This study examines quaternion Dirac solutions for an infinite square well. The quaternion result does not recover the complex result within a particular limit. This raises the possibility that quaternionic quantum mechanics may not be understood as a correction to complex quantum mechanics, but it may also be a structure that can be used to study phenomena that cannot be described through the framework of complex quantum mechanics.

The aim of this article is to investigate specific aspects connected with visualization in the practice of a mathematical subfield: low-dimensional topology. Through a case study, it will be established that visualization can play an epistemic role. The background assumption is that the consideration of the actual practice of mathematics is relevant to address epistemological issues. It will be shown that in low-dimensional topology, justifications can be based on sequences of pictures. Three theses will be defended. First, the representations used (...) in the practice are an integral part of the mathematical reasoning. As a matter of fact, they convey in a material form the relevant transitions and thus allow experts to draw inferential connections. Second, in low-dimensional topology experts exploit a particular type of manipulative imagination which is connected to intuition of two- and three-dimensional space and motor agency. This imagination allows recognizing the transformations which connect different pictures in an argument. Third, the epistemic—and inferential—actions performed are permissible only within a specific practice: this form of reasoning is subject-matter dependent. Local criteria of validity are established to assure the soundness of representationally heterogeneous arguments in low-dimensional topology. (shrink)

The objective of this article is twofold. First, a methodological issue is addressed. It is pointed out that even if philosophers of mathematics have been recently more and more concerned with the practice of mathematics, there is still a need for a sharp definition of what the targets of a philosophy of mathematical practice should be. Three possible objects of inquiry are put forward: (1) the collective dimension of the practice of mathematics; (2) the cognitives capacities requested to the practitioners; (...) and (3) the specific forms of representation and notation shared and selected by the practitioners. Moreover, it is claimed that a broadening of the notion of ‘permissible action’ as introduced by Larvor (2012) with respect to mathematical arguments, allows for a consideration of all these three elements simultaneously. Second, a case from topology – the proof of Alexander’s theorem – is presented to illustrate a concrete analysis of a mathematical practice and to exemplify the proposed method. It is discussed that the attention to the three elements of the practice identified above brings to the emergence of philosophically relevant features in the practice of topology: the need for a revision in the definition of criteria of validity, the interest in tracking the operations that are performed on the notation, and the constant and fruitful back-and-forth from one representation to another in dealing with mathematical content. Finally, some suggestions for further research are given in the conclusions. (shrink)

Reunindo pesquisadores e intelectuais do Brasil, da França, da Bélgica e do Canadá nesse “Dossiê Cornelius Castoriadis”, a Revista Dissertatio celebra o centenário de nascimento desse que continua um pensador a ser descoberto e redescoberto pelo público brasileiro.

A short presentation of the moral doctrines inspired by the Confucian tradition.

The genealogical deconstruction of the notion of "good" by F.Nietzsche in Genealogy of Morals highlights the arbitrariness of the Platonic unification of various kinds of good, a unification that is still shared by both objectivists and subjectivists. For the same reasons, the attempt of G.E. Moore and other neo-intuitionists to define a single property that is common to all uses of the term "good" and the specular denial of the existence of this property by the emotionalism of A.J. Ayer and (...) Ch.L. Stevenson perhaps debate a false problem. The revival of various forms of Aristotelianism has proposed again Aristotle's answer to Plato: when we say something is good, we want to know what is good, and the answer will be different for different goods. (shrink)

A short reconstruction of the origin and evolution of Islamic moral doctrines and their re-interpretation by Arabic philosophers.

A short reconstruction of the method of casuistry in Medieval and early Modern moral theology.

KOINONIA/ASETT MINGA/MUTIRÃO DE REVISTAS DE TEOLOGIA LATINO-AMERICANAS Una nueva dimensión epistemológica para la teología: la Teología de la Liberación y el desafío epistemológico (A new epistemological dimension to theology: liberation theology and epistemological challenge).

