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)

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.

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)

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)

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)

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)

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)

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)

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)

ArgumentPost-Stalinist reforms resulted in dramatic changes in the ways of operation of Soviet science: one can say that they altered the very understanding of what science was, or should be, in the socialist society. A new vision came about as a result of political and rhetorical efforts of scientists, who pushed forward their various, often conflicting, agendas acting in accordance with specific rules of Soviet polity. The most visible part of the reform came with the 1961 administrative reorganization of the (...) USSR Academy of Sciences. The related series of changes, however, was much broader and comprehensive, modifying the relationships between science and ideology, politicians and academic researchers, and establishing the very division between fundamental and applied research, which had been strongly rejected during the preceding Stalinist period. (shrink)

We say that two arithmetical formulas A, B have the Σ1-interpolation property if they have an ‘interpolant’ σ, i.e., a Σ1 formula such that the formulas A→σ and σ→B are provable in Peano Arithmetic PA. The Σ1-interpolability predicate is just a formalization of this property in the language of arithmetic.Using a standard idea of Gödel, we can associate with this predicate its provability logic, which is the set of all formulas that express arithmetically valid principles in the modal language with (...) two modal operators, □ for provability in PA and for Σ1-interpolability. In this paper we determine this provability logic .It turns out that this problem appears to be quite similar to the problem of such modal description of relative interpretability, a problem, solved by Berarducci and Shavrukov. However, the present case is sometimes easier. In particular, we prove in this paper the fixed point property and the Craig interpolation property for our modal system ELH. (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)

How is time transformed when signs appear? In the sign system of the conditioned reflex, the sign (conditioned stimulus) reverses, changes the direction of time, and overcomes its unidirectionality and irreversibility. In a sense, there is a “return” to the past in the form of the future when the sign is introduced. The sign serves as a “Time machine” of sorts. The mechanism of time transformation is possible because a mirror is embedded inside the sign, the surface of which represents (...) the psychological present time. When past experience meets that surface in the present, it may be reflected in the form of a future event. In the course of reflection, time changes its direction: if earlier time flowed from the event (the cause), it subsequently flows to other events (the purpose). Previously inaccessible past experience is now projected into the present, “comes to life” in it and is transformed into the future. In humans, unlike in animals, signs of the second order appear. Inside the signs of the second order, a mirror is built in, and the experience of the past as a subject is reflected in the future form as an object. An individual has the opportunity to consider oneself externally as an object. It goes beyond the subjective form. Thus, secondary signs once again change time direction. Due to this phenomenon, time becomes doubly reversible: first it turns around in a conditioned stimulus, and then in a secondary sign. (shrink)

Cet article apporte, pour la première fois, des arguments confortant l'identification de l'emporion de Pistiros, attesté épigraphiquement dans la « Grande inscription » du village de Vetren, avec le site archéologique d'époque classique et hellénistique de la région d'Adžijska Vodenica, situé à 2 km de l'endroit où l'inscription a été trouvée. Les éléments en faveur de cette identification sont les suivants : 1) la relation entre l'emplacement de l'inscription — de l'autre côté de l'ancienne « Voie diagonale » reliant Byzance (...) à Serdica, près des ruines de la station romaine de Bona Mansio — et la vocation historique de Vemporion durant le règne de Philippe II de Macédoine ; 2) la tradition antique du nom de Pistiros jusqu'à son dernier avatar : Kapisturia ; 3) l'étymologie du nom Pistiros/Bistiros, toponyme que l'on trouve près d'une vaste étendue d'eau ; 4) l'interprétation de l'hapax epaulistes comme désignant un envoyé du roi thrace qui était obligé de passer la nuit avant le défilé de Succi (aujourd'hui Porte de Trajan) avant de poursuivre son chemin vers l'Ouest le lendemain ; 5) la localisation des Emporta Belana, d'après l'inscription, au pied du versant Sud du mont Orbélos (aujourd'hui Mt Belasitza). Historiquement Xemporion de Pistiros peut être identifié avec le chorion Masteira, mentionné par Démosthène. Des données sûres le concernant nous ont été transmises par l'historien Anaximène de Lampsaque. On tente aussi, pour la première fois, de localiser le chorion Drongilon, à partir de l'ancienne forteresse de Dingion dans la moyenne vallée de l'Hébros. L'article donne enfin une interprétation nouvelle du terme Thraces tetrachoritai, qui désignerait la zone d'occupation macédonienne à l'intérieur de la Thrace, où les quatre garnisons de Philippe II (Drongilon, Kabyle, Philippopolis et Masteira) furent en butte à la révolte. Du point de vue chronologique, cette zone fut établie au moins en deux étapes : en 352/1 et 342/1 av. J.-C. (shrink)

The COVID-19 pandemic in 2020 has had a lasting impact on all areas of personal life. However, the political, economic, legal and healthcare system, as well as the education system have also experienced the effects. Universities had to face new challenges and requirements in teaching and examinations as quickly as possible in order to be able to guarantee high-quality education for their students.This study aims to examine how the German-speaking medical faculties of the Umbrella Consortium of Assessment Network have dealt (...) with the challenges but also the opportunities that the outbreak of the COVID-19 pandemic created in medical education and whether digitalisation has been driven forward as a result. In an initial online-survey we focused our questions on the current teaching situation with regard to digitised teaching content, the support or establishment of adequate framework conditions by the medical faculties and IT facilities and also the execution of examinations during the summer semester 2020.Between August and September 2020, a total of 88 examiners, educators, dean of study and/or technical admins from 32 partner faculties took part in the survey. Students were not included in our survey. Most respondents stated that a switch to a digital semester had worked, the use of e-learning increased compared to previous semesters and that most courses could be converted, with the exception of practical courses, which were largely cancelled. The respondents also indicated that most examinations could still be taken, with the exception of practical examination formats, like Objective Structured Clinical Examinations. However, in the case of face-to-face examinations, strict distance and hygiene conditions had to be obeyed or there had to be a switch to distance-online examinations, which raised many open issues such as equal opportunities of students and attempts at deception.In conclusion, we identified several issues regarding the rapid transition to a digital semester due to COVID-19 which were categorised into the following topics: Face-to-face teaching could not take place, know-how of educators, integrity aspects, technical aspects, additional personnel required, additional time and effort required for implementation of digital teaching. Our study shows that a switch to digital teaching and distance online examinations is feasible, but many problems were encountered concerning academic integrity and basic ethical principles still need to be solved. In order to investigate whether above mentioned issued could be solved one year after the transition to a digital semester, we conducted a second survey in which the 32 initially surveyed institutions were questioned again. (shrink)

Konstantin Pollok offers the first book-length analysis of Kant's theory of normativity that covers foundational issues in theoretical and practical philosophy as well as aesthetics. Interpreting Kant's 'critical turn' as a normative turn, he argues that Kant's theory of normativity is both original and radical: it departs from the perfectionist ideal of early modern rationalism, and arrives at an unprecedented framework of synthetic a priori principles that determine the validity of our judgments. Pollok examines the hylomorphism in Kant's theory (...) of normativity and relates Kant's idea of our reason's self-legislation to the 'natural right' tradition, revealing Kant's debt to his predecessors as well as his relevance to contemporary debates on normativity. This book will appeal to academic researchers and advanced students of Kant, early modern philosophy and intellectual history. (shrink)