The Schur-Zassenhaus Theorem is one of the fundamental theorems of finite group theory. Here is its statement:Fact1.1 (Schur-Zassenhaus Theorem). Let G be a finite group and let N be a normal subgroup of G. Assume that the order ∣N∣ is relatively prime to the index [G:N]. Then N has a complement in G and any two complements of N are conjugate in G.The proof can be found in most standard books in group theory, e.g., in [S, Chapter 2, Theorem 8.10]. (...) The original statement stipulated one ofNorG/Nto be solvable. Since then, the Feit-Thompson theorem [FT] has been proved and it forces eitherNorG/Nto be solvable. (The analogous Feit-Thompson theorem for groups of finite Morley rank is a long standing open problem).The literal translation of the Schur-Zassenhaus theorem to the finite Morley rank context would state that in a groupGof finite Morley rank a normal π-Hall subgroup (if it exists at all) has a complement and all the complements are conjugate to each other. (Recall that a groupHis called aπ-group, where π is a set of prime numbers, if elements ofHhave finite orders whose prime divisors are from π. Maximal π-subgroups of a groupGare called π-Hall subgroups. They exist by Zorn's lemma. Since a normal π-subgroup ofGis in all the π-Hall subgroups, if a group has a normal π-Hall subgroup then this subgroup is unique.)The second assertion of the Schur-Zassenhaus theorem about the conjugacy of complements is false in general. As a counterexample, consider the multiplicative group ℂ* of the complex number field ℂ and consider thep-Sylow for any primep, or even the torsion part of ℂ*. LetHbe this subgroup.Hhas a complement, but this complement is found by Zorn's Lemma (consider a maximal subgroup that intersectsHtrivially) and the use of Zorn's Lemma is essential. In fact, by Zorn's Lemma, any subgroup that has a trivial intersection withHcan be extended to a complement ofH. Since ℂ* is abelian, these complements cannot be conjugated to each other. (shrink)

One of the purposes of this paper is to prove a partial Schur-Zassenhaus Theorem for groups of finite Morley rank.Theorem 2.Let G be a solvable group of finite Morley rank. Let π be a set of primes, and let H ⊲ G a normal π-Hall subgroup. Then H has a complement in G.This result has been proved in [1] with the additional assumption thatGis connected, and thought to be generalized in [2] by the authors of the present article. Unfortunately in (...) the last section of the latter paper there is an irrepairable mistake. Here we give a new proof of the Schur-Zassenhaus Theorem using the results of [2] up to the last section and a new result that we are going to state below.The second author has shown in [11] that a nilpotentω-stable group is the central product of a divisible subgroup and a subgroup of bounded exponent, generalizing a well-known result of Angus Macintyre about abelian groups [8]. One could ask a similar question for solvable groups: are they a product of two subgroups, one divisible, one of bounded exponent? One is allowed to be hopeful because of the well-known decomposition of the connected solvable algebraic groups over algebraically closed fields as the product of the unipotent radical and a torus. (shrink)

A recent proposal by Norton (2003) to show that a simple Newtonian system can exhibit stochastic acausal behavior by giving rise to spontaneous movements of a mass on the dome of a certain shape is examined. We discuss the physical significance of an often overlooked and yet important Lipschitz condition the violation of which leads to the existence of anomalous nontrivial solutions in this and similar cases. We show that the Lipschitz condition is closely linked with the time reversibility of (...) certain solutions in Newtonian mechanics and the failure to incorporate this condition within Newtonian mechanics may unsurprisingly lead to physically impossible solutions that have no serious metaphysical implications. ‡I thank Steven Savitt of the Philosophy Department at the University of British Columbia for drawing my attention to the Lipschitz condition, and Alexei Cheviakov of the Mathematics Department at the University of British Columbia for useful discussions. †To contact the author, please write to: Department of Philosophy, University of British Columbia, Vancouver, BC, V6T 1Z1, Canada; e-mail: korolev@interchange.ubc.ca. (shrink)

The singularity arising from the violation of the Lipschitz condition in the simple Newtonian system proposed recently by Norton (2003) is so fragile as to be completely and irreparably destroyed by slightly relaxing certain (infinite) idealizations pertaining to elastic phenomena in this model. I demonstrate that this is also true for several other Lipschitz-indeterministic systems, which, unlike Norton's example, have no surface curvature singularities. As a result, indeterminism in these systems should rather be viewed as an artefact of certain infinite (...) idealizations essential for these models, depriving them of much of their intended metaphysical import. (shrink)

A recent proposal to solve the halting problem with the quantum adiabatic algorithm is criticized and found wanting. Contrary to other physical hypercomputers, where one believes that a physical process “computes” a (recursive-theoretic) non-computable function simply because one believes the physical theory that presumably governs or describes such process, believing the theory (i.e., quantum mechanics) in the case of the quantum adiabatic “hypercomputer” is tantamount to acknowledging that the hypercomputer cannot perform its task.

