The original proof of the four-color theorem by Appel and Haken sparked a controversy when Tymoczko used it to argue that the justification provided by unsurveyable proofs carried out by computers cannot be a priori. It also created a lingering impression to the effect that such proofs depend heavily for their soundness on large amounts of computation-intensive custom-built software. Contra Tymoczko, we argue that the justification provided by certain computerized mathematical proofs is not fundamentally different from that provided by surveyable (...) proofs, and can be sensibly regarded as a priori. We also show that the aforementioned impression is mistaken because it fails to distinguish between proof search (the context of discovery) and proof checking (the context of justification). By using mechanized proof assistants capable of producing certificates that can be independently checked, it is possible to carry out complex proofs without the need to trust arbitrary custom-written code. We only need to trust one fixed, small, and simple piece of software: the proof checker. This is not only possible in principle, but is in fact becoming a viable methodology for performing complicated mathematical reasoning. This is evinced by a new proof of the four-color theorem that appeared in 2005, and which was developed and checked in its entirety by a mechanical proof system. (shrink)

This article is a commentary on ChatGPT and LLMs (Large Language Models) in general. It argues that this technology has matured to the point where calling systems such as ChatGPT “stochastic parrots” is no longer warranted. But it also argues that these systems continue to have serious limitations when it comes to reasoning. These limitations are much more severe than commonly thought. A large array of examples are given to support these claims.

In this paper, we tackle the widely held view that practice-oriented approaches to ethics are conservative, preserving the moral status quo, and, in particular, that they do not promote any change in our dealings with animals or formulate clear principles that help us to achieve such change. We shall challenge this view with reference to Wittgensteinian ethics. As a first step, we show that moral thought and action rest on basic moral certainties like: equals are to be treated equally and (...) unequals unequally. We then explore the relations between this insight and the notion of the difficulty of reality elaborated by Cora Diamond. Our goal is to show that a Wittgensteinian-Diamondian approach to animal ethics is not necessarily morally conservative. Indeed, it offers a profound practice-oriented approach to animal ethics that is capable of promoting change in human dealings with animals because it is compatible with radical critique. (shrink)

Published posthumously in 1908, Ecce Homo was written in 1888 and completed just a few weeks before Nietzsche’s complete mental collapse. Its outrageously egotistical review of the philosopher’s life and works—featuring chapters called Why I Am So Wise and Why I Write Such Good Books—are redeemed from mere arrogance by masterful language and ever-relevant ideas. In addition to settling scores with his many personal and philosophical enemies, Nietzsche emphasizes the importance of questioning traditional morality, establishing autonomy, and making a commitment (...) to creativity. Essential reading for students of philosophy, this unique memoir is crucial to an understanding of Nietzsche’s other works. (shrink)

Issues of reliability are claiming center-stage in the epistemology of machine learning. This paper unifies different branches in the literature and points to promising research directions, whilst also providing an accessible introduction to key concepts in statistics and machine learning – as far as they are concerned with reliability.

Although Walter Benjamin's writings are considered to be among the most powerful theoretical enterprises of the twentieth century, his ideas are resistant to cooptation by the doctrines of various critical programs. These essays engage this resistance by examining the ghostly in Benjamin's work. The contributors show that the haunting truths Benjamin offers point towards new forms of responsibility. These truths reside in a figurative elsewhere, a ghostly space that his texts delimit but never fully inhabit, and these essays seek to (...) do justice to the ghosts of Benjamin. Issues explored include: the status of the image in Benjamin's literary reflections and in his meditations on cinema and visual culture; abiding Benjaminian notions of messianism, aura, reproducibility, semblance, and melancholy; Benjamin's relation to Freud; his innovative rethinking of history, virtuality, and translation; and his reflections on tragedy and prophecy, the geometrical dimensions of writing, and the relation between eros and language. (shrink)

