extended Lewis–Stalnaker semantics for counterpossibles. I will argue that the standard version of the extended semantics, in which impossible worlds correspond to maximal, logically inconsistent entities, fails to give the correct semantic verdicts for many counterpossibles. In light of the negative arguments, I will then outline a new version of the extended Lewis–Stalnaker semantics that can avoid these problems. (shrink)

Logic diagrams have been increasingly studied and applied for a few decades, not only in logic, but also in many other fields of science. The history of logic diagrams is an important subject, as many current systems and applications of logic diagrams are based on historical predecessors. While traditional histories of logic diagrams cite pioneers such as Leibniz, Euler, Venn, and Peirce, it is not widely known that Kant and the early Kantians in Germany and England played a crucial role (...) in popularising Euler(-type) diagrams. In this paper, the role of the Kantians in the late eighteenth and early nineteenth centuries will be analysed in more detail. It shows that diagrams (or intuition in general) were a highly contentious topic that depend on the philosophical attitude and went beyond logic to touch on issues of physics, metaphysics, linguistics and, above all, mathematics. (shrink)

Attention is essential to the life of the mind, a central topic in cognitive science, neuroscience, and psychology. Traditional debates in philosophy stand to benefit from greater understanding of the phenomenon, whether on the nature of the self, the foundation of knowledge, the natural basis of consciousness, or the origins of action and responsibility. This book is at the crossroads of philosophy of mind and cognitive science, offering a new theoretical stance on the concept of attention and how it intersects (...) with other functions of the mind, such as perception, consciousness, and action. It presents attention as directed by a subject, essential for perception, but not consciousness or action. By taking seriously the existence of a subject it stands against current trends in philosophy and cognitive science. This book offers an account of the subject and its role in attention that will both help motivate a subject-centered account and avoid some of the common criticisms regarding its existence. It engages with work by many philosophers, psychologists, and neuroscientists, including Block, Campbell, Dickie, Husserl, James, Koch, Mack and Rock, Merleau-Ponty, Treisman, and Wu. (shrink)

The Groundwork of the Metaphysics of Morals is Kant's central contribution to moral philosophy, and has inspired controversy ever since it was first published in 1785. Kant champions the insights of 'common human understanding' against what he sees as the dangerous perversions of ethical theory. Morality is revealed to be a matter of human autonomy: Kant locates the source of the 'categorical imperative' within each and every human will. However, he also portrays everyday morality in a way that many readers (...) find difficult to accept. The Groundwork is a short book, but its argument is dense, intricate and at times treacherous. This commentary explains Kant's arguments paragraph by paragraph, and also contains an introduction, a synopsis of the argument, six short interpretative essays on key topics of the Groundwork, and a glossary of key terms. It will be an indispensable tool for anyone wishing to study the Groundwork in detail. (shrink)

In this paper, I investigate whether we can use a world-involving framework to model the epistemic states of non-ideal agents. The standard possible-world framework falters in this respect because of a commitment to logical omniscience. A familiar attempt to overcome this problem centers around the use of impossible worlds where the truths of logic can be false. As we shall see, if we admit impossible worlds where “anything goes” in modal space, it is easy to model extremely non-ideal agents that (...) are incapable of performing even the most elementary logical deductions. A much harder, and considerably less investigated challenge is to ensure that the resulting modal space can also be used to model moderately ideal agents that are not logically omniscient but nevertheless logically competent. Intuitively, while such agents may fail to rule out subtly impossible worlds that verify complex logical falsehoods, they are nevertheless able to rule out blatantly impossible worlds that verify obvious logical falsehoods. To model moderately ideal agents, I argue, the job is to construct a modal space that contains only possible and non-trivially impossible worlds where it is not the case that “anything goes”. But I prove that it is impossible to develop an impossible-world framework that can do this job and that satisfies certain standard conditions. Effectively, I show that attempts to model moderately ideal agents in a world-involving framework collapse to modeling either logical omniscient agents, or extremely non-ideal agents. (shrink)