O objetivo deste artigo é propor, de modo simples e saudável, uma releitura transformadora na relação entre os ministérios ordenados e a missão leiga, sobretudo no tocante à espiritualidade laical como colaboração eclesial. Com efeito, desde o tempo de Jesus, o protagonismo leigo, como cooperador à evangelização sempre foi ressaltado e muito bem aproveitado pelo Mestre; dessa forma, nota-se o quanto a Igreja carece hoje dessa ajuda primordial. Não por menos, o Concilio Vaticano II, no decreto Apostolicam Actuositatem, diz que (...) o fiel leigo é indispensável á missão da Igreja. Assim, entre tantas orientações, o mesmo decreto convoca a renovar e valorizar o ardor missionário com o apostolado leigo no interior da Igreja. Nesse sentido, é urgente a aplicação do pedido solicitado no Concílio Vaticano II para os tempos atuais, visando à sua concretização e não ficar somente em uma longínqua teoria. É nesta óptica, que a V CELAM, realizada em Aparecida, enfatiza mais uma vez a indispensabilidade do leigo como colaborador profícuo na missão eclesial. Por fim, vemos em muito a realização exemplar de muitos fiéis leigos batizados em seu exercício de ministros não-ordenados que oferecem subsídios riquíssimos para santificar a vida na Igreja. (shrink)

COSTA, Alexandre da. Fundamentos da bioética: estudo sobre o pensamento de Hugo Tristram Engelhardt Jr. FERREIRA, Amauri Carlos. O imaginário religioso e modos de vida urbana: experiência e memória da Juventude Católica em Belo Horizonte – MG, anos 80. GONÇALVES, Davidson Sepini. O Panóptico de Jeremy Bentham: por uma leitura utilitarista. GÓIS, Aurino José. Parque Municipal de Belo Horizonte: público, apropriações e significados. FARIA, Paulo Antônio Couto. Teologia no limiar da filosofia: a modernidade e o encontro fé e razão (...) na obra de Henrique Cláudio de Lima Vaz. (shrink)

TOPOGRAPHICAL MISSIONS ΤΟ LATO I (2005-2007): A CRITICAL ANALYSIS OF THE PLAN BY J. DEMARGNE AND V. SEYK (1901) In the years 2005 and 2007 the site of Lato in Crete was the object of three new topographical and geomorphological study campaigns. The works carried out over the entire site permitted in particular the analysis of the only to date available complete plan of the city, that of J. Demargne and the architect V. Seyk undertaken in 1900. The objectif was (...) to establish its documentary interest and limits in use, and thus better prepare new measurements and guide renewed field work. To do this, it was first necessary (I) to retrace the history of previous graphic documentation, (II) to analyse the work of J. Demargne and V. Seyk, so as (III) to gauge its value against the standards of current research, and (IV) to establish its interest in terms of the cultural resource management of the site. A second paper to appear in BCH will develop, on basis of a new documentation, the urban and morphological analysis of the remains of Lato. (shrink)

La polémique entre V. Soloviev et L. Lopatine met en lumière les recherches de la philosophie russe sur son mode propre de compréhension du Moi. Pour Soloviev, on ne peut attribuer au sujet de la conscience en tant que tel une réalité autre que phénoménologique. Lopatine propose une variante, proche de Leibniz, selon laquelle le Moi est une conscience subjective, présente aux différents niveaux du développement spirituel. Cette interprétation est reprise et développée, dans une certaine mesure, par N. Losski. G. (...) Chpet tire un bilan de la discussion, en posant le caractère « communautaire » [ obščnost ’] particulier du Moi, qui se réalise non par la « généralisation » [ obobščenie ] mais par la « communication » [ obščenie ]. (shrink)

This is a long-awaited reprint of the major work of the late Alexandre Koyré, one of the greatest masterpieces of the history of Western philosophy. The early nineteenth century saw a revival of Boehme studies but even the commentaries of Franz von Baader could not be substituted for a scholarly synthesis of Boehme's thought. Boehme is a universe of his own, and only the immense learning of a man like Koyré, with his rare ability to synthesize and clarify, could (...) have done justice to him. Through and beyond the rich and baroque splendor of the cosmic poetry of the Dawn of the Mysterium Magnum, we see the birth of the modern philosophical spirit. What Boehme offers us is a philosophy of freedom, and, despite the modesty of his comparisons, Koyré does not fail to show how all this anticipates the greatest Idealistic systems.--M. J. V. (shrink)

