The Curry-Howard isomorphism states an amazing correspondence between systems of formal logic as encountered in proof theory and computational calculi as found in type theory. For instance, minimal propositional logic corresponds to simply typed lambda-calculus, first-order logic corresponds to dependent types, second-order logic corresponds to polymorphic types, sequent calculus is related to explicit substitution, etc. The isomorphism has many aspects, even at the syntactic level: formulas correspond to types, proofs correspond to terms, provability corresponds to inhabitation, proof normalization corresponds to (...) term reduction, etc. But there is more to the isomorphism than this. For instance, it is an old idea---due to Brouwer, Kolmogorov, and Heyting---that a constructive proof of an implication is a procedure that transforms proofs of the antecedent into proofs of the succedent; the Curry-Howard isomorphism gives syntactic representations of such procedures. The Curry-Howard isomorphism also provides theoretical foundations for many modern proof-assistant systems (e.g. Coq). This book give an introduction to parts of proof theory and related aspects of type theory relevant for the Curry-Howard isomorphism. It can serve as an introduction to any or both of typed lambda-calculus and intuitionistic logic. Key features - The Curry-Howard Isomorphism treated as common theme - Reader-friendly introduction to two complementary subjects: Lambda-calculus and constructive logics - Thorough study of the connection between calculi and logics - Elaborate study of classical logics and control operators - Account of dialogue games for classical and intuitionistic logic - Theoretical foundations of computer-assisted reasoning · The Curry-Howard Isomorphism treated as the common theme. · Reader-friendly introduction to two complementary subjects: lambda-calculus and constructive logics · Thorough study of the connection between calculi and logics. · Elaborate study of classical logics and control operators. · Account of dialogue games for classical and intuitionistic logic. · Theoretical foundations of computer-assisted reasoning. (shrink)

Die Rede ist von einer merkwürdigen Variante deutscher Italiensehnsucht: Dem Wunsch, in Rom begraben zu werden, der im Fall Wilhelm von Humboldts mit einem konkreten Glücksgefühl korreliert. Das ist schon deshalb bemerkenswert, weil Humboldts römischer Aufenthalt vom Sterben dreier seiner Kinder und seines Freundes Schiller überschattet wurde. Die Frage nach dem Niederschlag, den die Auseinandersetzung mit dem Tod in Humboldts Texten fand, rekonstruiert die vorliegende Untersuchung als Form einer Werkpolitik, die es unternimmt, den eigenen Nachruhm in verschiedenen Diskursen zu steuern. (...) Humboldts Terminologie, die den christlich besetzten Begriff,Unsterblichkeit? durch den Begriff,Unendlichkeit? ersetzt, wird in sechs privilegierten Lektüren nachgegangen. (shrink)

This book offers an examination of the political dimensions of a number of Jean-Luc Godard’s films from the 1960s to the present. The author seeks to dispel the myth that Godard’s work abandoned political questions after the 1970s and was limited to merely formal ones. The book includes a discussion of militant filmmaking and Godard’s little-known films from the Dziga Vertov Group period, which were made in collaboration with Jean-Pierre Gorin. The chapters present a thorough account of Godard’s investigations on (...) the issue of aesthetic-political representation, including his controversial juxtaposition of the Shoah and the Nakba. Emmelhainz argues that the French director’s oeuvre highlights contradictions between aesthetics and politics in a quest for a dialectical image. By positing all of Godard’s work as experiments in dialectical materialist filmmaking, from Le Petit soldat to Adieu au langage, the author brings attention to Godard’s ongoing inquiry on the role filmmakers can have in progressive political engagement. (shrink)

Rage in the ‘Nibelungenlied’ is a positive, aboriginal energy. The more easily the hero can access this energetic source, the more powerful he becomes. Marshal charisma is essentially associated with the primary emotion of rage – a fact supremely exemplified by Siegfried. However, charismatic army commanders are quite different from political leaders. The position of the ruler is characterized by a high degree of self-control. Yet the disciplined king depends on his warriors, since the buttressing of his own cognitive distance (...) is accompanied by a weakening of his physical power. Representatives of this position are Gunther in the first part, and in the second, Etzel and his vassal Dietrich. Suspense in the ‘Nibelungenlied’ is thus built around the ambivalent qualities associated with anger. As a basic affect, anger's power stems from the sheer power of life itself; it helps those who admire the hero to identify with him and even feel a sense of delight in doing so. But whilst wrathful devotion is largely celebrated, it emerges elsewhere as the ugly face of general social impotence. The ecstasy of battle, which suggests narcissistic invulnerability, leads to deeply felt mourning amongst the survivors. Thus in the ‘Nibelungenlied’, anger is celebrated and unmasked simultaneously and in equal measure. (shrink)