Die gängigen Prognosen, nach denen die Religionen im Kontext der Moderne oder im Zuge der Globalisierung an Bedeutung verlieren würden, haben sich nicht bestätigt. Das Gegenteil ist der Fall: Jenseits von nihilistischen Entwürfen und virtuellen Konstruktionen öffneten sich auch und gerade in der Literatur Räume für die Belebung religiöser Weltsicht. Ausgehend von Heinrich Böll und seiner Anfang der 1960er Jahre eingeleiteten Distanzierung von der Institution Kirche, wird am Beispiel von Botho Strauß und Peter Handke, die seit den 1970er und 1980er (...) Jahren eine ins Metaphysische zielende Subjektivität repräsentieren, eine Renaissance des Religiösen konstatiert, die sich in den Werken des jüngeren Autors Ralf Rothmann seit den 1990er Jahren mit selbstbewusster Deutlichkeit fortschreibt. Anhand der geistesgeschichtlichen Trias Gnostizismus, Philosophie und Mystik nimmt die Verfasserin eine Fokussierung vor, die die ästhetischen Konzeptionen der Autoren deutlich werden lässt und sie zueinander in Beziehung setzt. (shrink)

Gerhard Richter's groundbreaking study argues that the concept of "afterness" is a key figure in the thought and aesthetics of modernity. It pursues questions such as: What does it mean for something to "follow" something else? Does that which follows mark a clear break with what came before it, or does it in fact tacitly perpetuate its predecessor as a consequence of its inevitable indebtedness to the terms and conditions of that from which it claims to have departed? Indeed, (...) is not the very act of breaking with, and then following upon, a way of retroactively constructing and fortifying that from which the break that set the movement of following into motion had occurred? The book explores the concept and movement of afterness as a privileged yet uncanny category through close readings of writers such as Kant, Kafka, Heidegger, Bloch, Benjamin, Brecht, Adorno, Arendt, Lyotard, and Derrida. It shows how the vexed concepts of afterness, following, and coming after shed new light on a constellation of modern preoccupations, including personal and cultural memory, translation, photography, hope, and the historical and conceptual specificity of what has been termed "after Auschwitz." The study's various analyses—across a heterogeneous collection of modern writers and thinkers, diverse historical moments of articulation, and a range of media—conspire to illuminate Lyotard's apodictic statement that "after philosophy comes philosophy. But it has been altered by the 'after.'" As Richter's intricate study demonstrates, much hinges on our interpretation of the "after." After all, our most fundamental assumptions concerning modern aesthetic representation, conceptual discourse, community, subjectivity, and politics are at stake. (shrink)

The article attempts to compare personalist aspects in the works of Vasily Zenkovsky and Vladimir Lossky. It is shown that two types of philosophical personalism (metaphysical and existentialist) in the history of Russian thought set the framework for two types of theological personalism presented respectively by Zenkovsky and Lossky. The philosophy of Lev Lopatin was the important source for the principles of Zenkovsky’s personalist vision. The relevant philosophical background on Lossky’s personalism is provided by Nikolai Berdyaev’s works. The article considers (...) the deep criticism by the French theologian Jean-Claude Larchet, who seeks to demonstrate philosophical and existentialist sources of Lossky’s theological personalism, rather than patristical ones. It is noted that the criticism addressed to Lossky’s theory may slide to challenging the very possibility of an Orthodox theological personalism as a line of thought. It is shown that Zenkovsky’s works, presenting a nonexistentialist type of personalism, do not provoke such criticism. It’s concluded that whereas Lossky’s legacy in its personalistic aspect is challenged, Zenkovsky’s personalism enables another way of conceiving “Orthodox theological personalism.”. (shrink)

PA is Peano Arithmetic. Pr(x) is the usual Σ1-formula representing provability in PA. A strong provability predicate is a formula which has the same properties as Pr(·) but is not Σ1. An example: Q is ω-provable if PA + ¬ Q is ω-inconsistent (Boolos [4]). In [5] Dzhaparidze introduced a joint provability logic for iterated ω-provability and obtained its arithmetical completeness. In this paper we prove some further modal properties of Dzhaparidze's logic, e.g., the fixed point property and the Craig (...) interpolation lemma. We also consider other examples of the strong provability predicates and their applications. (shrink)

