The negative impacts of agriculture on the environment and the inequity that limits access to healthy food for the entire population impede sustainable development. This article reflects contributions to food security and alternatives for transitioning to sustainable food systems. It is concluded that food, as a human right, is a complex and transdisciplinary issue, which must be integrated as a transversal axis in the economic, social, environmental, governance, and cultural dimensions to contribute to sustainable development and therefore the convenience of (...) making the transition from the concept of food security to that of food sustainability. (shrink)

“The world of life which is comprised of the lithosphere, the hydrosphere and the atmosphere”: this definition of the biosphere is not complete since it does not express the determining influence of living organisms on its composition, on its structure and on the processes of its continuing evolution. The part of living matter in the biosphere is relatively small (about 0.25%), but this part has a considerable influence on its structure.The biosphere should be considered as the universal source of all (...) food products without exception. Mankind's ability to feed itself depends on the productivity of this biosphere in the first place. Moreover, its condition determines not only the quantity but also the quality of nourishment. The problem is a critical one today because of the increasing pollution of the biosphere by products poured into it by various human activities. (shrink)

Esta reflexión evidencia cómo desde los años sesenta Amílcar Osorio produce una práctica artística en procura de la desinstitucionalización de la literatura y del arte, al situar sus objetivos estéticos no solo en las letras como posibilidad narrativa y poética, sino en la utilización de lo visual, el espacio y la vida misma como recurso artístico. Con esto el autor consigue difuminar las fronteras entre literatura, artes visuales y de acción, y logra producir lo que se puede considerar hoy una (...) práctica intermedial, al tomar estrategias propias del arte conceptual que le permiten conectar la vida cotidiana, la literatura, las ideas como expresión artística, la imagen y la performance. (shrink)

O artigo analisa, a partir sobretudo do pensamento de Hannah Arendt, o desafio que representa para a política “viver junto”. Embora a expressão origine-se com o ensaísta francês Roland Barthes, o objetivo do artigo é quadruplo: (1) apresentar seu fundamento ontológico na condição humana ou existencial de “ser-com”, ou seja, de ser junto aos outros, pensada desde Martin Heidegger; (2) descrever seu sentido político pela conjugação entre isonomia e diferença na forma da pluralidade pela qual cada pessoa pode aparecer singularmente (...) em atos e palavras, de acordo com uma liberdade frente a quaisquer predeterminações; (3) demonstrar como a recente situação da pandemia de Covid-19 radicalizou o impasse de viver junto – e separado – em sociedade, particularmente no caso do Brasil, colocando em relevo uma dimensão coletiva da liberdade pela interdependência entre os seres humanos; e (4) apontar a importância da forma de governo da república, mas também os perigos da sua fragilização nas democracias contemporâneas no que se refere à dificuldade de responder – como viver junto? (shrink)

This article summarizes the recommendations concerning robotics as issued by the Commission for the Ethics of Research in Information Sciences and Technologies (CERNA), the French advisory commission for the ethics of information and communication technology (ICT) research. Robotics has numerous applications in which its role can be overwhelming and may lead to unexpected consequences. In this rapidly evolving technological environment, CERNA does not set novel ethical standards but seeks to make ethical deliberation inseparable from scientific activity. Additionally, it provides tools (...) and guidance for researchers and research institutions. (shrink)

In this paper we propose that the term skill acquisition, as commonly used in traditional psychology, and the philosophy, education, movement science and performance development literatures, has been biased by an organismic asymmetry. In cognitive and experimental psychology, for example, it refers to the establishment of an internal state or representation of an act which is believed to be acquired as a result of learning and task experience. Here we elucidate an ecological perspective which suggests that the term skill acquisition (...) may not refer to an entity but rather to the emergence of an adaptive, functional relationship between an organism and its environment, thus avoiding an inherent organismic asymmetry in theorizing. In this respect, the terms 'skill adaptation' or 'skill attunement' might be more suitable to describe this process. (shrink)

This chapter provides a brief history of Kantianism in Russia since the late eighteenth century and identifies the main themes of Kantianism in Russia. It considers the reasons for the uneven and intermittent spread of Kantianism, the main motives behind the fierce resistance to Kantianism within the framework of certain trends of Orthodox thought, and the ways in which this philosophical polemic was reflected in the Russian literature. The achievements of Russian Kantianism are analyzed with attention to both its undeniable (...) merits and its weaknesses and inconsistencies. In addition, the scope and scale of Russian Kantianism will be compared with Schellingism and Hegelianism in Russia. On the basis of this comparison, I will argue against the stereotype that Russian philosophy is resistant to Kant. (shrink)