Should one trust experts? My answer to this question is a qualified ‘no’. In this paper I explore the conditions under which it is rational to trust and defer to experts, and those under which it may be rational to refrain from doing so. I draw on two important factors for an actor’s trust in a partner: trust depends on the partner’s competence and on the partner’s interests. I propose that the conditions under which it is rational to trust and (...) defer to experts depend on the competences of the layperson and the expert, and the degree of interest alignment. I present a model that demonstrates that it can be practically infeasible and even logically impossible to determine the expert’s level of competence and the degree of interest alignment. Although it may sound pessimistic that one can rationally refrain from trusting experts, I will also explore some more optimistic conclusions. (shrink)

Machine intelligence already helps medical staff with a number of tasks. Ethical decision-making, however, has not been handed over to computers. In this proof-of-concept study, we show how an algorithm based on Beauchamp and Childress’ prima-facie principles could be employed to advise on a range of moral dilemma situations that occur in medical institutions. We explain why we chose fuzzy cognitive maps to set up the advisory system and how we utilized machine learning to train it. We report on the (...) difficult task of operationalizing the principles of beneficence, non-maleficence and patient autonomy, and describe how we selected suitable input parameters that we extracted from a training dataset of clinical cases. The first performance results are promising, but an algorithmic approach to ethics also comes with several weaknesses and limitations. Should one really entrust the sensitive domain of clinical ethics to machine intelligence? (shrink)

Das neue Buch des bereits mit zahlreichen Arbeiten besonders zum Vierten Kreuzzug hervorgetretenen Autors setzt sich aus drei unterschiedlichen, wenn auch eng miteinander verwobenen Teilen zusammen: einer Untersuchung zur Familie und zur Biographie des Dogen Enrico Dandolo, einer Darstellung von Politik und Verfassungsgeschichte Venedigs im 12. Jahrhundert und einer Geschichte des Vierten Kreuzzugs. Die Erzähl- und Argumentationsstränge der drei Teile sind vielfach miteinander verschränkt und verfolgen gemeinsam ein viertes Ziel: anschaulich zu machen, daß die politischen und verfassungsrechtlichen Entwicklungen des 12. (...) Jahrhunderts, besonders aber die mit der Person des Enrico Dandolo eng verbundenen Geschehnisse des Vierten Kreuzzugs die Stadt Venedig fundamental veränderten und sie von einer Kaufmannsrepublik (merchant republic) zu einer Seemacht (maritime empire) werden ließen. (shrink)

Do responsibility voids exist? That is, are there situations in which the group is collectively morally responsible for some outcome although no member can be held individually morally responsible for it? To answer these questions, I draw a distinction between competitive and cooperative decision contexts based on the team-reasoning account of cooperation. Accordingly, I provide a reasoning-based analysis of cooperation, competition, moral responsibility, and, last, potential responsibility voids. I then argue that competitive decision contexts are free of responsibility voids. The (...) conditions for the existence of responsibility voids in cooperative decision contexts depend on the type of uncertainty the group faces, either external or coordination uncertainty. (shrink)

This paper examines two strands of literature regarding economic models of cooperation. First, payoff transformation theories assume that people may not be exclusively motivated by self-interest, but also care about equality and fairness. Second, team reasoning theorists assume that people might reason from the perspective of the team, rather than an individualistic perspective. Can these two theories be unified? In contrast to the consensus among team reasoning theorists, I argue that team reasoning can be viewed as a particular type of (...) payoff transformation. However, I also demonstrate that many payoff transformations yield actions that team reasoning rules out. (shrink)

In this paper I argue for the "incompleteness thesis" of Kant's General Metaphysics before completing a full analysis of the power of judgment which only occurred in the Critique of Judgment-Power. Kant scholars have argued that Kant's General Metaphysics was completed with the Critique of Pure Reason and the Third Critique added nothing significant to this quest. One of the issues in this paper is to understand Kant's various "transition problems" and their solution to unify knowledge under a metaphysics, all (...) of which has implications for the natural and cognitive sciences even today. (shrink)