Zusammenfassung Der Beitrag widmet sich der Entstehung des Faches Religionsgeschichte in Frankreich. Die Vorgeschichte zu diesem Prozess beginnt mit Benjamin Constants Religionsphilosophie der 1810–1820er Jahre, in der die lokalen und diachronen Veränderungen des allgemein menschlichen religiösen Gefühls als ein Schlüssel zur Religionsgeschichte verstanden wurden. Nach einer langen Pause wird das Thema des religiösen Gefühls in Albert Révilles liberaltheologischem Projekt wieder aktuell. Ausgehend von Schleiermachers Voraussetzungen hoffte Réville dadurch die Apologetik zu modernisieren wie auch den Weg zum theologischen Inklusivismus zu bahnen. (...) Sein Sohn Jean, ebenfalls Theologe, neutestamentlicher Forscher und Sentimentalist, arbeitete mit dem Vater zusammen an der Institutionalisierung des Faches Religionsgeschichte in Frankreich. Albert Réville leitete von 1886 bis zu seinem Tod 1906 die fünfte (religionswissenschaftliche) Sektion der École Pratique des Hautes Études, gleichzeitig war Jean Réville seit 1884 Herausgeber der Fachzeitschrift Revue de l’histoire des religions. Révilles theoretischer Standpunkt wurde von É. Durkheim und seinen Gleichgesinnten H. Hubert und M. Mauss, die die weitere weltanschauliche Säkularisierung förderten, nach 1898 stark kritisiert. Diese Serie von Erwiderungen zeigt die Kluft zwischen der Methodologie der (dem Ursprung nach) evangelischen Religionsgeschichte und der durkheimischen Religionssoziologie. (shrink)

According to a common philosophical intuition, the deep nature of things is hidden from us, and the world as we know it through perception and science is somehow shallow and lacking in reality. For all we knwo, the intuition goes, we could be living in a cave facing shadows, in a dream or even in a computer simulation, This “intuition of unreality” clashes with a strong, but perhaps more naive, intuition to the effect that the world as we know it (...) seems perfectly real. Shadows, dreams, or informational structures appear too unreal to be identical to the world as we know it! This clash between the two intuitions forms the basis of the "problem of reality." At the turn of the nineteenth century psychiatrists encountered patients they referred to as “metaphysician doubters” who constantly questioned the reality of the world. This essay draws on the study of these patients to reject, and indeed diagnose, the intuition of unreality and recent metaphysical doctrines drawing on it, such as structuralism, digitalism, and virtual realism. (shrink)

Avne Shelomoh -- Zikhron Shelomoh -- Daʻat Shelomoh.

The article shows that Borisov’s direct solution to the problem of skepticism about meaning using a special type of introspection is associated with the assumption of the agent’s direct access to their own consciousness. This assumption has two complicating consequences: the analogy with Moore’s paradox and the Platonic concept of meaning. It is also shown that direct access to meaning as a way of Borisov’s direct solution of the skeptical paradox significantly uses the performativity of the speech act, narrowing the (...) scope of analysis of the original problem. The little-studied problem of distinction in the analysis of the skeptical paradox of meaningful and formalized mathematics is noted. (shrink)

Sexuality education is fundamental in higher and tertiary education institutions (HTEIs). Evidence suggests that its effective education is through translations into the first language of learners. However, in global and multilingual cultural communities such as HTEIs, the foundations for these translations are still a researchable area. Notably, in HTEIs adolescents, young adults and adults co-exist and therefore, any translations must be toned to balance across these groups. The aim of this study was to establish strategies that could enable sexuality educators (...) to effectively transfer information that is steeped in indigenous language, religious and cultural meaning without precipitating stigma and taboo issues. The study setting was the National University of Science and Technology where a cross section of indigenous cultures, languages and religions co-existed with other global cultures. A University Community-based Participatory Research (CBPR) methodology was administered by the researchers using a Delphi research approach to students and staff. Multilingual, multilayered, multireligious, and multicultural nature of the setting presented serious challenges that compromised the prevention of stigma and taboo issues when dealing with sexuality education. We recommend that the strategy to present sexuality education in indigenous languages to the generality of HTEIs population should, in the first instance, involve systematic identification of appropriate interventions that are religious, cultural, and language-specific. Contribution: This research reveals paramount ethical and religious violations that have a potential to precipitate opportunistic sexual relationships that may lead to impediments in capacity building for learners. This research can be utilised by academics on the field of Practical Theology, specifically youth ministry and pastoral care. (shrink)

Nous proposons une logique épistémique quadrivalente AR4.