La Base de français médiéval (BFM) fait partie des corpus de français médiéval (9e-15e s.) les plus anciens et les plus utilisés par les linguistes diachroniciens et plus largement par tous ceux qui s’intéressent à l’histoire du français. Elle est le fruit d’une collaboration entre linguistes-philologues et spécialistes de la méthode textométrique implémentée dans la plateforme TXM. L’article présente un état des lieux du corpus BFM2022 focalisé sur la représentativité et l’interopérabilité des données. Il illustre l’apport des outils numériques pour (...) l’équilibrage des données et présente la stratégie de standardisation multi-niveau (structure textuelle, références, métadonnées, annotations) ayant permis à la Base de s’intégrer à des corpus diachroniques plus étendus pour des recherches en diachronie longue. (shrink)

Critics attack normative ethical stakeholder theory for failing to recognize the special moral status of shareholders that justifiesthe fiduciary duties owed to them at law by managers. Stakeholder theorists reply that there is nothing morally significant about shareholders that can underwrite those fiduciary duties. I advance an argument that seeks to demonstrate both the special moral status of shareholders in a firm and the concomitant moral inadequacy of stakeholder theory. I argue that (i) if some relations morally requirefiduciary duties, and (...) (ii) the shareholder-manager relation possesses the features that make fiduciary duties morally necessary to thoserelations, then (iii) stakeholder theory is morally lacking. (shrink)

Introduction. The problems of state and local governance in sparsely populated and rural areas is relevant for the Russian Federation due to the presence of depressed areas, depopulation of the countryside, small towns, monotowns, migration of the rural population to large cities, regional capitals, other regions and abroad. These processes are typical for many other modern states. Solving the problems of rural and sparsely populated areas includes providing socially significant services, protecting the health and safety of residents, developing education, creating (...) and maintaining social infrastructure, and creating jobs. The purpose of the article is to identify the most important management problems in rural and sparsely populated areas and reveal possible solutions to these problems using the example of Great Britain. Methods. The research is based on a systematic approach to management in rural and sparsely populated areas. Analysis of factual data, legal sources, published survey results, foreign Internet sources. Comparative analysis of problems and measures of state policy in different states. Scientific novelty of the research. The author highlights the current measures taken in the UK at the central, local levels in order to overcome the problems of rural and sparsely populated areas. These activities as a basis for developing practical recommendations may be important for solving similar problems in Russian regions, including in the context of the COVID-19 epidemic and economic problems in the near future. Results. As a result the author identifies problems in the field of management in rural and sparsely populated and hard-to-reach areas, as well as possible directions of state policy in the UK and Russia to overcome these problems. Conclusions. The most important direction of state policy for solving the problems highlighted in the study is the development of local interests of the community, the integration of state support measures and local events. As measures aimed at solving social and infrastructural problems of sparsely populated areas in the UK, one can single out government programs implemented at the national and regional levels with the participation of industrial enterprises and businesses, a grant mechanism for the implementation of financial support, combined with the empowerment of local communities. There is no such policy in Russia yet. (shrink)

Os textos reunidos neste livro foram originalmente apresentados no Colóquio Internacional Kátharsis, realizado pelo programa de pós-graduação em Filosofia da FAFICH/UFMG. Os textos têm como tema compartilhado o conceito de catarse e apresentam perspectivas bem distintas - vão desde a origem do conceito na Grécia antiga até sua atualidade no mundo contemporâneo, levando em consideração seus diferentes momentos e apresentando grande diversidade nos enfoques adotados pelos colaboradores.

Este artigo intenta apresentar uma visão panorâmica da complexidade histórica das relações entre sociedade, estado e meio ambiente no Brasil. Argumenta que a genealogia dessas relações evidencia uma trajetória não linear, multifacetada e conflituosa. Há diversas tradições no palco dos confrontos políticos atuais: o Brasil se destaca por uma longa história de destruição, que remonta ao início da colonização do território, mas também por uma fértil tradição de pensamento conservacionista, significativas lutas socioambientais, e pelo pioneirismo nas pautas globais em prol (...) do ambiente. Recuperar e valorizar a complexidade das relações entre sociedade e ambiente pode ser um ato decisivo na construção de caminhos futuros diversos para a questão socioambiental no Brasil, projetando e demonstrando a riqueza e o vigor de diferentes atores e práticas dissonantes. (shrink)