Dieser Artikel stellt Cora Diamonds Begriff des Mitgeschöpfs dar und untersucht dessen Relevanz für tierethische und tierpolitische Diskurse. Die traditionelle Tierethik hat eine rationalistische, naturalistische und reduktionistische Tendenz. Diamonds Moralphilosophie stellt dem einen praxissensitiven Ansatz gegenüber, der Emotionen und die moralische Imagination umfasst, wobei Diamond die Bedeutung des Menschseins betont. Letztere entspringt zwar einem epistemischen Anthropozentrismus, jedoch folgt aus diesem keine Mensch-Tier-Hierarchie: Diamond plädiert dafür, andere Tiere als Mitgeschöpfe, als Gefährten auf sterblichen Pfaden, zu begreifen. Dabei zeigt Diamond an ihrer (...) Interpretation von J.M. Coetzees The Lives of Animals, wie Konzepte von anderen Tieren auf das eigene Selbstverständnis rückwirken. Abschließend erörtert der Artikel den Vorwurf des Quietismus und die Schwierigkeit der politischen Umsetzbarkeit in Diamonds Philosophie. -/- [This article outlines Cora Diamond’s concept of the fellow creature and examines its relevance for animal ethics and animal politics. Diamond’s moral philosophy contrasts the rationalistic, naturalistic, and reductionistic tendency of traditional animal ethics with a practice-oriented approach that encompasses emotions and the moral imagination. Diamond emphasizes the importance of being human, which emanates from an epistemic anthropocentrism, but from which no human-animal hierarchy follows: She pleads for recognizing other animals as fellow creatures, as companions on mortal paths. In her interpretation of J.M. Coetzee’s The Lives of Animals, Diamond shows how conceptualizing other animals influences one’s own self-understanding. Finally, the article discusses the reproach of quietism and the difficulty of political feasibility in Diamond’s philosophy.]. (shrink)

Intense or industrial animal husbandry is morally bad. This consensus in animal ethics led to the emergence of veganism which is recently in decline in favour of ‘conscientious carnivorism’ which advocates eating animal products from animal-friendly animal husbandry in response to the moral problems of industrial farming. Advocates of animal-friendly husbandry justify rearing and killing ‘happy animals’ by highlighting that the animals live pleasant lives and would not have existed if not reared for human consumption. In this paper, I tackle (...) this ‘logic of the larder’ by showing that it serves as a purification strategy to conceal the harm that animals experience in this alleged animal-friendly type of farming. Defenders of ‘happy meat’ claim that animal-friendly animal husbandry is in the animals’ best interests and that it is in effect a ‘win-win situation’ for humans and farm animals alike. Departing from two critics of animal-friendly animal husbandry, I will show that the problem of this logic is that it evades the fact that moral residuals, which is the experienced harm by the animals, remain by engaging in this practice. Even if there may be strong reasons for the consumption of meat and derivatives of ‘happy animals’, the experienced harm for the animals will not be extinguished. I will denote the detachment that derives from the strategy of rendering the animals’ experienced harm in animal-friendly animal husbandry invisible as guilt. I will conclude that instead of purifying eating animals the ‘good way’, we should face the responsibility we have when killing ‘happy animals’ for ‘happy meat’. (shrink)

Various publications claim that medical AI systems perform as well, or better, than clinical experts. However, there have been very few controlled trials and the quality of existing studies has been called into question. There is growing concern that existing studies overestimate the clinical benefits of AI systems. This has led to calls for more, and higher-quality, randomized controlled trials of medical AI systems. While this a welcome development, AI RCTs raise novel methodological challenges that have seen little discussion. We (...) discuss some of the challenges arising in the context of AI RCTs and make some suggestions for how to meet them. (shrink)

Mental health professionals who care for asylum seekers in Western European countries increasingly encounter problems for which standard diagnostic and therapeutic protocols and institutional healthcare policies offer no ready answers. In the following case vignettes some of these problems can be identified.