This paper proposes a logical framework for studying the structure of moral responsibility for outcomes. The analysis incorporates two vital features: an agency condition and a negative condition of an alternative possibility. The logical language allows us to identify and disambiguate seven plausible criteria for moral responsibility. To accommodate interdependent decision contexts, the semantics are given in terms of so-called responsibility games. The logical framework enables us to classify the logical relations between these seven criteria for moral responsibility. Although all (...) seven criteria are logically distinct, I also identify circumstances where the seven criteria locally reduce to only three. (shrink)

Many philosophers are convinced that rationality dictates that one’s overall set of intentions be consistent. The starting point and inspiration for our study is Bratman’s planning theory of intentions. According to this theory, one needs to appeal to the fulfilment of characteristic planning roles to justify norms that apply to our intentions. Our main objective is to demonstrate that one can be rational despite having mutually inconsistent intentions. Conversely, it is also shown that one can be irrational despite having a (...) consistent overall set of intentions. To overcome this paradox, we argue that it is essential for a successful planning system that one’s intentions are practically consistent rather than being consistent or applying an aggregation procedure. Our arguments suggest that a new type of norm is needed: whereas the consistency requirement focuses on rendering the contents of one’s intentions consistent, our new practical consistency requirement demands that one’s intentions be able to simultaneously and unconditionally guide one’s action. We observe that for intentions that conform to the ‘own-action condition’, the practical consistency requirement is equivalent to the traditional consistency requirement. This implies that the consistency requirement only needs to be amended in scenarios of choice under uncertainty. (shrink)

In the present paper I investigate the role that analogy plays in eighteenth-century biology and in Kant’s philosophy of biology. I will argue that according to Kant, biology, as it was practiced in the eighteenth century, is fundamentally based on analogical reflection. However, precisely because biology is based on analogical reflection, biology cannot be a proper science. I provide two arguments for this interpretation. First, I argue that although analogical reflection is, according to Kant, necessary to comprehend the nature of (...) organisms, it is also necessarily insufficient to fully comprehend the nature of organisms. The upshot of this argument is that for Kant our understanding of organisms is necessarily limited. Second, I argue that Kant did not take biology to be a proper science because biology was based on analogical arguments. I show that Kant stemmed from a philosophical tradition that did not assign analogical arguments an important justificatory role in natural science. Analogy, according to this conception, does not provide us with apodictically certain cognition. Hence, sciences based on analogical arguments cannot constitute proper sciences. (shrink)

Historically, blatantly untrue and defamatory conspiracy theories had disastrous consequences for those who were portrayed in them as evil-doers. At the same time, conspiratorial agreements at the expense of the common good between powerful groups in society do exist and have occasionally been uncovered. Against this background, the article describes different ways in which critical theory has looked at conspiracies. First, an attempt is made to show that Max Horkheimer's notes on `rackets' are an ambitious but flawed attempt to theorize (...) conspiracy. It is argued that Horkheimer's theory is imbued by the very conspiracy thinking that he proposed to criticize. Second, the author suggests recovering Franz Neumann's concept of `political alienation' as a more appropriate starting point to think critically about the ethical and epistemological questions raised by conspiracy theories. (shrink)

Kant is well known for his restrictive conception of proper science. In the present paper I will try to explain why Kant adopted this conception. I will identify three core conditions which Kant thinks a proper science must satisfy: systematicity, objective grounding, and apodictic certainty. These conditions conform to conditions codified in the Classical Model of Science. Kant’s infamous claim that any proper natural science must be mathematical should be understood on the basis of these conditions. In order to substantiate (...) this reading, I will show that only in this way it can be explained why Kant thought (1) that mathematics has a particular foundational function with respect to the natural sciences and (2) as such secures their scientific status. (shrink)