ObjectiveTo provide insights on emergent ethical tensions experienced by mental health practitioners during system re-organisation, which is sufficiently grounded in empirical data at the local level to inform policy on recovery at institutional and provincial levels.MethodEthnographic methods using narrative and critical phenomenological resources over 24 months.FindingsEveryday ethical tensions emerged at the confluence of different experiences of time, for example, how a context of increasing pressure to decrease patients’ length of stay at the hospital challenged efforts to listen to and advocate (...) for what mattered to patients and maintain the integrity of interventions. In this context, practitioners drew on clinical language and that of personal recovery to strategically ‘push back’, ‘play with’ or ‘take back’ time.DiscussionExamining everyday practices through ethnographic methods can illuminate the everyday ethical tensions that arise when mental health professionals and psychiatrists grapple with, often competing, goods. Critical phenomenological resources can help expand the structural considerations in empirical ethics, excavate underground practices and raise questions about the conceptual categories undergirding normative ethics. Experiencing-with practitioners in clinical contexts as they encounter and creatively resolve ethical tensions also propose a normative ethics of possibility, to help bridge the gap between empirical and normative ethics.ConclusionFocus on the relationship between policy, temporal practices and ethics suggests a reconfiguration of time and re-imagination of ethics in institutional settings in ways that can ultimately benefit patients and professionals alike. (shrink)

The article is devoted to the well-known dispute between R. Carnap and W.V.O. Quine on the meaning of statements with names of abstractions, which also revealed their disagreements on the more general question of the nature of the dependence of ontology on the choice of language of knowledge. According to Quine, the choice of language carries with it certain ontological commitments – judgments of existence that must be true for anyone who appropriately uses the language in question. The language of (...) abstractions (using appropriate names and indications) is widely used not only in philosophy and everyday communication, but also in the sciences, including natural sciences. The names of abstractions (or, alternatively, quantification by corresponding entities) cannot be completely excluded from science, as Carnap, in particular, points out. He also considers it wrong to attribute to a scientist with empiricist views the belief in the existence of something that he, as an empiricist, is not ready to consider existing. In his view, the choice of language (framework) does not carry any ontological obligations: it determines what should be the correct answer to the so-called internal questions of the theory but does not affect metaphysical questions. Carnap interprets meaningful statements about abstractions as analytical truths, while Quine believes that most references to abstractions are removable from the language of science, and those that are not removable create additional ontological obligations, which, however, for some reason say nothing about reality itself. But why this is so, if the theory implicating them claims to describe reality, is not clear. This debate about the role of judgments about abstractions in scientific knowledge gave rise to a whole branch of metaphysical and ontological research, best known as metaontology. The main parties in this dispute are realists, who interpret irreducible abstractions as part of reality and denotations of certain names, and anti-realists, who, as a rule, deny the connection of statements with such names with reality, treating them as pseudo-statements or something similar. The solution to the problem, which is proposed in this article, consists in abandoning the belief, widespread both in philosophy and in everyday thought, which can be generally called “The theory of reference” and which consists in the fact that the contribution of names and certain other types of expressions to communication is their denotations. If we assume that names have no denotations at all and their semantic contribution to statements is only their senses or something similar, then the names of abstractions in this respect will be no different from other types of names. In this case, it would be no need to either assume that they designate some “Platonic” entities in order for some statements with them being true, nor interpret these judgments as pseudo-statements or as truths of some special kind that are not related to reality. The interpretation of statements with such names and their evaluation will not pose any special problem for the empiricist with this approach. (shrink)

‘I am not data’ has been produced in collaboration with a creative coder from the Netherlands. Over a period of six months around 4600 images were chosen from approximately 20,000 images of LatinX femmes. The images were then fed into a generative adversarial network (GAN) simulation that produced this film. The resulting work seeks to elucidate a process of lumping together foreign bodies as a method of amalgamation that works to create ‘new’ information. It exists in tandem with ‘Second Nature’, (...) a body of work on Mexican femme bodies and algorithmic web searches, from which some images are included in this article. The process behind the GAN used for this film becomes a mere reference to a human shape. Its processes of synthesis work as a metaphor for systems of human classification in which the bodies of foreigners become fuel for monstrous stereotypes. There is a sense of history repeating itself through the ways that these technological tools are used in artificial intelligence (AI) which launches questions regarding equality and progress in pursuit of social justice. (shrink)

