The COVID-19 virus was unveiled to the world as a health crisis and later also as an economic crisis. For some organisations, it has become an ethical crisis. This is certainly the case for large organisations in Australia, where the way many enterprises handled a government wage subsidy called JobKeeper led to a public backlash, media pressure, and a variety of responses ranging from ‘We acted legally’ to the full return of the subsidy. Some organisations later reported profits, and the (...) public response indicated concern about this behaviour, many considering it immoral despite it being legally compliant. It is, we contend, a question to which stakeholder theory can be applied, examining how organisations view and respond to the public. We use content analysis of mainstream media to provide information about public reactions and information from official sources to confirm corporate action. We show that there is a significant ethical component in the public response to the behaviour of organisations as they respond to the crisis. COVID has been an ethical, health, and financial crisis for these organisations. Public pressure, exerted in and through the media, made the general public a definite stakeholder. (shrink)

Graciela De Pierris presents a novel interpretation of the relationship between skepticism and naturalism in Hume's epistemology, and a new appraisal of Hume's place within early modern thought. Contrary to dominant readings, she argues that Hume does offer skeptical arguments concerning causation and induction in Book I, Part III of the Treatise, and presents a detailed reading of the skeptical argument she finds there and how this argument initiates a train of skeptical reasoning that begins in Part III and (...) culminates in Part IV. She goes on to demonstrate that Hume was committed to the Newtonian inductive method while rejecting the place of the supernatural in our understanding of nature. (shrink)

In this paper we analyze and discuss the historical and philosophical development of the notion of logical possibility focusing on its specific meaning in classical and quantum mechanics. Taking into account the logical structure of quantum theory we continue our discussion regarding the Aristotelian Square of Opposition in orthomodular structures enriched with a monadic quantifier. Finally, we provide an interpretation of the Orthomodular Square of Opposition exposing the fact that classical possibility and quantum possibility behave formally in radically different manners.

In lieu of an abstract, here is a brief excerpt of the content:Journal of the History of Philosophy 39.3 (2001) 351-383 [Access article in PDF] Hume's Pyrrhonian Skepticism and the Belief in Causal Laws Graciela De Pierris Hume endorses in no uncertain terms the normative use of causal reasoning. The most striking example of this commitment is Hume's argument in the Enquiry against the possibility of miracles. The argument sanctions, in particular, the use of scientific reflection on uniform experience (...) issuing in causal laws of nature (E 114): "A miracle is a violation of the laws of nature; and as a firm and unalterable experience has established these laws, the proof against a miracle, from the very nature of the fact, is as entire as any argument from experience can possibly be imagined." 1 These words should give us pause; for how can Hume so confidently say, after his skeptical conclusions concerning our causal beliefs, that "a firm and unalterable experience has established" the laws of nature, and that we can therefore produce "proofs" against miracles? The Treatise gives rise to the same puzzle. In this text, too, Hume confidently prescribes methodical reflection based on causal reasoning. For example, in Book One, Part Three, Section Fifteen, Hume offers eight "Rules by which to judge of causes and effects." These rules are more than descriptions of our natural causal inferences. They are meant to guide us in making better causal inferences; in Hume's words they "ought to regulate" our probable reasoning since (T 149): "by them we learn to distinguish the accidental circumstances from the efficacious causes." 2Moreover, Hume consistently takes Newtonian science as a model for the proper employment of causal inferences in inquiries into matters of fact and, [End Page 351] in particular, as a model to be followed in his own science of human nature. 3 This paradigm of what the science of nature ought to be is understood by Hume as an inductive, experimental inquiry. 4 In the Enquiry, for example, Hume uses the label "sciences" for "politics, natural philosophy, physic, chemistry, &c." and in the preceding discussion argues that these sciences are not a priori but are based on causal reasoning (E 164-165). Thus, there are for Hume inquiries into matters of fact and existence that amount to more than blindly following natural propensities and habit. The sciences and many of our causal inferences in common life involve more than mere belief as a sentiment. They involve, in addition, careful reflection that results in improved causal inferences and thus provides normative standards. Yet, in thus upholding the normative use of causal reasoning in science and in everyday life, Hume appears to contradict his own radical skeptical conclusions concerning our knowledge of causation and induction. I here propose a novel way to resolve this puzzle.To acknowledge the existence of a puzzle, however, amounts to accepting the now controversial view that Hume provides, and takes at face value, a radical skeptical argument concerning our knowledge of causation and induction. 5 Moreover, the attempt to resolve this puzzle involves rejecting the suggestion [End Page 352] that Hume, without awareness or concern, happily holds flatly inconsistent views. 6 It also goes against the more sophisticated suggestion that Hume lightly alternates among different psychological moods, or perhaps different perspectives, which might eventually issue in results that contradict each other but are sufficiently localized so as to prevent serious conflict. Such a view might lead us to conceive Hume's texts as an unstructured and arbitrary patchwork of reflections, driven by different psychological moods or by the embellishments of a radiant literary style. This kind of reading is unacceptable as an interpretative tool, however, as H. J. Paton has acutely noted in his criticism of the patchwork interpretation of Kant's Critique of Pure Reason. 7 For such a reading would place no constraints at all on the task of establishing which parts of Hume's text belong to which moods or perspectives. The suggestion that Hume offers an unstructured patchwork of reflections masks the novel and systematic distinction Hume draws between his radical philosophical... (shrink)