This article explores Professor T.F.J. Dreyer's definition for preaching that he developed for preaching in the Netherdutch Reformed Church of Africa (NRCA) three decades ago. Dreyer's own homiletical perspective towards preaching developed continuously through numerous philosophical paradigm shifts since 1989. His basis theory plays an important role in the theological training of the church's students today. The aim of the research is to reflect on the changes, following Dreyer's homiletical development over three decades. The research discovers a strong prophetical character (...) in the homiletical approach of Dreyer and concludes by asking how a kairos moment of prophetical speech can benefit the NRCA. CONTRIBUTION: This research hopes to contribute to the existing research that was done in the homiletical field of traditional Afrikaans-speaking churches in South Africa. The research also contributes by identifying some homiletical perspectives that can help the church to proclaim the gospel in times of transition. (shrink)

This essay deals with a particularly recalcitrant problem in the history of ideas, that of irrationalism. It emerged to full consciousness in mid-eighteenth century thought. Irrationalism was a logical consequence of individualism which in turn was a direct outcome of the Cartesian self-reflective subject. In time these tendencies produced the "critical" Zeitgeist and the "epoch of taste" during which Kant began thinking about such matters. Like Alfred Bäumler, I argue that irrationalism could not have arisen in ancient or medieval philosophical (...) discourse, as they both lacked a certain type of rationalism required as its conceptual antipode. Only after the Lisbon earthquake (1755), and the ensuing reason vs. passion debate acknowledging for the first time both human powers as equal contenders, did the specter of irrationalism arise and become a focus. Kant's revolution in thought produced "transcendental psychology" reconciling "pure" sensibility and "pure" reason and provided, I argue, the conceptual wherewithal to grant aesthetic feeling and irrationalism a philosophical niche. (shrink)

This essay deals with a particularly recalcitrant problem in the history of ideas, that of irrationalism. It emerged to full consciousness in mid-eighteenth century thought. Irrationalism was a logical consequence of individualism which in turn was a direct outcome of the Cartesian self-reflective subject. In time these tendencies produced the "critical" Zeitgeist and the "epoch of taste" during which Kant began thinking about such matters. Like Alfred Bäumler, I argue that irrationalism could not have arisen in ancient or medieval philosophical (...) discourse, as they both lacked a certain type of rationalism required as its conceptual antipode. Only after the Lisbon earthquake (1755), and the ensuing reason vs. passion debate acknowledging for the first time both human powers as equal contenders, did the specter of irrationalism arise and become a focus. Kant's revolution in thought produced "transcendental psychology" reconciling "pure" sensibility and "pure" reason and provided, I argue, the conceptual wherewithal to grant aesthetic feeling and irrationalism a philosophical niche. (shrink)

I argue that once one holds (as Kant does) that the mind is equipped with innate, pre-existing, i.e. a priori structures, one can ask (as materialists or empiricists would), Is there an identifiable source of such structures and what does it imply? Already Schopenhauer, Moses Mendelssohn and others have taken that route of argument, without fully drawing the implications. In this paper I attempt to do so, posing the query: Is Kant's very explicit separation of the transcendent from the transcendental (...) necessary in his critical system? I try to answer from various perspectives. (shrink)

This study focuses on Kant's attempt to find the link between feeling and cognition on a priori grounds in the three Critiques to make philosophical judgment possible. As such it treats the area of aesthetics and its formal principles. This work explores the enigma: How is it that Kant values the talent to judge more than understanding and reason; indeed the lack of it «no school can make good». Yet, even though Kant demonstrates how a priori synthetic judgments and a (...) priori moral judgments are possible as particular pronouncements, he analyzes the power of judgment itself as an independent faculty only in the last Critique. The author argues that the aesthetic factor plays a recalcitrant, yet vital and necessary role in all human judging. Finding an adequate niche for feeling and its a priori principles becomes a key problem not just for Kant but for the entire philosophical enterprise. (shrink)

KANT AND HEGEL FIND THEMSELVES ON SIMILAR PATHS toward their respective goals to give a total account of reality. They share a deep commitment to science, Wissenschaftlichkeit, and raise the question: Where does science begin? Similarly, they answer: It begins with sense knowledge yet it is not founded in the senses. This essay attempts to reflect on, with the aim of cautiously reassessing, the nonsensible, universal features of sense experience from an idealist perspective. A study of the “science of sensibility,” (...) raised to new levels of interest in recent debates of how the mind works, seems to have lost nothing of its fascination, indeed urgency in contemporary discussions, in the Kant-Hegel scholarship, in the philosophy of mind, philosophy of science as well as the natural and cognitive sciences in general. (shrink)