This paper presents a new theoretical justification for the Cournot–Bertrand model to arise in equilibrium when firms have, at the outset, the same cost structure and sell symmetrically differentiated products. The Cournot–Bertrand model assumes some firms compete on price, adjusting their production to meet demand, while others set quantities and let their price adjust until market equilibrium is reached. We show that this may occur endogenously due to the possibility of entry, which may be deterred when some of the incumbents (...) decide to set prices, while others free ride on this behavior and choose quantities. (shrink)

O estudo do valor é indissociável da análise dos conceitos de bom e Bem, pelo que qualquer base metodológica que lhe sirva de alicerce tem de partir do exame destes. Assumindo os riscos do sem-sentido, recusamos uma redução relativista do bom predicativo a bom atributivo e de bom a bom para, bom do ponto de vista de, bom relativo a, e avançamos para a discussão de algumas tentativas de identificação do bom, nomeadamente com o prazer, o desejo e o escolhido. (...) Seguindo-se o esforço de mostrar como bom é insusceptível de uma remissão para o psicológico ou para o subjectivo, o ensaio procura evidenciar a ideia de Bem como o conceito fundamental e indefinível para a compreensão do bom, a partir da sua estruturação teleológica. Propomo-nos, portanto, estabelecer bom = aquilo que remete para o Bem, sendo o conceito de valor o reflexo da relação mediada com o Bem, indissociável do domínio ético. Por fim, consagra-se a possibilidade de uma nova fundação de um método na teoria do valor baseado nos preceitos alcançados, distinguindo-se o estudo do valor em analítico, substantivo e prático. The study of value is inseparable from the analysis of the concepts of good and the Good, so any methodological basis which serves as groundwork must take from these. Assuming the risks of non-sensicality, we propose to refuse a relativistic reduction of predicative good to attributive good and of good to good for, good from the point of view of and good-relative-to and discuss some attempts to identify good, particularly with pleasure, desire and choice. Following the effort to show how good is not liable to be ascribed to the psychological or subjective, the essay seeks to highlight the idea of the Good as the fundamental concept - therefore undefinable - to understand good as from its teleological structure. We therefore propose to establish good = what refers to the Good, and the concept of value as one which reflects the mediated relationship with the Good, inseparable from the ethical. Finally, we establish the possibility of a new foundation of a method of the theory of value based in the reached percepts, distinguishing between analytical, substantive and practical inquiries on value. (shrink)

We argue that the Rawlsian social contract argument advanced for stakeholder theory by R. Edward Freeman, writing alone and with William M. Evan, fails in three main ways. First, it is true to Rawls in neither form, nor purpose, nor the level of knowledge (or ignorance) required to motivate the veil of ignorance. Second, it fails to tailor the veil of ignorance to the fairness conditions that are required to solve the moral problem that Freeman and Evan set out to (...) solve (whereas Rawls’s own use of the device surely tailors the veil of ignorance to the problem of designing a just social order). Third, the argument, considered apart from its claimed Rawlsian pedigree, fails to bolster the stakeholder theory because it fails to demonstrate the rationality of adopting the institutional rules that Freeman and Evan favor. (shrink)

ABSTRACT This article contributes to methodological debates in contemporary critical theory regarding the scope and features of immanent critique. I spell out the philosophical commitments presupposed by this approach to criticism and identify its basic features by comparing it with more recognizable argumentative or interpretative strategies. This comparison yields three immanent-critical requirements – for inherence, contradiction, and access – which bring into relief the heuristic and ampliative character of immanent criticism. Yet, these requirements also imply that “immanent critique” is not (...) a method in any strict sense, since they are multiply interpretable and hence generative of distinctive critical comportments. (shrink)

We study when classes can have the disjoint amalgamation property for a proper initial segment of cardinals. Theorem A For every natural number k, there is a class $K_k $ defined by a sentence in $L_{\omega 1.\omega } $ that has no models of cardinality greater than $ \supset _{k - 1} $ , but $K_k $ has the disjoint amalgamation property on models of cardinality less than or equal to $\mathfrak{N}_{k - 3} $ and has models of cardinality $\mathfrak{N}_{k (...) - 1} $ . More strongly, we can have disjoint amalgamation up to $\mathfrak{N}_\alpha $ for α > ω, but have a bound on size of models. Theorem B For every countable ordinal a, there is a class $K_\alpha $ defined by a sentence in $L_{\omega 1.\omega } $ that has no models of cardinality greater than $ \supset _{\omega 1} $ , but K does have the disjoint amalgamation property on models of cardinality less than or equal to $\mathfrak{N}_\alpha $ . Finally we show that we can extend the $\mathfrak{N}_\alpha $ to $ \supset _\alpha $ in the second theorem consistently with ZFC and while having $\mathfrak{N}_i \ll \supset _i $ for 0 > i < α. Similar results hold for arbitrary ordinals α with |α|= K and $L_{k + ,\omega } $. (shrink)