The objective of the work is to analyze the intersectional discriminations that operate in the multiple identities of regional migrant women in the field of health in Argentina during the present pandemic. We will begin with the critical study of key categories and the origin of the inequalities of law of the aforementioned discrimination in migration policies. Second, we will address de facto inequalities, particularly examining the socio-economic inequalities suffered by migrants during the pandemic. Thirdly, in order to enable alternative (...) forms of care and self-care from the recognition of their ethnicity and the inseparable care of the earth, we propose the application of the concept of territorial participatory justice as a condition of intercultural dialogue in health. As a proposal, it seeks to promote dialogues of knowledge located outside the bureaucratic councils and expanding the social base of health rights from the pluriculturality exercised in care networks of migrant women in the territory and not from their domesticated participation. (shrink)

By giving the proper emphasis to both radical skepticism and naturalism as two independent standpoints in Hume, I wish to propose a more satisfactory account of some of the more puzzling Humean claims on causation. I place these claims alternatively in either the philosophical standpoint of the radical skeptic or in the standpoint of everyday and scientific beliefs. I characterize Hume’s radical skeptical standpoint in relation to Hume’s perceptual model of the traditional theory of ideas, and I argue that Hume‘s (...) radical skeptical argument concerning our causal inferences is inextricably linked to his skeptical argument concerning our idea of a necessary connection between cause and effect. I discuss Hume’s naturalistic account of the origin of our idea of necessity and offer a new reading of Hume’s two “definitions” of cause. I argue along the way against central aspects of two opposing styles of interpretation---Norman Kemp Smith’s and Annette Baier’s, on the one hand, and Robert Fogelin’s, on the other---that in my view do not appreciate the mutual autonomy of radical skepticism and naturalism in Hume. (shrink)

En República, libro X, Platón justifica su exclusión de la poesía imitativa mediante argumentos metafísicos y psicológicos. Al hacerlo, enfatiza la distancia de los productos de la imitación respecto de la verdad, y los condena porque apelan al elemento inferior del alma. En Sofista 233d- 236c, se propone una crítica similar contra la sofistería. El imitador puede hacer eidola, que puede ser considerado como real por un ignorante. En ambos casos Platón se refiere a la distancia respecto de la verdad (...) que guardan tanto los objetos hechos por los imitadores –pintores, poetas o sofistas– como los destinatarios de tales artes –espectadores u oyentes–. Los paralelismos entre ambos tratamientos son abundantes. Tal «distancia», como tratamos de mostrar, ofrece una clave no sólo para entender la crítica platónica de la mímesis, sino que también arroja luz sobre algunos pasajes de República cuya conexión con el tratamiento de la imitación no es evidente de inmediato: la sección eikasía de la «línea dividida», así como ciertos pasajes de la alegoría de la caverna. Ambos textos, independientemente de las variadas lecturas e interpretaciones que han merecido, aclaran la naturaleza de la mimesis y las críticas de Platón contra ella. Además, testifican la confianza de Platón en que el contacto directo con lo real neutraliza los efectos perniciosos de la imitación Palabras clave: Mímesis; Verdad; DistanciaIn Republic Book X, Plato justifies his exclusion of imitative poetry by means of metaphysical and psychological arguments. In doing that, he emphasizes the distance from truth of the products of imitation, and condemns them because they appeal to the lower element of the soul. In Sophist 233d-236c, a similar critique is directed against sophistry. The imitator can make eidola, which can be taken by an ignorant as being real. In both cases Plato refers to the distance that both the objects made by imitators –painters, poets or sophists– and the recipients of such arts –spectators or auditors– have from truth. The parallelisms between both treatments are abundant. Such «distance», as we try to show, offers a key not only to understand Platonic criticism of mimesis. It also throws light on some passages of Republic whose connection with the treatment of imitation is not immediately evident: the eikasía section of the «divided line», and certain passages of the allegory of the cave. Both texts, independently of the various readings and interpretations they have deserved, clarify the nature of mimesis and Plato’s criticisms against it. In addition, they testify Plato’s confidence that direct contact with the real neutralizes the pernicious effects of imitation. Keywords: Mimesis; Truth; Distance. (shrink)