One of the key ethical debates in Russian religious thought, initiated by Leo Tolstoy, concerned the question of nonresistance to evil by force. The purpose of this article is to assess the influence of Kant’s ethics and philosophy of religion on the course of this debate and to determine the place and significance of the arguments and considerations expressed on this issue by Semyon Frank in the early and late periods (1908 and 1940s) of his work. To this end I (...) reconstruct the general course of the debate, notably the positions and arguments of Leo Tolstoy, Vladimir Solovyov, Ivan Ilyin and Nikolai Berdyaev. Beginning with Tolstoy, Russ­ian thinkers introduced the original ethical content of the idea of nonresistance derived from the Gospel into the ethics of duty borrowed from Kant. The Tolstoy version of this idea was challenged mainly from two directions: from the Kantian grounding of the legitimacy of coercion and attempts to bring in styles of moral thinking other than the ethic of duty. Ilyin’s apolo­gia for the use of force in the struggle against evil prompted Russian émigré thinkers to take a closer look at Tolstoy’s ethical concept and pay attention to its positive content. On this basis Berdyaev and especially Frank create their version of the Christ-centered ethic of salvation which, in the perspective of “protecting the world against evil” includes the ethic of duty and links it with the possibility of using force, always a wrongful act, but one justified “in a situation of extreme need”. (shrink)

Creativity is an emerging field of research for philosophy. A diachronic cultural value and fundamental human ability, creativity poses a host of questions that challenge us both on a theoretical and practical level. In this paper we explore creativity through the use of problem-solving lateral thinking techniques, as part of the C2Learn European Community research program. Lateral thinking is defined and then classified into three distinct kinds: conceptual, diagrammatic and emotive. Each kind is then explicated and its basic principles examined, (...) in an effort to shed light on the different ways the space of possible solutions is affected by each kind of lateral thought. It is this active engagement with the space of possibilities itself, that separates a mere problem-solver from an actual creator. (shrink)

In the famous exchange between Passennus Paulus and Javolenus Priscus at Plin. Ep. 6.15, it has not been previously recognized that Priscus’ reply is metrical and carries on the hexameter begun by Paulus. This opens up some interesting new possibilities for the interpretation of the letter.

Gegen das Streben der Moderne nach Widerspruchsfreiheit, Ordnung und Einheit aktiviert die Postmoderne die Begriffe Differenz, Widerstreit und Ambivalenz. Dieser Wandel lat auch die Bildungsphilosophie nicht unberuhrt. In diesem Buch wird untersucht, welche Auswirkungen postmoderne Ideen auf Bildungsphilosophie und -praxis haben konnen. Im Zentrum der Auseinandersetzung steht die Kritik an der modernen Identitats- und Subjektkategorie und der Versuch, diese aus postmoderner Sicht neu zu bestimmen und gewinnbringend auf die Erwachsenenbildung zu beziehen.

When it comes to invasive manipulation of animals on the biological level, reactions of disgust are common and often influential on people’s moral judgments. As a case in point, the Belgian Blue, a breed of hyper-enhanced cattle which will serve as a case study for the present article, has historically been met with revulsion. Traditionally, in bio- and animal ethics, this ‘yuck factor,’ has been denied any productive role in proper moral justification, since rationalism is still a dominant paradigm in (...) those disciplines. This is not surprising since rationalism offers the fulfilment of certain expectations we have of morality, like universality, intersubjective communicability, and objectivity. Increasingly, however, the preconceptions of rationalism have been brought into question, both through empirical as well as philosophical insights. In this paper, we will explore a way in which researchers who are, accordingly, critical of rationalism, and who wish to take seriously the role disgust plays in the formation of moral judgments when it comes to biological manipulation of animals, can do so without abandoning those virtues of rationalism which make it such an appealing position. We will do so by offering what we call a ‘tempered’ kind of rationalism, that is, one which conceives of rationality in the terms of Mary Midgley, not as distinct from, but as a possible function of, well-ordered emotion. (shrink)