The Oxford Handbook of Carl Schmitt collects thirty original chapters on the diverse oeuvre of one of the most controversial thinkers of the twentieth century. Carl Schmitt was a German theorist whose anti-liberalism continues to inspire scholars and practitioners on both the Left and the Right. Despite Schmitt's rabid anti-semitism and partisan legal practice in Nazi Germany, the appeal of his trenchant critiques of, among other things, aestheticism, representative democracy, and international law as well as of his theoretical justifications of (...) dictatorship and rule by exception is undiminished. Uniquely located at the intersection of law, the social sciences, and the humanities, this volume brings together sophisticated yet accessible interpretations of Schmitt's sprawling thought and complicated biography. The contributors hail from diverse disciplines, including art, law, literature, philosophy, political science, and history. In addition to opening up exciting new avenues of research, The Oxford Handbook of Carl Schmitt provides the intellectual foundations for an improved understanding of the political, legal, and cultural thought of this most infamous of German theorists. A substantial introduction places the trinity of Schmitt's thought in a broad context. (shrink)

This paper discusses the constitution relation within the framework of the mechanistic approach to neurobiological explanation. It develops a regularity theory of constitution as an alternative to the manipulationist theory of constitution advocated by some of the proponents of the mechanistic approach. After the main problems of the manipulationist account of constitution have been reviewed, the regularity account is developed based on the notion of a minimal type relevance theory. A minimal type relevance theory expresses a minimally necessary condition of (...) a given type that consists of a disjunction of minimally sufficient conditions of that type. Afterwards, the attained definition is successfully applied in an analysis of the logical structure of the explanation of spatial learning and memory in rats as a paradigm neurobiological explanation. The overall result is a more robust and more precise version of the mechanistic approach to neurobiological explanations. (shrink)

Kant’s concept of conscience has been largely neglected by scholars and contemporary moral philosophers alike, as has his concept of “indirect” duty. Admittedly, neither of them is foundational within his ethical theory, but a correct account of both in their own right and in combination can shed some new light on Kant’s moral philosophy as a whole. In this paper, I first examine a key passage in which Kant systematically discusses the role of conscience, then give a systematic account of (...) “indirect” duties and the function of hypothetical imperatives in the course of their generation. I then turn to the possibility of moral error and the part “indirect” duty can play in its prevention. In conclusion, I try to show how clarifying the concept of “indirect” duty can help us to shed light on the nature of Kantian ethics as a whole. (shrink)

What happens when human beings fail to do as reason bids? This book is an attempt to address this age-old question within Kant’s mature practical philosophy, i.e. the practical philosophy that emerged with the watershed discovery of autonomy in the mid-1780s. As always, Kant is good for a surprise. There is, it is argued, not one answer but two: he advocates Socratic intellectualism in the realm of prudence whilst defending an anti-intellectualist or volitional account of immoral action. This ‘hybrid’ theory (...) of practical failure is more than a philosophical curiosity. There are ramifications for Kant’s theory of practical reason as a whole. In particular, the hybrid account emphasizes the divide between pure and empirical practical rationality to the extent that the latter, while containing practically relevant propositions, no longer counts as a branch of practical reason at all. Hypothetical and categorical imperatives exemplify two entirely distinct kinds of normativity. In fact, the dichotomy between pure and empirical determining grounds of the will goes hand in hand with many other dualisms and dichotomies that, whether we like them or not, continue to define Kant’s mature ethical thought. (shrink)

The mechanistic view of computation contends that computational explanations are mechanistic explanations. Mechanists, however, disagree about the precise role that the environment – or the so-called “contextual level” – plays for computational explanations. We advance here two claims: Contextual factors essentially determine the computational identity of a computing system ; this means that specifying the “intrinsic” mechanism is not sufficient to fix the computational identity of the system. It is not necessary to specify the causal-mechanistic interaction between the system and (...) its context in order to offer a complete and adequate computational explanation. While the first claim has been discussed before, the second has been practically ignored. After supporting these claims, we discuss the implications of our contextualist view for the mechanistic view of computational explanation. Our aim is to show that some versions of the mechanistic view are consistent with the contextualist view, whilst others are not. (shrink)