Peut-on prouver que l’âme raisonnable est par elle-même et essentiellement forme du corps? C’est pour résoudre cette question que des générations de lecteurs d’Averroès recourent à la distinction entre forme inhérente et forme assistante. On examine l’histoire de cette distinction dans l’après-coup du concile de Vienne (1312) et du concile de Latran V (1513), dans sa triple dimension noétique, ontologique et anthropologique. On présente les sources et les divers aspects de la théorie averroïste de la forme assistante, de Siger de (...) Brabant à la scolastique tardive et à la première modernité, selon laquelle l’intellect n’est ni forme inhérente ni moteur séparé, mais forme séparée. (shrink)

L’auteur relève les différents enjeux de la médecine prédictive pour le secteur de l’assurance.

The advent of the Web is one of the defining technological events of the twentieth century, yet its impact on the fundamental questions of philosophy has not yet been explored, much less systematized. The Web, as today implemented on the foundations of the Internet, is broadly construed as the space of all items of interest identified by URIs. Originally a space of linked hypertext documents, today the Web is rapidly evolving as a universal platform for data and computation. Even swifter (...) is the Web‐driven transformation of many previously unquestioned philosophical concepts of privacy, belief, intelligence, cognition, and even embodiment in surprising ways. The ensuing essays in this collection hope to explore the philosophical foundation of the World Wide Web and open the debate on whether or not the changes caused by the Web to technology and society warrant the creation of a philosophy of the Web. (shrink)

Trata-se da tradução de um ensaio clássico publicado por Rudolf Carnap na revista Erkenntnis. A tradução é precedida por um texto de apresentação, que situa o ensaio e sua importância no contexto da filosofia contemporânea e na obra de Carnap. No ensaio, Carnap indica as principais características que distinguem o que ele chama de nova lógica (a lógica simbólica matemática derivada das obras de Frege, Peano e Hilbert, entre outros) da lógica filosófica tradicional e explica a sua importância como novo (...) método do filosofar. (shrink)

This article aims to enhance social technology as a resource that induces education and well-being in maternal and child health, more specifically in contexts of social vulnerability. This is an action research, with social technology characteristics, developed between July/2022 and December/2023, with 17 women (pregnant and postpartum women) from a vulnerable community in the central region of Rio Grande do Sul. Based on education in health and in an interprofessional approach, the social technology developed and called “Endowing lives” is the (...) result of demands previously identified, discussed and implemented with the research participants and local health professionals. The social technology developed expanded interprofessional possibilities, promoted preventive health measures and contributed to the empowerment of pregnant and postpartum women in decision-making. (shrink)

Wedin considers the relation between the ontological commitment in the Categories and the semantical theory of underlying ontological configurations for standard categorical statements. According to Wedin, Aristotle's fourfold division of beings, which divides things according to whether they are, or are not, said of, and/or present in a subject, is a meta‐ontology that is concerned with beings per se, i.e. the fundamental things that are. Wedin explains that the primacy of c‐substance involves an asymmetry in the relation between c‐substance and (...) everything else, or between the substantial and the nonsubstantial. This is because there is an ontological dependence of non‐substances, and also of secondary substances, on substances: everything is either said of, or in, primary substance. The argument of this chapter, then, is that the world of the Categories is a world of individuals: all ontological relations needed for semantics can be accommodated by appeal to individuals only. (shrink)

Wedin argues that Aristotle makes form the substance of c‐substances because it is the essence of the c‐substance. Much of this chapter consists of a careful examination of a passage in Metaphysics Zeta 4, which Wedin calls the ‘New Primacy Passage’, that is crucial to Wedin's overall thesis, because here Aristotle appeals to a notion of definitional primacy, as opposed to the ontological primacy of the Categories. Z.4 focuses on this claim that form must be essence: Wedin argues that essence (...) is a certain kind of form, a form of a genus ; this does not mean ‘species’, as some commentators have thought. This is because the species is a combination of form and matter, whereas the genous eidos, Wedin argues, is the formal part only of the definition that applies to the thing. On Wedin's account, Aristotle introduces the notion of explanatory primacy of form in Z.4. (shrink)