El artículo tiene como finalidad justificar por qué es importante incluir las pedagogías propias de los pueblos originarios en los programas de formación docente de educación básica a nivel nacional, como valores compartidos de su patrimonio cultural tangible e intangible. Este patrimonio cultural es el pilar histórico de México, que por supuesto no se encuentra sólo en los pueblos originarios, sino que responde a un proceso histórico social determinado de la nación y que, a pesar de la conquista europea, siguió (...) prevaleciendo en las pedagogías y valores propios de los pueblos originarios. Proponemos cristalizar estos patrimonios culturales de los pueblos originarios para ser considerados como pedagogías propias en los programas de formación docente y desde este campo de formación compartir los valores culturales a través de sus saberes, sabidurías y prácticas culturales que han prevalecido a lo largo de la historia y que den cuenta en los planes y programas de estudio con igualdad y equidad cultural en el Sistema Educativo Nacional. Asimismo, se exponen los procesos de contradicción que los pueblos originarios han vivido y han asumido a lo largo de las políticas educativas dirigidas a la educación indígena. Finalmente, se plantean algunas consideraciones para estos programas de formación docente. (shrink)

I wish to discuss in this paper some of the problems involved in determining whether subjects on particular occasions are justified in coming to believe a proposition. I will argue that in attributing actual justification to a particular subject–subjective justification–we have to take into account factual-psychological questions and that these are the source of fundamental difficulties. These factual-psychological questions concern the beliefs someone uses in the process of acquiring another belief and the actual connections she makes among her beliefs.But why (...) should epistemologists be interested in making attributions of actual justification to particular subjects? After all, if the central goal of epistemology is to guide us in choosing rational strategies for supporting our beliefs, or to assess whether theories are well grounded or acceptable, epistemologists should be concerned with the justification a theory or proposition might have independently of anyone actually coming to believe it. This may be so, but it has to be shown that it is so. Moreover, the consideration of the factual-psychological questions involved in attributions of subjective justification seems to be necessary in some recent hybrid forms of naturalized epistemology. I call them ‘hybrid’ because, unlike Quine’s naturalized epistemology, they include in the epistemological task more than naturalistic explanations of how we acquire our language and beliefs. Besides taking into consideration the actual processes of our coming to believe or accept sentences, they also make use of epistemic notions like justification, warrant, relevant or right connection among beliefs, and so forth. (shrink)

Introducción al Dosier: Ética, derechos humanos, migraciones y salud.

En este trabajo realizo un examen crítico del reciente libro de Silvana Gabriela Di Camillo sobre la crítica de Aristóteles a la teoría platónica de las Ideas. El libro de Di Camillo es un trabajo muy serio cuya lectura recomiendo ampliamente. Sin embargo, considero que cuatro de las principales tesis que la autora defiende tienen varias dificultades y mi objetivo aquí es presentar argumentos detallados en contra de ellas: la interpretación de la distinción entre argumentos más y menos rigurosos del (...) tratado Sobre las Ideas; la tesis de que la separación es el blanco esencial de las críticas aristotélicas a las Ideas; la interpretación de las opciones que Platón tiene para responder al argumento del tercer hombre, y la tesis de que la separación de las Ideas debe entenderse como homonimia. In this paper I examine Silvana Gabriela Di Camillo's recent book on Aristotle's criticisms of Plato's theory of Ideas. Di Camillo's book is a very serious work that I highly recommend. Nevertheless, I consider that four of the main theses that the author defends face several difficulties and my aim here is to offer detailed arguments against them: the interpretation of the distinction between more and less accurate arguments of the treatise On Ideas; the thesis that separation is the essential target of Aristotle's criticisms against Plato's Ideas; the interpretation of the options available to Plato to reply to the third man argument; and the thesis that the separation of Ideas should be understood as homonymy. (shrink)