To reconcile the standard possible worlds model of knowledge with the intuition that ordinary agents fall far short of logical omniscience, a Stalnakerian strategy appeals to two components. The first is the idea that mathematical and logical knowledge is at bottom metalinguistic knowledge. The second is the idea that non-ideal minds are often fragmented. In this paper, we investigate this Stalnakerian reconciliation strategy and argue, ultimately, that it fails. We are not the first to complain about the Stalnakerian strategy. But (...) in contrast to existing complaints, we want to cause trouble for the strategy directly on its home turf. That is, we will advance our objection while granting both the plausibility of the fragmentation component—save for an extreme version of it—and that of the metalinguistic component. Once our central objection to the Stalnakerian strategy is in place, we will show how it negatively affects Adam Elga and Augustín Rayo’s recent attempt to apply the Stalnakerian strategy in the context of Bayesian decision theory. (shrink)

Eristic has been studied more and more intensively in recent years in philosophy, law, communication theory, logic, proof theory, and A.I. Nevertheless, the modern origins of eristic, which almost all current researchers see in the philosopher Arthur Schopenhauer, are considered to be a theory of the illegitimate use of logical and rhetorical devices. Thus, eristic seems to violate the norms of discourse ethics. In this paper, I argue that this interpretation of eristic is based on prejudices that contradict the original (...) intention of modern eristic. Eristic is not an art of being right or winning an argument, but an art of protecting oneself from the one who deliberately violates norms of discourse ethics to gain argumentative acceptance. For this reason, eristic must be seen as a discipline of Enlightenment philosophy and a correlate of discourse ethics. Especially in the age of alternative facts and post-factual politics, this makes eristic a valuable discipline. (shrink)

The mechanistic view of computation contends that computational explanations are mechanistic explanations. Mechanists, however, disagree about the precise role that the environment – or the so-called “contextual level” – plays for computational explanations. We advance here two claims: Contextual factors essentially determine the computational identity of a computing system ; this means that specifying the “intrinsic” mechanism is not sufficient to fix the computational identity of the system. It is not necessary to specify the causal-mechanistic interaction between the system and (...) its context in order to offer a complete and adequate computational explanation. While the first claim has been discussed before, the second has been practically ignored. After supporting these claims, we discuss the implications of our contextualist view for the mechanistic view of computational explanation. Our aim is to show that some versions of the mechanistic view are consistent with the contextualist view, whilst others are not. (shrink)

According to luck egalitarianism, it is not unfair when people are disadvantaged by choices they are responsible for. This implies that those who are disadvantaged by choices that prevent disadvantage to others are not eligible for compensation. This is counterintuitive. We argue that the problem such cases pose for luck egalitarianism reveals an important distinction between responsibility for creating disadvantage and responsibility for distributing disadvantage which has hitherto been overlooked. We develop and defend a version of luck egalitarianism which only (...) holds people responsible for creating disadvantage. This revision enables luck egalitarianism to offer compensation to those who are disadvantaged by preventing disadvantage to others, like dependent caretakers, without compromising the responsibility–sensitivity at the heart of luck egalitarianism. (shrink)

The mechanistic view of computation contends that computational explanations are mechanistic explanations. Mechanists, however, disagree about the precise role that the environment – or the so-called “contextual level” – plays for computational explanations. We advance here two claims: Contextual factors essentially determine the computational identity of a computing system ; this means that specifying the “intrinsic” mechanism is not sufficient to fix the computational identity of the system. It is not necessary to specify the causal-mechanistic interaction between the system and (...) its context in order to offer a complete and adequate computational explanation. While the first claim has been discussed before, the second has been practically ignored. After supporting these claims, we discuss the implications of our contextualist view for the mechanistic view of computational explanation. Our aim is to show that some versions of the mechanistic view are consistent with the contextualist view, whilst others are not. (shrink)