Wedin offers an interpretation of Metaphysics Zeta 13, a very important and difficult chapter, where Aristotle apparently denies that substance is a universal, having, on most accounts, already claimed that form is substance, and that form is a universal. This interpretation of the argument of Z.13, Wedin argues, threatens the possibility of attaining a definition of substance, and places in doubt what has gone before in the treatise. According to Wedin, what Aristotle is concerned with in Z.13 is not the (...) denial that substance is a universal but rather with the denial that anything predicated universally of a c‐substance is the substance‐of the c‐substance, which Wedin calls ‘Weak proscription’. In Wedin's account of Z.13, then, Aristotle is continuing to pursue issues first raised in Z.10–11 that have to do with the relations between form and definition, and form and the universal. Wedin also argues that the dilemma at the conclusion of Z.13, regarding the definability of substance, is resolved in Z.16, with the notion of ‘Dual Complexity’, according to which the parts of a form exist potentially in the form, just as the parts of the c‐substance exist potentially in the c‐substance. (shrink)

Wedin addresses the debate over whether nonsubstantial individuals, that inhere in a subject but are not said of a subject, i.e. accidents, such as the pallor of Socrates, are nonrecurring particulars or a kind of determinate universal. Wedin examines the secondary literature on this topic and divides it into two schools of thought, determined by the contributions of J.L. Ackrill and G.E.L. Owen. According to Ackrill, individuals in non‐substance categories are particular to the substance they are in; Owen critiques Ackrill's (...) view, and proposes that these items can recur in more than one subject and hence are a sort of universal. Wedin finds Owen's thesis unsatisfactory, even after supplementing it with an improved version due to Michael Frede; instead, Wedin argues for a revised version of Ackrill's interpretation of nonsubstantial individuals as nonrecurrent particulars. According to Wedin, Aristotle is committed to individuals only—e.g. to Socrates and to the particular bit of pallor in him: this conclusion has an important bearing on the ontological status of individuals and on the primacy of substance to nonsubstantial items. (shrink)

Wedin considers the problem of the compatibility of the Categories account of primary substance with the theory of substantial form of the Metaphysics. Wedin collects from the secondary literature the most important arguments for incompatibilism, and offers some proposals for restoring their harmony. While admitting the evident differences in the way Aristotle treats the question of substance in each treatise, Wedin is keen to argue that these differences are not sufficient to conclude that the treatises are incompatible. Wedin singles out (...) for particular attention, and criticism, Michael Frede and Gunther Patzig's account of Metaphysics Zeta, according to which the primary substance of the Metaphysics and the basic subject of predications is the form. Wedin considers two ‘philosophical’ arguments and one ‘Aristotelian’ argument for the subjecthood of forms, and argues that the textual evidence does not support the claim that form is the subject of accidents. (shrink)

Chapters 10 and 11 are critical to the argument of Metaphysics Zeta: these chapters are concerned with the purification of form. Z.10 introduces the apparatus of part and whole and consists of an argument to the end that form and its parts have priority over the other internal structural components of c‐substances, i.e. matter and the compound of form and matter; while in Z.11 Aristotle argues that form and its parts cannot involve any admixture of matter. Wedin argues that the (...) causal role of form presupposes its purity: if form is to explain why a certain portion of matter constitutes a c‐substance of a given kind, then matter—whether this latter is understood as functional, or remnant matter—cannot already be contained in the form. This is the ‘purity thesis’, as Wedin calls it: matter cannot be included in the definitions of natural organisms, Wedin points out, because that would make the explanandum a part of the principle that explains it. Wedin also argues that form must be sufficiently complex to provide definitions of the natures of particular compounds, which are complex, even though form itself is a kind of universal. (shrink)

In the Metaphysics, Aristotle often says that ‘form is substance’: in this chapter, Wedin argues that ‘substance’ in this context means the ‘substance‐of’ c‐substances. Wedin begins by examining Aristotle's use, and retention, of the framework of the Categories in Metaphysics Zeta, before turning to discuss Z.3, which is crucial to understanding the relation between the Categories and Metaphysics theories of substance, because it is usually thought that here Aristotle departs from the substance of the Categories. Wedin denies that Z.3 involves (...) a rejection of the Categories subjecthood criterion for primary substance: Aristotle rejects only the claim that one thing is the substance of another simply if it is the primary underlying subject of the other. Wedin argues that in Z.3 Aristotle introduces the idea of the ‘substance‐of’ a thing, and identifies as candidates for the substance of c‐substances the internal structural components form, matter, and the compound of form and matter. (shrink)