La noción estándar de axiomática que se atribuye a Aristóteles supone un conjunto de proposiciones básicas a partir del cual se infiere un conjunto numéricamente mayor de proposiciones derivadas. Esto se conoce como parsimonia de los principios. Además, el conocimiento de los principios se reduce a una captación intelectual directa. Se pretende mostrar que tales atribuciones no son correctas para el caso de Acerca del cielo I. Se brindan elementos para una alternativa de lo que puede entenderse por axiomatización en (...) Aristóteles. Para ello se trabajará en la reconstrucción de los argumentos de algunos pasajes de Acerca del cielo I. The standard notion of axiomatics attributed to Aristotle presupposes a set of basic propositions on the basis of which a larger set of derived propositions is inferred. This is known as the principle of parsimony. Moreover, the knowledge of principles is limited to direct intellectual apprehension. Our objective is to demonstrate that said attributions are not correct in the case of On the Heavens I and to provide elements for what could be understood as axiomatization in Aristotle. To that effect we reconstruct the arguments set forth in some passages of On the Heavens I. (shrink)

Translation of Aristotle's Posterior Analytics II into Portuguese, with a few notes, experimental glossary and introduction. The translation, which was made at 2002 (with a new printing in 2004), was preliminary and its publication was intended to provide a didactic tool for courses as well as a provisional resource in research seminars. It needs some revision. I am currently working (slowly...) on the revision of the translation and a new revised one will surely appear at some point.

Translation of Aristotle's Posterior Analytics I into Portuguese, with a few notes, experimental glossary and introduction. The translation, which was made at 2003/4, was preliminary and its publication was intended to provide a didactic tool for courses as well as a provisional resource in research seminars. It needs some revision. I am currently working (slowly...) on the revision of the translation and a new revised one will surely appear at some point.

In Posterior Analytics 71b9 12, we find Aristotle’s definition of scientific knowledge. The definiens is taken to have only two informative parts: scientific knowledge must be knowledge of the cause and its object must be necessary. However, there is also a contrast between the definiendum and a sophistic way of knowing, which is marked by the expression “kata sumbebekos”. Not much attention has been paid to this contrast. In this paper, I discuss Aristotle’s definition paying due attention to this contrast (...) and to the way it interacts with the two conditions presented in the definiens. I claim that the “necessity” condition ammounts to explanatory appropriateness of the cause. (shrink)

Most interpretations of Aristotle’s Posterior Analytics believe that the term ‘ameson’ is used to describe the principles or foundations of a given system of justification or explanation as epistemically prior to or more fundamental than the other propositions in the system. Epistemic readings (as I shall call them) arguably constitute a majority in the secondary literature. This predominant view has been challenged by Robin Smith (1986) and Michael Ferejohn (1994; 2013), who propose interpretations that should be classified as non-epistemic according (...) to the definition above. My aim in this article is purely negative. I intend to show that these non-epistemic interpretations are liable to serious objections and are in conflict with some important features of Aristotle’s theory of demonstration. (shrink)

This paper concerns Aristotle's kind‐crossing prohibition. My aim is twofold. I argue that the traditional accounts of the prohibition are subject to serious internal difficulties and should be questioned. According to these accounts, Aristotle's prohibition is based on the individuation of scientific disciplines and the general kind that a discipline is about, and it says that scientific demonstrations must not cross from one discipline, and corresponding kind, to another. I propose a very different account of the prohibition. The prohibition is (...) based on Aristotle's scientific and metaphysical essentialism, according to which a scientific demonstration must take as its starting point a set of per se properties of a subject, if these make up a single, unitary definition. The subject of demonstration here is a kind, although not the general kind associated with a discipline, but rather the particular kind that the particular demonstration is about. (shrink)

The paper is devoted to Aristotle's solution to Meno's paradox: a person cannot search for what he knows -- he knows it, and there is no need to search for such a thing -- nor for what he doesn't know -- since he doesn't know what he's searching for. The autor argues that Aristotle proposes solutions of this paradox for every stage of cognition, not only for exercising available scientific knowledge as regarded by most Aristotelian scholars. He puts more focus (...) on the importance of the distinction between 'progignoskein' (pre-existing cognition) and 'proepistasthai' (pre-existong knowledge) for Aristotle's solution of this paradox. [In Russian]. (shrink)

The ancient Greek method of analysis has a rational reconstruction in the form of the tableau method of logical proof. This reconstruction shows that the format of analysis was largely determined by the requirement that proofs could be formulated by reference to geometrical figures. In problematic analysis, it has to be assumed not only that the theorem to be proved is true, but also that it is known. This means using epistemic logic, where instantiations of variables are typically allowed only (...) with respect to known objects. This requirement explains the preoccupation of Greek geometers with questions as to which geometrical objects are ?given?, that is, known or ?data?, as in the title of Euclid's eponymous book. In problematic analysis, constructions had to rely on objects that are known only hypothetically. This seems strange unless one relies on a robust idea of ?unknown? objects in the same sense as the unknowns of algebra. The Greeks did not have such a concept, which made their grasp of the analytic method shaky. (shrink)