The relationship between Adam Smith's official methodology and his own actual theoretical practice as a social scientist may be grasped only against the background of the Humean project of Moral Newtonianism. The main features in Smith's methodology are (i) the provisional character of explanatory principles, (ii) 'internal' criteria of truth, (iii) the acknowledgement of an imaginative aspect in principles, with the related problem of the relationship between internal truth and external truth understood as mirroring 'real' causes. Smith's Newtonian (as opposed (...) to Cartesian) methodology makes room for progress in social theorizing as it allows for a decentralization of the various fields of Moral Science, contributing to the shaping of political economy. On the other hand, the Cartesian legacy in Smith's Newtonian methodology makes the relationship problematic between phenomena and principles. (shrink)

Este artículo analiza las estrategias utilizadas por Descartes para «desencantar el mundo», a fin de suprimir los elementos herméticos de las explicaciones científicas cartesianas y someter todos los fenómenos naturales a nuestro control. Para ello, apelo a la distinción entre elementos causales —cualidades ocultas— y sus efectos —efectos admirables— como las dos dimensiones que deben ser incorporadas bajo las explicaciones científicas para garantizar el cálculo de los fenómenos y su dominio.

A completely Lorentz-invariant Bohmian model has been proposed recently for the case of a system of non-interacting spinless particles, obeying Klein-Gordon equations. It is based on a multi-temporal formalism and on the idea of treating the squared norm of the wave function as a space-time probability density. The particle’s configurations evolve in space-time in terms of a parameter σ with dimensions of time. In this work this model is further analyzed and extended to the case of an interaction with an (...) external electromagnetic field. The physical meaning of σ is explored. Two special situations are studied in depth: (1) the classical limit, where the Einsteinian Mechanics of Special Relativity is recovered and the parameter σ is shown to tend to the particle’s proper time; and (2) the non-relativistic limit, where it is obtained a model very similar to the usual non-relativistic Bohmian Mechanics but with the time of the frame of reference replaced by σ as the dynamical temporal parameter. (shrink)

The word “legitimacy” and its derivations (legitimate, legitimation, etc.) are widely employed in scientific language as they also are in current usage. In fact, we find them in several areas, from that of reasoning (“this conclusion is legitimate”) to that of law (“judgment of legitimacy”, “legitimate family”) and politics (“legitimate sovereign”). It is particularly in this latter domain, however, that they have their normal use as qualifications for power, and it is this particular aspect that I shall consider in this (...) paper. In accredited political language “legitimacy” designates a principle, or criterion, of justification for power (acting and commanding) and, correlatively, of the obedience that is its due. (shrink)

It is necessary to reconsider P. M. S. Hacker’s assessment of Kant and Wittgenstein’s philosophical affinities and the question concerning Wittgenstein’s alleged use of “transcendental arguments”. First, Alfred Norman’s reading of the Tractatus Logico-Philosophicus as a thought experiment receives revision to develop a view of the Critique of Pure Reason as a large-scale thought experiment that shares important logical features with the Tractatus. Then the question is addressed whether the middle Wittgenstein and the pre-critical Kant employed any thought experiments that (...) could be equally characterised as “transcendental arguments”. A rational reconstruction of both thinkers’ arguments is carried out in the light of the contemporary literature on thought experimenting. The novelty and relevance of this approach is the emphasis laid upon a largely neglected affinity between Kant and Wittgenstein, namely the systematic use of thought experiments in their epistemological pursuits. The conclusions are: i) Wittgenstein’s and Kant’s magna opera can be seen as philosophical thought experiments that attempt to try out the limits of language and the limits of possible experience respectively; ii) Both philosophers developed arguments that can be designated as transcendental if only from a methodological standpoint; and iii) some key arguments put forward by the middle Wittgenstein in the determination of the structure of visual space could be characterised better as thought experiments than transcendental arguments. (shrink)

A short reconstruction of the vicissitudes of the notion of ethical naturalism through American late nineteenth-century 'naturalism', Moore criticism of so-called naturalistic ethics, reaching Anscombe, Geach and Foot and their particular kind of anti-non-naturalism. The conclusion is that the notion of ethical naturalism is little more than a mere 'flatus vocis' used to indicate three heterogeneous kinds of ethical theories.