Against the well-established critical rejection of rights a growing literature in the tradition of agonistic democracy asserts their emancipatory role in the struggles for social change. However, agonistic theorists, invested as they are in the idea of democratic innovation as a process of gradual ‘augmentation’ of existing rules, institutions and practices, fail to account for the ruptural capacity, and hence for the full radical potential, of rights. Using the performative approach, I develop a conception of rights claiming as a defiant (...) practice to express the ruptural dimension of certain forms of rights politics. I demonstrate how defiant rights claiming articulates immanent critique by declaring the incapacity of putative duty-bearer institutions and governments to uphold the claimed right due to structural constraints, thereby generating inevitable contradictions within the extant order and creating the necessity for an alternative one. Moreover, in order to fully capture the emancipatory potential and creative capacity of rights, this article argues for understanding certain forms of rights politics both as augmentation and rupture, taking the two to be different dimensions of the same radical democratic practice. I present the creative use of rights discourse by the Landless Workers’ Movement in Brazil and the transnational network of agrarian movements, La Via Campesina, as precisely such a combination of the practice of augmentation and defiant claims, which has led to the transformation of the right to food and land into the right to food sovereignty, demonstration of the structural embeddedness of rights violations in the existing global regime of food production and distribution, and authorisation of an alternative vision of the future. (shrink)

Two short typescripts by G. Lukács from the archive, dating from 1941/42, shed light on his appraisal of the cultural ‘inner reserves’ of Germany and the ‘moral reserves’ of the democracies involved in the Second World War, as well as on Lukács’s political philosophy at that time. The conception of an intrinsic interrelation of a humanist philosophical anthropology and rationalist epistemology elucidates his egalitarian and democratic account. Both texts are located within the intellectual development of the author in an introduction (...) by the editor, which sketches the historical background and indicates relevant contemporaneous theoretical and political debates, such as the controversies over realism and humanism and, also in dispute with K. Jaspers, on German collective guilt. (shrink)

Synchronic norms of theory choice, a traditional concern in scientific methodology, restrict the theories one can choose in light of given information. Diachronic norms of theory change, as studied in belief revision, restrict how one should change one’s current beliefs in light of new information. Learning norms concern how best to arrive at true beliefs. In this paper, we undertake to forge some rigorous logical relations between the three topics. Concerning, we explicate inductive truth conduciveness in terms of optimally direct (...) convergence to the truth, where optimal directness is explicated in terms of reversals and cycles of opinion prior to convergence. Concerning, we explicate Ockham’s razor and related principles of choice in terms of the information topology of the empirical problem context and show that the principles are necessary for reversal or cycle optimal convergence to the truth. Concerning, we weaken the standard principles of agm belief revision theory in intuitive ways that are also necessary for reversal or cycle optimal convergence. Then we show that some of our weakened principles of change entail corresponding principles of choice, completing the triangle of relations between,, and. (shrink)

Книга представляет собой реконструкцию и анализ томистской концепции бессмертия человеческой души в общем контексте философии Фомы Аквинского.

В книге рассматриваются некоторые попытки построения "Третьего Христианства", очищенного от скверны.

Dieser Band untersucht wichtige Stationen der Vor- und Fruhgeschichte der Aufklarung, zentrale Denker und Tendenzen der Aufklarungsepoche und deren Fortwirken. Es wird gezeigt, wie aufklarerische Impulse konzeptualisiert wurden und in Rezeption und Kritik mit aufklarungskritischen Positionen verflochten sind. Die Autoren rekonstruieren ursprungliche Entwurfe, Korrekturen und Uberbietungen und leisten so selbst eine Fortfuhrung der Aufklarung, indem die aufklarerische Vernunft mit Kritik angereichert und dadurch reflexiv eingeholt wird. Nur die uber ihre eigene Geschichte und ihre blinden Flecke aufgeklarte Vernunft kann der ursprunglichen (...) Intention einer Emanzipation durch Kritik unter den komplexen Bedingungen der Gegenwart gerecht werden.". (shrink)