By giving the proper emphasis to both radical skepticism and naturalism as two independent standpoints in Hume, I wish to propose a more satisfactory account of some of the more puzzling Humean claims on causation. I place these claims alternatively in either the philosophical standpoint of the radical skeptic or in the standpoint of everyday and scientific beliefs. I characterize Hume’s radical skeptical standpoint in relation to Hume’s perceptual model of the traditional theory of ideas, and I argue that Hume‘s (...) radical skeptical argument concerning our causal inferences is inextricably linked to his skeptical argument concerning our idea of a necessary connection between cause and effect. I discuss Hume’s naturalistic account of the origin of our idea of necessity and offer a new reading of Hume’s two “definitions” of cause. I argue along the way against central aspects of two opposing styles of interpretation---Norman Kemp Smith’s and Annette Baier’s, on the one hand, and Robert Fogelin’s, on the other---that in my view do not appreciate the mutual autonomy of radical skepticism and naturalism in Hume. (shrink)

In this paper we enrich the orthomodular structure by adding a modal operator, following a physical motivation. A logical system is developed, obtaining algebraic completeness and completeness with respect to a Kripkestyle semantic founded on Baer*-semigroups as in [22].

Resumen: Siguiendo la inspiración de Merleau-Ponty, B. Waldenfels se ocupa de la corporalidad y pone énfasis en su dimensión responsiva, es decir, en modos de comportamiento y experiencia corporales que responden a interpelaciones de lo extraño. Desde esta perspectiva, este trabajo aspira a elucidar el entrelazamiento cuerpo-Naturaleza con la intención de mostrar que la Naturaleza entendida como otro aspecto del hombre implica una alteridad que no se reduce ni a la lógica de la intencionalidad ni a la lógica de la (...) comunicación. La interpelación que proviene de la Naturaleza tiene, por una parte, el significado de una apelación, comprendida como alocución a alguien, y, por otra, el de una pretensión, en el sentido de una interpelación a algo. Con base en estos presupuestos, la segunda parte de la exposición apunta a ilustrar la manera como a través de la pintura se pone en marcha un actuar responsivo, que se orienta por los caracteres singularidad, ineludibilidad, posterioridad, asimetría e innovación que caracterizan a la lógica de la respuesta.: Following Merleau-Ponty´s inspiration, B. Waldenfels deals with embodiment emphasizing its responsive dimension, i.e., modes of bodily behavior and experience that respond to interpellations of the strange. From this view, the article aims to explaining the intertwining of body and nature with the intention of showing that nature, understood as another side of human being, implies an alterity that cannot be reduced to the logic of intentionality nor to the logic of communication. The interpellation that arises from Nature has, on the one hand, the meaning of appeal in the sense of an address to somebody, and, on the other, of pretention as an interpellation to something. Based on these presuppositions, the second part of the article tries to show how, by means of painting, a responsive action is set in motion. The features of singularity, unavoidableness, subsequence, asymmetry, and innovation that characterize the logic of the answer guiding this action. (shrink)

En este artículo realizaremos una lectura crítica de la teoría de la dominación propuesta por Bourdieu en el capítulo octavo de El sentido práctico, titulado “Los modos de dominación”. Allí se distinguen con claridad dos modos de dominación: la violencia abierta y la violencia simbólica, aseguradas en su reproducción por el pasaje de las relaciones interpersonales en “la sociedad tradicional” a la institucionalización vía mecanismos objetivos en la sociedad capitalista. En ese sentido, mostraremos continuidades y diferencias relativas a la versión (...) inicial de esta teoría presente en La reproducción, y, luego, propondremos una revisión crítica de esta teoría y de la distinción, tan clásica como problemática, entre objetividad y subjetividad con el propósito de contribuir al desarrollo de una fenomenología social de la dominación con fundamento en la obra de Bourdieu. (shrink)

En este artículo realizaremos una lectura crítica de la teoría de la dominación propuesta por Bourdieu en el capítulo octavo de El sentido práctico, titulado “Los modos de dominación”. Allí se distinguen con claridad dos modos de dominación: la violencia abierta y la violencia simbólica, aseguradas en su reproducción por el pasaje de las relaciones interpersonales en “la sociedad tradicional” a la institucionalización vía mecanismos objetivos en la sociedad capitalista. En ese sentido, mostraremos continuidades y diferencias relativas a la versión (...) inicial de esta teoría presente en La reproducción, y, luego, propondremos una revisión crítica de esta teoría y de la distinción, tan clásica como problemática, entre objetividad y subjetividad con el propósito de contribuir al desarrollo de una fenomenología social de la dominación con fundamento en la obra de Bourdieu. (shrink)

In this article we discuss the contextual character of quantum mechanics in the framework of modal interpretations. We investigate its historical origin and relate contemporary modal interpretations to those proposed by M. Born and W. Heisenberg. We present then a general characterization of what we consider to be a modal interpretation. Following previous papers in which we have introduced modalities in the Kochen-Specker theorem, we investigate the consequences of these theorems in relation to the modal interpretations of quantum mechanics.