I argue that Malthus’s Essay on Population is more a treatise in applied ethics than the first treatise in demography. I argue also that, as an ethical work, it is a highly innovative one. The substitution of procreation for sex as the focus makes for a drastic change in the agenda. What had been basically lacking in the discussion up to Malthus’s time was a consideration of human beings’ own responsibility in the decision of procreating. This makes for a remarkable (...) change also in the approach, namely, the discussion becomes an examination of a well-identified issue, taking cause-effect relationships into account in order to assess possible lines of conduct in the light of some, widely shared and comparatively minimal, value judgements. This is more or less the approach of what is now called applied ethics, at least according to one of its accounts, or perhaps to the account shared by a vast majority of its practitioners. In a sense, both the subject matter, sexuality, was substituted with a more restricted issue, namely reproduction, and the traditional approach, moral doctrine, was substituted with a more modest approach, in Malthus’s own words, the ‘moral and political science’. Such a drastic transformation brought about a viable framework, for a discussion of ethical issues that were still unforeseen by Malthus, namely those having to do first with the technical feasibility of eugenics programs and secondly with the scientific discovery of genetics as a field of study but also of possible intervention. Malthus’s ethics had obviously enough nothing to say on those unforeseen issues in so far as it was meant to treat just the ‘quantitative’ dimension of procreation, that is, ‘how many’. Later discussions and controversies will arise around different dimensions, that is, not just ‘how many’ but also ‘how healthy, how strong, how far empowered’. Yet, what Malthus’s lesson can still teach to proponents of opposite views is that the mentioned questions can be construed in such a way as to avoid unending controversy. (shrink)

Following the line of thought articulated by Gallegos-Ordorica (2019), the main goal of this article is to argue that the 19th century Venezuelan-Chilean polymath Andrés Bello should be included within the history of the pragmatist tradition as an important precursor insofar as his masterpiece, Filosofía del Entendimiento (Philosophy of the Understanding), exhibits many views and attitudes that are characteristic of pragmatism. A second and narrower goal of this article is to show that the specific kind of proto-pragmatist position that Bello (...) endorses in Philosophy of the Understanding bears remarkable similarities to the neo-pragmatist view of Huw Price and to argue that Bello’s metaphorical idea-signs can be potentially useful in explaining the great variety of functions that what Price calls “i-representations” have within his functional pluralism. (shrink)

El renovado interés que ha adquirido el pensamiento político desde la segunda mitad del siglo veinte ha dado lugar a nuevas perspectivas para su estudio. Sin embargo, el desarrollo teórico de las ciencias sociales no ha tenido una interacción fluida entre las disciplinas que la componen. En este trabajo argumentaré que los desarrollos metodológicos sobre la posibilidad histórica de la teoría política deberían estar interconectados con los desarrollos en el campo de la historiografía. Para sostener mi posición me propongo realizar (...) una aproximación problemática en torno a la posibilidad de construir un conocimiento histórico-científico de la teoría política, a partir de los siguientes tópicos: la temporalidad histórica; el vínculo entre temporalidad y pensamiento, y la politización del pensamiento. (shrink)

In the course of the eighteenth and nineteenth centuries the paradigm of a new science, political economy, was established. It was a science distinct from the Aristotelian sub-disciplines of practical philosophy named oikonomía and politiké, and emphasis on its character of science not unlike the natural sciences – still called ‘natural philosophy’ – mirrored precisely a willingness to stress its autonomy from two other sub-disciplines of practical philosophy, that is, ethics and politics. However, the new science resulted from a transformation (...) of part of traditional practical philosophy, allowing the inclusion of bodies of knowledge accumulated by experts of commerce and public finance. Such bodies of knowledge were unified by the (true or alleged) discovery of regularities, mechanisms, causal connections making for a new partial order within the overall social order. How far this paved the way to a science similar to mathematics rather left a normative discipline as alive as ever was a recurrent question for at least a century, until the marginalist revolution opened the way for a sharp division, leaving ‘economics’ as a science of causes and effects facing ‘economic policy’ as a discourse on ends. (shrink)

A short historical overview of the idea of equality from early modernity to the twentieth century.

A reconstruction of the history of the wording civil society and of the curious twist in its usage and meaning, highlighting why the term had an important role in Continental political thinking and was ignored until comparatively recently in Anglo-Saxon political discourse.

Esta contribución examina la solución al problema mente-cuerpo que Kant formula en el marco de su primera explicación causal. Se analiza tanto el planteamiento metafísico como la solución interaccionista de Kant a este problema en su obra sobre las “fuerzas vivas” y, mediante orientaciones metodológicas de la historia intelectual, se contrastan con los planteamientos y soluciones de dos pensadores que influyeron en la formación del pensamiento kantiano: Marquardt y Knutzen, exponentes de algunas de las principales doctrinas causales de la época (...) como la de la armonía preestablecida y el influjo físico. En un sentido, la solución kantiana se plantea como una vía intermedia entre estas dos doctrinas y, en otro, como una postura crítica frente a ambas. (shrink)