Introduction : the art of reading -- Adorno and the uncoercive gaze -- Buried possibility : Adorno and Arendt on tradition -- The inheritance of the constellation : Adorno and Hegel -- Judging by refraining from judgment : Adorno's artwork and its Einordnung -- The literary artwork between word and concept : Adorno and Agamben reading Kafka -- The artwork without cardinal direction : notes on orientation in Adorno -- False life, living on : Adorno with Derrida -- Conclusion : (...) a kind of leave-thinking. (shrink)

In lieu of an abstract, here is a brief excerpt of the content:Konstantin Kolenda IMMORTALITY REVISITED In his essay, "Poets and Thinkers: Their Kindred Roles in the Philosophy of Martin Heidegger," J. Glenn Gray points out that Heidegger "does not treat imaginative literature and other works of art qua literature and art but as aspects of philosophy or meditative thought." To Heidegger's question, "How long are we going to prevent ourselves from experiencing the actual as actual?", Gray is inclined (...) to answer as follows: "Until we have become aware that the poetic eye is capable of seeing as deeply into nature and man as the scientific eye," and he adds that "there is hope that philosophers may once again take seriously the discoveries of creative writers who are not consciously seeking to 'do' philosophy."2 There is little evidence that Gray's hope has materialized to any great extent; few philosophers are paying much attention to discoveries of creative writers, thus bearing out Heidegger's contention that "at this moment in the world's history we have first to learn that the making of poetry, too, is a matter of thinking."3 But it should not surprise us that when philosophers turn to the thinking of poets they will not necessarily agree in their interpretations. Although it has been remarked that Rilke translated Nietzsche into poetry and then in turn Heidegger translated Rilke into prose, when we look at what Heidegger actually says about Rilke's ideas, we may find that these ideas allow alternative interpretations.4 Nevertheless, the fact that alternative interpretations are possible bears out the soundness of Heidegger's and Gray's claim that at least some poetic thought is worth taking seriously. In this article we shall examine Rilke's view of the relationship between life and death, as expressed in his Duino Elegies. Since this is a theme which figures prominently in Heidegger's philosophy, it is only proper to begin by pointing out certain basic correspondences between the views of the two thinkers on this topic. But as we pursue the matter further it soon becomes apparent that Rilke has set forth an intriguing and original, albeit unorthodox, notion of immortality, a notion that 167 1 68Philosophy and Literature does not need to be tied down to Heidegger's philosophy as a whole but can be defended in its own right. This article constitutes such a defense. In Being and Time, Heidegger suggests that death "belongs" to Dasein. "In Dasein there is undeniably a constant 'lack of totality' which finds an end with death. This 'not-yet' 'belongs' to Dasein as long as it is; this is how things stand phenomenally." Rilke's way of expressing a similar thought is to say, in the First Elegy, that "all of the living make the mistake of drawing too sharp distinctions." The contrast he speaks of is that between life and death. Like Heidegger, Rilke calls attention to phenomena that seem to go against the ingrained tendency to view life and death as belonging to two separate realms. Both manage to break the hold of pictures which for so long have led our thinking on this topic into dead ends. The radical temporality of human existence, its inevitable mortality, leads Heidegger to include the resolute acceptance of "being-toward-death" as a necessary condition of authentic existence. The "not-yet" of eventual death is always with us; since we cannot escape it, we must not keep denying our mortality by self-deception or by resigned waiting but should take it up into a resolute anticipation. The factor of death must be included in the consciousness of our vital decisions. In other words, death is to be taken up into human life and is to be viewed, paradoxically perhaps, as its essential component. Thus, the radical contrast between life and death is undermined. The taming of death is one of the central themes in Rilke's poem. Like Novalis before him, Rilke thought of death as the night-side of life. "Death is the side of life that is turned away from us and is unillumined for us."7 But he made use of still another notion to break down a distinction which, in his opinion, we the... (shrink)