La noción de sistema de equivalencias adquiere en la fenomenología merleaupon-tyana un lugar central, puesto que allí subyace una función general de transposición tácita. Se trata de un principio de comprensión sin explicación analógica, una síntesis sin análisis, tal como puede observarse, por ejemplo, en la plasticidad, la transferi-bilidad y la analogicidad que caracteriza a los hábitos. Sobre esta base, este artículo seguirá un camino regresivo a fin de desvelar que el sentido de las equivalencias y transposiciones está latente en (...) "las matrices simbólicas", que ofrecen una clave para comprender que los fenómenos de expresión, que tienen lugar en el mundo a través del cuerpo, del lenguaje, de la historia y del arte, deben ser vistos como nudos, emblemas de sentido en los que se hace visible una dimensión temporal. Las matrices simbólicas son "centros organizadores" y, por lo tanto, "centros de significación" que se retoman una y otra vez. The notion of a system of equivalences comes to have in Merleau-Ponty's phe-nomenology a central place because lying under there is a general function of tacit transposition. It is a principle for understanding without analogical explanation, i.e., a synthesis without analysis, as can be seen, for example, in the plasticity, transferability, and likeliness that characterizes habits. On this basis, the article will follow a regres-sive way in order to show that the meaning of the equivalences and transpositions is latent in "the symbolic matrixes" that offer a clue to understand that the phenomena of expression, which occur in the world by means of the body, language, history, and art, should be seen as nodes or emblems of meaning in which a temporal dimension shows itself. Symbolic matrixes are "organizing centers", and thus "centers of signi-ficance" that are taken up over and over again. (shrink)

Commentaries on Hume's Treatise 1.4.1, "Of scepticism with regard to reason," have focused on the argument that an initial lack of certainty concerning the conclusion of an inference gradually diminishes to zero. In my view, Hume offers this famous argument only after, and as corollary to, a far more interesting skeptical argument concerning demonstrative reasoning, which occurs at the very beginning of Treatise 1.4.1. I focus on this neglected argument, point to its Cartesian roots, and draw a distinction between ordinary (...) doubts and a radical skeptical doubt about the inevitable interference of fallible faculties in our demonstrative inferences. Hume suggests that, in common life and science, solutions to ordinary doubts concerning human fallibility themselves rely on causal reasoning-that we have applied inferential rules correctly in any given instance is a "matters of fact" conclusion, thus it is supported by the only kind of evidence that such a conclusion can have. Hume's argument brilliantly reverses the force of the increased confidence normally acquired on the basis of such causal reasoning. Once we have realized, in the radically skeptical frame of mind, that in our attempts to improve and evaluate demonstrative reasoning we use merely causal reasoning, there is no longer the hope of a progressive adjustment of the exercise of our faculties to an assumed objective validity of our demonstrative rules. The increase in assurance by causal methods only amounts to "the addition of new probabilities," and there is no gradual transition from probability to demonstratively certain knowledge. Hume thereby reaches a radical skeptical doubt regarding the possibility of our ever attaining genuinely certain demonstrative knowledge - and, unlike Descartes, he reaches this doubt without the external device of an all-powerful deceiver. Los comentarios sobre la sección "Of scepticism with regard to reason" en A Treatise on Human Nature de David Hume se han concentrado en el argumento según el cual, la falta inicial de convicción certera acerca de la conclusión de una inferencia cualquiera disminuye gradualmente a cero. Sostengo que Hume ofrece este famoso argumento solamente después y como corolario de un argumento escéptico mucho más interesante acerca del razonamiento deductivo, el cual aparece al principio de esta sección. Me concentro en este primer argumento, señalo sus raíces cartesianas, y establezco una distinción entre dudas comunes y una duda escéptica radical acerca de la interferencia inevitable, en nuestros razonamientos deductivos, de facultades mentales falibles. Hume sugiere que, en la vida cotidiana y en la ciencia, las soluciones a las dudas acerca de la falibilidad humana, en sí mismas se apoyan en razonamientos de carácter causal: si hemos aplicado correctamente una regla inferencial o no, en una instancia específica, es en sí misma una conclusión acerca de lo que Hume llama "matters of fact". Por lo tanto, está basada en el único tipo de evidencia que tal conclusión puede poseer. El argumento brillante de Hume invierte negativamente la confianza creciente que normalmente adquirimos sobre la base de tal razonamiento causal. Una vez que tomamos en cuenta, desde el punto de vista escéptico radical, que en nuestros intentos de mejorar y evaluar razonamientos deductivos usamos meramente razonamientos causales, se cierra la posibilidad de ajustar progresivamente el ejercicio de nuestras facultades mentales a una supuesta validez objetiva de las reglas de deducción. El aumento de la confianza en nuestras inferencias está basado en métodos causales, por lo tanto resulta en "la adición de nuevas probabilidades", y no existe una transición gradual desde la probabilidad más alta hasta el conocimiento certero demostrativo. De esta manera, Hume llega a una duda escéptica radical acerca de la posibilidad de lograr conocimiento demostrativo genuinamente certero. A diferencia de Descartes, Hume obtiene esta duda radical sin apelar a un elemento externo a nuestras facultades mentales, tal como el todopoderoso que engaña en la Primera Meditación de Descartes. (shrink)