This article analyzes the interpretation proposed by Michel Foucault of the Iranian Revolution, i.e. the popular uprisings and revolts that took place in Iran in 1978 and their consequences in the formation of the Islamic Republic in 1979, with the aim of systematizing the thought of the philosopher about this question and of going further in a highly potent matrix in his production which unfortunately has been partly eclipsed by the shallow and hasty criticisms it received. For this purpose, I (...) will proceed to the exam of the problematic cores and the conceptual categories arising from what can be called Foucault’s dossier Iran accounting for the relationship between the subject, politics and history. Likewise, I will highlight the main axes of that interpretation following the link with the researches and central lines that Foucault is developing at that moment, in particular, the relationship he establishes between life, government and truth and the reformulation of the problem of power in terms of the problem of government which will enable him to deploy that aspect of his analyses of power and politics relating to resistance, freedom and the critique of the present. Finally, I will propose an assessment in perspective, underlining the scope and the potentialities of the Foucauldian ideas about these events. (shrink)

Neste artigo, discute-se algumas das contribuições de Hannah Arendt para a reflexão acerca do fenômeno da desobediência civil. Inicialmente, interroga-se em que medida a contestação civil pode ser identificada com a objeção de consciência. Discutir essa questão permite compreender o desenvolvimento da argumentação de Arendt que visa ressaltar o sentido político dos atos de desobediência civil em oposição à caracterização negativa deste fenômeno, defendida por juristas, na tentativa de incluir pelo direito ações extralegais de contestação. Com efeito, essa leitura jurídica, (...) que se baseia na ideia de que a contestação tem por fundamento a moralidade de consciência, negligencia determinados aspectos que são fundamentais para a compreensão da desobediência civil segundo a perspectiva de Arendt, sobretudo seu caráter público, o compartilhamento de um interesse ativo no mundo e, por fim, a não-violência. Em um segundo momento, explicita-se a influência da tradição filosófica na maneira típica de se compreender a desobediência civil, sendo Sócrates e Henry Thoreau elencados por Arendt como seus interlocutores neste debate. Com esse percurso argumentativo, pretende-se mostrar alguns potencias do ensaio de Arendt que contribuem para reatualizar a discussão sobre o papel político central do ato de divergir publicamente. (shrink)

En este texto se elabora un análisis historiográfico, filosófico y teórico en torno a diversas propuestas de caracterización, demarcación, y explicación de la conducta y la cognición. Asimismo, se construyen argumentos para favorecer una comprensión más integral y elaborada de los programas de investigación acerca de la conducta y la cognición. Con este fin, en la primera sección analizaremos y cuestionaremos tres mitos acerca de la historia de la psicología: la tesis de los paradigmas hegemónicos y los reemplazos revolucionarios, la (...) tesis de los paradigmas incomparables, y la tesis que exige un único paradigma dominante como requisito de cientificidad. Dado que estos mitos se derivan de ciertas ideas problemáticas de Kuhn, en la segunda sección ofreceremos una propuesta alternativa basada en la filosofía de la ciencia de Bunge. En las secciones tercera y cuarta exploraremos los significados de las palabras “conducta” y “cognición”, y su relevancia para corregir ciertos malentendidos que obstaculizan los debates entre los programas de investigación conductistas y cognitivos. En las secciones quinta y la sexta, discutiremos algunos mitos acerca del conductismo y del cognitivismo, y en la última sección ofreceremos algunas conclusiones sobre los temas abordados. Las herramientas que analizaremos permiten establecer un debate más racional entre programas de investigación científica, generar puentes de discusión y desarrollo teórico de una manera más integral y completa, y evitar caer tanto en el dogmatismo y la descalificación injustificada, como en las actitudes eclécticas. (shrink)

These two volumes consist of a critical edition and English translation of the two earliest known Armenian sets of scholia on the Heavenly Hierarchy of Dionysius the Areopagite. Composed in the monastic schools of Erznka in the late thirteenth century, these scholia provide significant insight into how the Heavenly Hierarchy in particular, and Armenian translations of Greek texts in general, were understood by Armenian scholars in the Middle Ages. This editio princeps of the scholia represents a rare critical edition of (...) a native Armenian composition from the medieval period. In addition to the text and translation, these volumes include a textual commentary as well as a critical collation and English translation of a number of scholia from the Armenian version of the Greek scholia on the Heavenly Hierarchy. (shrink)