Mediante un lenguaje paradojal, la obra de Miguel de Unamuno plantea de modo recurrente la cuestión de Dios, especialmente en el libro Del sentimiento trágico de la vida. Lo plantea bajo dos perspectivas: la del Dios pensado y la del Dios sentido. En ambos casos se trata de un Dios personal cuyo encuentro tiene lugar por vía de la intuición vivencial y el recogimiento. Se reconocen allí coincidencias con San Juan de la Cruz, y en general, con la mística al (...) privilegiar el sentimiento frente al entendimiento, la vivencia frente a la racionalidad. (shrink)

Life has semiotic nature; and as life forms differ in their complexity, functionality, and adaptability, we assume that forms of semiosis also vary accordingly. Here we propose a criterion to distinguish between the primitive kind of semiosis, which we call “protosemiosis” from the advanced kind of semiosis, or “eusemiosis”. In protosemiosis, agents associate signs directly with actions without considering objects, whereas in eusemiosis, agents associate signs with objects and only then possibly with actions. Protosemiosis started from the origin of life, (...) and eusemiosis started when evolving agents acquired the ability to track and classify objects. Eusemiosis is qualitatively different from protosemiosis because it can not be reduced to a small number of specific signaling pathways. Proto-signs can be classified into proto-icons that signal via single specific interaction, proto-indexes that combine several functions, and proto-symbols that are processed by a universal subagent equipped with a set of heritable adapters. Prefix “proto” is used here to characterize signs at the protosemiotic level. Although objects are not recognized by protosemiotic agents, they can be reliably reconstructed by human observers. In summary, protosemiosis is a primitive kind of semiosis that supports “know-how” without “know-what”. Without studying protosemiosis, the biosemiotics theory would be incomplete. (shrink)

En los tiempos que corren parece ser que se ha ido gestando un nuevo tipo de sociedad en la que el consumismo es el núcleo moral de la vida. Todo hoy está sometido a la lógica de un mercado que tiene como nota preponderante la seducción; de ahí que lo lúdico y lo estético pretendan operar hoy en día como ejes integradores de la cultura. Embellecerse exteriormente y divertirse han devenido deberes, tanto que la gente suele sentirse avergonzada de trabajar (...) mucho y no gozar más, de no disponer de más tiempo libre para disfrutar más, con lo cual resulta evidente que seguimos viviendo bajo el signo de la desmesura: en la Modernidad vivimos para trabajar, hoy trabajamos para consumir. (shrink)

Vocación es una categoría ética, que alude a la perspectiva en que ponemos nuestra vida y a las preferencias que la van orientando en la praxis cotidiana. En sentido ético, la vocación tiene cuatro notas definitorias: Las elecciones cotidianas, la prudencia, la realización efectiva del proyecto fundamental y la entrega personal y comunitaria a un quehacer, y a éstas hay que adicionarles la vertiente religiosa o trascendente. La tarea moral, consiste en llegar a ser lo que se puede ser, con (...) lo que se es, de donde resulta que el verdadero destino es nuestro ser mismo: «Llega a ser el que eres». La vocación más que un llamado es «un êthos de fidelidad a sí mismo», un programa de vida, un afán de ser responsable y «tomarse en serio la vida», buscando que sea auténtica y plena. (shrink)

We outline the Gödel-McKinsey-Tarski Theorem on embedding of Intuitionistic Propositional Logic Int into modal logic S4 and further developments which led to the Generalized Embedding Theorem. The latter in turn opened a full-scale comparative exploration of lattices of the (normal) extensions of modal propositional logic S4, provability logic GL, proof-intuitionistic logic KM, and others, including Int. The present paper is a contribution to this part of the research originated from the Gödel-McKinsey-Tarski Theorem. In particular, we show that the lattice ExtInt (...) of intermediate logics is likely to be the only constructing block with which ExtS4, the lattice of the extensions of S4, can be formed. We, however, advise the reader that our exposition is different from the historical lines along which some of the results discussed below came to light. Part 1, presented here, deals mostly with structural issues of extensions of logics, where algebraic semantics, though underlying this approach, is used merely occasionally. Part 2 will be devoted to algebraic analysis of the Embedding Theorem. (shrink)