I wish to discuss in this paper some of the problems involved in determining whether subjects on particular occasions are justified in coming to believe a proposition. I will argue that in attributing actual justification to a particular subject–subjective justification–we have to take into account factual-psychological questions and that these are the source of fundamental difficulties. These factual-psychological questions concern the beliefs someone uses in the process of acquiring another belief and the actual connections she makes among her beliefs.But why (...) should epistemologists be interested in making attributions of actual justification to particular subjects? After all, if the central goal of epistemology is to guide us in choosing rational strategies for supporting our beliefs, or to assess whether theories are well grounded or acceptable, epistemologists should be concerned with the justification a theory or proposition might have independently of anyone actually coming to believe it. This may be so, but it has to be shown that it is so. Moreover, the consideration of the factual-psychological questions involved in attributions of subjective justification seems to be necessary in some recent hybrid forms of naturalized epistemology. I call them ‘hybrid’ because, unlike Quine’s naturalized epistemology, they include in the epistemological task more than naturalistic explanations of how we acquire our language and beliefs. Besides taking into consideration the actual processes of our coming to believe or accept sentences, they also make use of epistemic notions like justification, warrant, relevant or right connection among beliefs, and so forth. (shrink)

Hume’s discussion of space, time, and mathematics at T 1.2 appeared to many earlier commentators as one of the weakest parts of his philosophy. From the point of view of pure mathematics, for example, Hume’s assumptions about the infinite may appear as crude misunderstandings of the continuum and infinite divisibility. I shall argue, on the contrary, that Hume’s views on this topic are deeply connected with his radically empiricist reliance on phenomenologically given sensory images. He insightfully shows that, working within (...) this epistemological model, we cannot attain complete certainty about the continuum but only at most about discrete quantity. Geometry, in contrast to arithmetic, cannot be a fully exact science. A number of more recent commentators have offered sympathetic interpretations of Hume’s discussion aiming to correct the older tendency to dismiss this part of the Treatise as weak and confused. Most of these commentators interpret Hume as anticipating the contemporary idea of a finite or discrete geometry. They view Hume’s conception that space is composed of simple indivisible minima as a forerunner of the conception that space is a discretely (rather than continuously) ordered set. This approach, in my view, is helpful as far as it goes, but there are several important features of Hume’s discussion that are not sufficiently appreciated. I go beyond these recent commentators by emphasizing three of Hume’s most original contributions. First, Hume’s epistemological model invokes the “confounding” of indivisible minima to explain the appearance of spatial continuity. Second, Hume’s sharp contrast between the perfect exactitude of arithmetic and the irremediable inexactitude of geometry reverses the more familiar conception of the early modern tradition in pure mathematics, according to which geometry (the science of continuous quantity) has its own standard of equality that is independent from and more exact than any corresponding standard supplied by algebra and arithmetic (the sciences of discrete quantity). Third, Hume has a developed explanation of how geometry (traditional Euclidean geometry) is nonetheless possible as an axiomatic demonstrative science possessing considerably more exactitude and certainty that the “loose judgements” of the vulgar. (shrink)