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)

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)

Hume follows Newton in replacing the mechanical philosophy’s demonstrative ideal of science by the Principia’s ideal of inductive proof ; in this respect, Hume differs sharply from Locke. Hume is also guided by Newton’s own criticisms of the mechanical philosophers’ hypotheses. The first stage of Hume’s skeptical argument concerning causation targets central tenets of the mechanical philosophers’ conception of causation, all of which rely on the a priori postulation of a hidden configuration of primary qualities. The skeptical argument concerning the (...) causal inductive inference then raises doubts about what Hume himself regards as our very best inductive method. Hume’s own “Rules” further substantiate his reliance on Newton. Finally, Locke’s distinction between “Knowledge” and “Probability” does not leave room for Hume’s Newtonian notion of inductive proof. (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)

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)

Traditionally the modern theory of ideas has been discussed primarily in reference to its alleged introduction of a veil of mental items between the mind and the world, which leads, through the empiricists, to radical skepticism about the existence of an external world. Here I propose to emphasize an entirely different aspect of the Cartesian theory of ideas which, in my view, is more fundamental in opening the empiricist path that leads to Hume’s radical skepticism. I argue that what I (...) call the “phenomenological presentation” model of ultimate justification is rooted in a fundamental ambiguity between sensible and intellectual apprehension insinuated by Descartes’s view of “clear and distinct” ideas together with his emphasis on the priority of intuition over logical inference. Sensible apprehension relies on immediate acquaintance with items phenomenologically and ostensively present before the mind as given particulars. The phenomenological presentation model takes its clues from sensible apprehension, although the items present before the mind might themselves be either ideas of the understanding, images of the imagination, sensory impressions, or material external objects. Intellectual apprehension, by contrast, as I illustrate with Leibniz’s model of our knowledge of concepts and truths of reason, consists in the discursive, non-ostensive grasping of the generality of abstract concepts and of formal structures . For Leibniz, all intellectual apprehension is unambiguously “logical discursive apprehension” as opposed to “direct ostensive apprehension.” Thus, Leibniz unmistakably disambiguates Descartes’s model in favor of a precise intellectual model. The empiricists, by contrast, correspondingly disambiguate Descartes’s conception in favor of an entirely sensible model. (shrink)

Traditionally the modern theory of ideas has been discussed primarily in reference to its alleged introduction of a veil of mental items between the mind and the world, which leads, through the empiricists, to radical skepticism about the existence of an external world. Here I propose to emphasize an entirely different aspect of the Cartesian theory of ideas which, in my view, is more fundamental in opening the empiricist path that leads to Hume’s radical skepticism. I argue that what I (...) call the “phenomenological presentation” model of ultimate justification is rooted in a fundamental ambiguity between sensible and intellectual apprehension insinuated by Descartes’s view of “clear and distinct” ideas together with his emphasis on the priority of intuition over logical inference. Sensible apprehension relies on immediate acquaintance with items pheno-menologically and ostensively present before the mind as given particulars. The phenomenological presentation model takes its clues from sensible apprehension, although the items present before the mind might themselves be either ideas of the understanding, images of the imagination, sensory impressions, or material external objects. Intellectual apprehension, by contrast, as I illustrate with Leibniz’s model of our knowledge of concepts and truths of reason, consists in the discursive, non-ostensive grasping of the generality of abstract concepts and of formal structures . For Leibniz, all intellectual apprehension is unambiguously “logical discursive apprehension” as opposed to “direct ostensive apprehension.” Thus, Leibniz unmistakably disambiguates Descartes’s model in favor of a precise intellectual model. The empiricists, by contrast, correspondingly disambiguate Descartes’s conception in favor of an entirely sensible model.Tradicionalmente, a teoria moderna das idéias foi discutida principalmente em conexão com a sua suposta introdução de um véu de itens mentais entre a mente e o mundo que leva, por meio dos empiristas, ao ceticismo radical sobre a existência de um mundo externo. Aqui eu proponho enfatizar um aspecto completamente diferente da teoria Cartesiana das idéias que, na minha visão, é mais fundamental no que diz respeito a abrir o caminho empirista que conduz ao ceticismo radical de Hume. Eu argumento que o que eu chamo de o modelo de “apresentação fenomenológica” de justificação última está baseado em uma ambigüidade fundamental entre apreensão sensível e intelectual insinuada pela visão de Descartes de idéias “claras e distintas” junto com a sua ênfase na prioridade da intuição sobre inferência lógica. A apreensão sensível confia no contato imediato com itens presentes fenomenologicamente e ostensivamente perante a mente como particulares dados. O modelo de apresentação fenomenológica está inspirado na apreensão sensível, embora os itens que se apresentam perante a mente poderiam ser eles mesmos idéias do entendimento, figuras da imaginação, impressões sensórias, ou objetos externos materiais. A apreensão intelectual, por contraste, como eu ilustro com o modelo de Leibniz de nosso conhecimento de conceitos e verdades da razão, consiste na compreensão discursiva e não-ostensiva da generalidade de conceitos abstratos e de estruturas formais . Para Leibniz, toda a apreensão intelectual é claramente “apreensão discursiva lógica” por oposição a “apreensão ostensiva direta”. Assim, Leibniz claramente desfaz a ambigüidade do modelo de Descartes em favor de um modelo intelectual preciso. Os empiristas, por contraste, desfazem a ambigüidade da concepção de Descartes em favor de um modelo completamente sensível. (shrink)

In the First Chapter, I give an interpretation of Kant's characterization of a priori knowledge which sharply distinguishes Kant's from an innatist conception; in this way, I distinguish Kant's transcendental explanation of a prioricity from both innatist and naturalistic explanations. ;The arguments given by Kant to support his claim that we are in fact in possession of a priori knowledge rely on his criterion of a prioricity: if a truth is necessary then it must be justified a priori. I criticize (...) the criterion's failure to account for actual cases of being justified in believing necessary truths. Finally, I discuss whether Kant has arguments to show that there is a priori knowledge which are independent of the criterion. ;In the Second Chapter, I examine the similarities and differences between Kant's and Frege's conceptions of a priori knowledge. I argue that Frege, like Kant, concentrates exclusively on the ways we must justify our beliefs in certain truths . I show, however, that Frege does not have straightforward arguments to prove that we can and do know a priori any arithmetical or logical truths, and that he does not have any straightforward explanation of the a prioricity of the laws of logic. Finally, I argue that even though a priori items of knowledge play a privileged role in Frege's project, this role differs from the one that such items have in a Kantian-transcendental project. ;In the Third Chapter, I explore whether we can make sense of the notion of a prioricity and prove that there is a priori knowledge by adopting an approach to justification which differs from both Kant's and Frege's. This approach does not concentrate on the ways we must be justified, but on the actual ways we justify our beliefs. I argue that this approach faces enormous difficulties regarding a prioricity. The central difficulty is that the actual complete justification for a belief cannot be captured exclusively in propositional terms. If a belief is based on inference, practical abilities, tendencies or dispositions enter in its justification. . . . UMI. (shrink)

“Epistemology naturalized” has been extremely influential among contemporary analytical epistemologists. Current discussions about Quine´s thesis do not pay attention to a basic point: his main argument is a historical one. Quine tries to show that a naturalized epistemology is the best way out vis-à-vis the failures of traditional epistemology. In this paper, I argue that Quine´s argument is based on a fictitions historical account. If that is the case, his reasons for a naturalized epistemology are non-sufficient.