Although the term taxon is one of the most common concepts in biology, a range of its meanings cannot be comprehended by an universal definition. Usually, biologists construe their knowledge of “the same” taxon by substantially different interpretations, so they find themselves in need either to justify this “multiplication of taxon essences”, or to surmount their plurality unifying its interpretations into a single explanation of what a taxon is. In both cases, an ontological status (“reality”) of that taxon is questioned. (...) Therefore, discrepancy between universality of the taxon concept in biology and unavoidable plurality of its interpretations can be regarded as a source of problem of the taxon ontology. The present work aims to clarify the premises of this discrepancy using phenomenological approach. Three ways of the taxon positing (as a class, as a place in the world, and as a individualized body) have been distinguished. Taxon as a class is established by common essence that is shared by a set of living beings. These living beings are regarded as speculative objects beyond an idea of the world, i.e. as objects of the experimental science. A question about ontology of taxon as a class refers to the scholastic problem of universalia; its status can be defined within the scope of the nominalism/realism opposition. Taxon as a place of common appearance of the specimens is regarded in the context of the etiological relations unifying various entities into the entire world. Taxon as a place refers to a certain position in the Natural System that is construed as an etiological map of the world. In this case a specimen of a living being is known as a curiosity, i.e. representant of its relationships as well as of the place of its origin. Ontological status of a taxon as a place is to be clarified within the framework of the natural/artificial opposition. The positing of a taxon as a collective body marked off by limits of joint survival of living beings is characteristic for biology in the strict sense which arose in the very beginning of the 19 century. A taxon as a body established by the techniques of disciplinary power sensu M. Foucault extended from the human bodies to bodies of other living beings. The ontological status of a taxon as a collective body can be defined within the scope of the wild/domesticated opposition. Therefore, the discrepancy between the universality of the taxon concept and the plurality of its interpretations is underlayed by interpenetration of three distinct modi of taxon establishing. Distinguishing between these three modi can clarify sources of ontological problems concerned with the term taxon in each case when they arise. (shrink)

This essay offers a comparative analysis of the notion of trust in Hegel and Confucius. It shows that Hegel’s two senses of trust depend upon his theory of recognition and recognitive struggle. The competitive thrust of Hegel’s account of trust, it argues, introduces a series of problems that cannot be adequately resolved within his theory, since it presupposes the kinds of trusting relations—self-, intersubjective- and world-trust—that it purports to explain. This essay then turns to the Confucian notions of xin 心 (...) and li 理 to address the problems in the Hegelian account. It concludes by outlining the Confucian account’s salience for critical social theory. (shrink)

Nowadays, that part of Amazonia which is situated on Brazilian territory is more and more the focus of attention for communication methods and the international agenda. This enormous expanse of land covered by tropical forest of unequalled beauty, extending over several Brazilian states, possesses an extremely rich biodiversity, with a vast potential reserve of natural resources of all sorts, and inspires admiration as well as inevitable greed. The intensification of human activity in the region has given rise to problems such (...) as deforestation and a resulting loss of organic matter whose importance has yet to be properly evaluated; it has also led to conflict between the different local groups, such as the indigenous population, gold prospectors and the big landowners, and to the degradation of quite extensive areas, thus provoking questions on how best to promote sustained development in the region. (shrink)

We define an appropriate analog of the Morley rank in a totally transcendental homogeneous model with type diagram D. We show that if RM[p] = α then for some 1 ≤ n < ω the type p has n, but not n + 1, distinct D-extensions of rank α. This is surprising, because the proof of the statement in the first-order case depends heavily on compactness. We also show that types over (D,ℵ₀)-homogeneous models have multiplicity (Morley degree) 1.

The dominant research consensus in the history and philosophy of mathematics appears to be that the history of mathematics has little to do with the philosophy of mathematics, and that the philosophy of mathematics has little to do with the history of mathematics. The philosopher of mathematics works on a specialized set of problems with perhaps only an antiquarian regard to the history of mathematics, while the historian works on the historical transmission of mathematical texts and artifacts with perhaps only (...) a passing interest in the philosophical underpinnings of those developments. (shrink)