The Groundwork of the Metaphysics of Morals is Kant's central contribution to moral philosophy, and has inspired controversy ever since it was first published in 1785. Kant champions the insights of 'common human understanding' against what he sees as the dangerous perversions of ethical theory. Morality is revealed to be a matter of human autonomy: Kant locates the source of the 'categorical imperative' within each and every human will. However, he also portrays everyday morality in a way that many readers (...) find difficult to accept. The Groundwork is a short book, but its argument is dense, intricate and at times treacherous. This commentary explains Kant's arguments paragraph by paragraph, and also contains an introduction, a synopsis of the argument, six short interpretative essays on key topics of the Groundwork, and a glossary of key terms. It will be an indispensable tool for anyone wishing to study the Groundwork in detail. (shrink)

It has recently been argued that a sensitivity theory of knowledge cannot account for intuitively appealing instances of higher-order knowledge. In this paper, we argue that it can once careful attention is paid to the methods or processes by which we typically form higher-order beliefs. We base our argument on what we take to be a well-motivated and commonsensical view on how higher-order knowledge is typically acquired, and we show how higher-order knowledge is possible in a sensitivity theory once this (...) view is adopted. (shrink)

According to luck egalitarianism, it is not unfair when people are disadvantaged by choices they are responsible for. This implies that those who are disadvantaged by choices that prevent disadvantage to others are not eligible for compensation. This is counterintuitive. We argue that the problem such cases pose for luck egalitarianism reveals an important distinction between responsibility for creating disadvantage and responsibility for distributing disadvantage which has hitherto been overlooked. We develop and defend a version of luck egalitarianism which only (...) holds people responsible for creating disadvantage. This revision enables luck egalitarianism to offer compensation to those who are disadvantaged by preventing disadvantage to others, like dependent caretakers, without compromising the responsibility–sensitivity at the heart of luck egalitarianism. (shrink)

Ein Beispiel für die Rezeption und Fortführung der schopenhauerschen Logik findet man in den Mathematiklehrbüchern Friedrich Adolph Wilhelm Diesterwegs (1790–1866), In diesem Aufsatz werden die historische und systematische Dimension dieser Anwendung von Logikdiagramme auf die Mathematik skizziert. In Kapitel 2 wird zunächst die frühe Rezeption der schopenhauerschen Logik und Philosophie der Mathematik vorgestellt. Dabei werden einige oftmals tradierte Vorurteile, die das Werk Schopenhauers betreffen, in Frage gestellt oder sogar ausgeräumt. In Kapitel 3 wird dann die Philosophie der Mathematik und der (...) Logik Schopenhauers vorgestellt. Es wird gezeigt, dass Schopenhauers Logikdiagramme auf Ideen der Mathematiker Leonhard Euler (1707–1783), Bernhard Friedrich Thibaut (1775–1832) und Franz Ferdinand Schweins (1780–1856) zurückgehen und dass Schopenhauer diese Logikdiagramme auch bereits zur Analyse mathematischer Begriffe verwendet. Kapitel 4 beschäftigt sich mit der Schopenhauer-Rezeption Diesterwegs. Es wird die Frage behandelt, inwieweit Diesterweg in der Mathematik von Schopenhauer beeinflusst war und welche Rolle dieser Einfluss auf sein Verständnis von Logik und Mathematik hatte. In Kapitel 5 wird schließlich gezeigt, dass Diesterweg die schopenhauersche Begriffsanalyse der Mathematik mit Hilfe von Logikdiagrammen aufgreift und weiterführt. Da Diesterweg einer der einflussreichsten Pädagogen und Mathematikdidaktiker des 20. Jahrhunderts war, ist anzunehmen, dass sich Spuren dieser Methode noch heute finden lassen. Inwiefern dies wahrscheinlich ist, wird in der Zusammenfassung (Kapitel 6) thematisiert. (shrink)