Moving from the problem of defining how medieval speculation conceived the aesthetic dimension of art, this essay purposes an insight into the aspects that describe the peculiarity of the Byzantine conception of beauty and art. Surpassing the noetic perspective established by Platonic thought – shared also by Western medieval philosophy – according to which beauty is an intelligible model subsisting in itself as an autonomous entity, the Byzantine proper vision conceives beauty as a divine energy. The implications of this perspective (...) lead us to investigate its connection with some of the most original achievements of Byzantine speculation, such as hypostatic ontology, theology of deification, eikonic thinking, and especially sophianic gnoseology, which permit us to overcome the dichotomy of the intelligible and the sensible domains of reality. (shrink)

Bernardino Telesio Dubbed “the first of the new philosophers” by Francis Bacon in 1613, Bernardino Telesio was one of the most eminent thinkers of Renaissance Italy, along with figures such as Pico, Pomponazzi, Cardano, Patrizi, Bruno, Doni, and Campanella. The young Telesio spent the early decades of his life under the guidance of his … Continue reading Telesio, Bernardino →.

Resumen: Se sostiene que en la Ciencia de la Lógica Hegel distingue, mediante la categoría de “fin subjetivo”, una dimensión puramente instrumental de la actividad del concepto. Tras delinear una lectura de conjunto de la Doctrina del Concepto se reconstruyen sectores clave del capítulo dedicado a la Teleología con vistas a detectar tanto los rasgos fundamentales como las limitaciones de esta dimensión puramente instrumental del concepto. Se concluye que es posible verificar en el capítulo una “lógica de la actividad instrumental” (...) e interpretar en dicha clave la posición sistemática del capítulo. Además, se subrayan los rasgos críticos del tratamiento hegeliano en vista del problema general de una mecanización y desgaste del mundo y de la vida, lo que proyecta el problema al tránsito desde el capítulo Teleología a la sección Idea.: This paper seeks to show that, in the Science of Logic Hegel, through the category of “subjective end”, distinguishes a purely instrumental dimension of the activity of concept. After delineating a general interpretation of the Doctrine of Concept, key aspects of the chapter dedicated of Teleology are re-constructed with the aim of detecting both the fundamental features and the limitations of this purely instrumental dimension of the concept. It is concluded that, in the chapter, it is possible to verify a ‘logic of the instrumentally activity’ and from this standpoint, to interpret the systematic position of the chapter. In addition, critical features of the Hegelian analysis are emphasized in regard to the general problem of mechanization and wear of the world and life, which projects the problem to the transit from chapter on Teleology to the Idea section. (shrink)

O texto visa contribuir, por um lado, à investigação acerca dos processos psicológicos, aos níveis subjetivo, lógico e intersubjetivo, inerentes a uma postura filosofante, remetendo a considerações metodológicas com relação ao ensino de Filosofia. Por outro, visa questionar a relação entre o filosofar e a História da Filosofia, visando à conexão entre o diálogo filosófico e o diálogo com a História da Filosofia.

SÍNTESE - Este texto visa contribuir ao debate sobre as condições para filosofar com crianças. Sugere que o aprendizado da relação é passivei a partir do resgate da nossa história pessoal e do exercício da admiração, o que se efetiva na relação com crianças. Tal aprendizado, configurando já uma postura filosófica, possibilita a reconstrução do dizer e do pensar, da relação entre o dizer e o pensar, do comunicar. Há uma perspectiva ética, à base do filosofar com crianças, a qual (...) relaciona a nossa história pessoal com a História. (shrink)

Este artículo analiza el problema de la integración latinoamericana, que ha sido abordado a lo largo de dos siglos por distintas generaciones de pensadores, sean éstos intelectuales o políticos, generando un rico pensamiento que tiene un valor en si mismo. Sin embargo, el proyecto político no ha podido concluirse. Enfrentado además este pensamiento (desde 1989 en adelante) a una realidad internacional mucho más compleja, surge la pregunta por su vigencia. Se propone aquí una re-lectura de dicho pensamiento latinoamericano con arreglo (...) a las corrientes intelectuales y disciplinarias que han emergido en (o sobre) América Latina en las últimas décadas. Ya iniciado el siglo XXI nos encontramos con un gran volumen de obras de pensadores integracionistas elaborados en la región, pero que no son equivalentes a la realidad socio-política de América Latina. Si bien han surgido acuerdos políticos, donde los más relevantes han sido ALALC, Pacto Andino, ALADI, MERCOSUR, UNASUR, éstos no han podido transformarse en una comunidad continental efectiva. Esta contribución se adentra en la búsqueda de un nuevo pensamiento latinoamericano, que considere los actuales fenómenos internos de la región (producto de los procesos globalizadores y descentralizadores) y las nuevas formas de actuación internacional. (shrink)