According to the standard and largely traditional interpretation, Aristotle’s conception of nous, at least as it occurs in the Posterior Analytics, is geared against a certain set of skeptical worries about the possibility of scientific knowledge, and ultimately of the knowledge of Aristotelian first principles. On this view, Aristotle introduces nous as an intuitive faculty that grasps the first principles once and for all as true in such a way that it does not leave any room for the skeptic to (...) press his skeptical point any further. Thus the tradi- tional interpretation views Aristotelian nous as having an internalist justificatory role in Aristotelian epistemology. In contrast, a minority (empiricist) view that has emerged recently holds the same internalist justificatory view of nous but rejects its internally certifiable infallibility by stressing the connection between nous and Aristotelian induction. I argue that both approaches are flawed in that Aristotle’s project in the Posterior Analytics is not to answer the skeptic on internalist justificatory grounds, but rather lay out a largely externalist explication of scientific knowledge, i.e. what scientific knowledge consists in, without worrying as to whether we can ever show the skeptic to his satisfaction that we do ever possess knowledge so defined. (shrink)

I discuss in this paper the six requirements Aristotle advances at Posterior Analytics A-2, 71b20-33, for the premisses of a scientific demonstration. I argue that the six requirements give no support for an intepretation in terms of “axiomatization”. Quite on the contrary, the six requirements can be consistently understood in a very different picture, according to which the most basic feature of a scientific demonstration is to explain a given proposition by its appropriate cause.

This paper discusses the contrast between scientific knowledge and opinion as it is presented by Aristotle in Posterior Analytics A.33. Aristotle's contrast is formulated in terms of understanding or not understanding some "necessary items". I claim that the contrast can only be understood in terms of explanatory relevance. The "necessary items" are middle terms (or explanatory factors) that are necessary for the fully appropriate explanation. This approach gives a coherent interpretation of each step in the chapter.

Este trabajo presenta lo que para la mayoría de los intérpretes de Aristóteles, que se ocupan del asunto del método en su obra, constituye el principal problema a resolver. Se trata del problema de determinar la relación existente entre la concepción aristotélica de ciencia demostrativa, consignada en los Analíticos Segundos, y la praxis investigativa de Aristóteles en sus diferentes tratados científicos, una praxis que los intérpretes dan frecuentemente en describir como dialéctica.

Equally surprisingly, Descartes’s paranoid belief was shared by several contemporary mathematicians, among them Isaac Barrow, John Wallis and Edmund Halley. (Huxley 1959, pp. 354-355.) In the light of our fuller knowledge of history it is easy to smile at Descartes. It has even been argued by Netz that analysis was in fact for ancient Greek geometers a method of presenting their results (see Netz 2000). But in a deeper sense Descartes perceived something interesting in the historical record. We are looking (...) in vain in the writings of Greek mathematicians for a full explanation of what this famous method was. And I will argue for an answer to the question why this lacuna is there: Not because Greek geometers wanted to hide this method, but because they did not fully understand it. It is instructive to note the ambivalent attitude of the most rigorous mathematician of the period, Isaac Newton, to the method of analysis. He used it himself in his own mathematical work and in the expositions of that work. Yet when the mathematical push came to physical and cosmological shove, he formulated his Principia entirely in.. (shrink)

Whether Aristotle wrote the treatises of Metaphysics with different conceptions of the science of Being in mind has long puzzled scholars. The particular question that causes them unease is whether Aristotle’s enterprise in establishing the science of Being through the several treatises of Metaphysics is marked by a general science of Being, studying all departments of Being whatsoever, or whether his investigation of this science reflects an attitude towards a special metaphysics seeking knowledge of a special department of Being, in (...) this case, God, and therefore should be regarded as a science that is eminently theological. In this thesis, I aim to show that Aristotle’s enterprise in Metaphysics does not necessarily hinder reconciliation between the universal and the theological dimensions of the science of Being and that although Aristotle's conception of the science of Being is eminently theological it does not conflict with its also being universal. Furthermore, I aim to show that had the conception of the science of Being in Aristotle’s mind not been theological, it would not be universal either. (shrink)

Pretendemos averiguar como Aristóteles concebe a passagem do nosso conhecimento prévio do mundo ao conhecimento científico, avaliando os pressupostos e consequências de sua resposta ao paradoxo de Mênon e atentando para a metodologia científica defendida nos Segundos Analíticos. Quanto ao conhecimento preliminar necessário à edificação da ciência, procuraremos caracterizar seus tipos e também os meios pelos quais ele pode vir a ser adquirido por nós. Buscaremos estabelecer também as propriedades que o conhecimento científico deve possuir em relação à sua necessidade, (...) universalidade e caráter explanatório. Buscaremos marcar, com precisão, a natureza da conclusão científica segundo a teoria científica aristotélica, argumentando que, nas conclusões, o atributo demonstrado, em relação com seu substrato, representa uma propriedade por si concomitante. Pretendemos averiguar como os diferentes tipos de demonstração e definição respondem a diferentes estágios de organização do saber prévio e a diferentes estágios na estruturação das demonstrações propriamente científicas, e, por conseguinte, como esses se organizam de modo a responder as quatro perguntas que toda investigação científica deve abarcar em seus dois estágios. (shrink)

Our purpose is to study Aristotle?s solution, in the second book of the Posterior Analytics, for the problem of the apprehension of the principles of science. We attend to the relations between the concepts of induction (epagoge) and intelligence (nous) found in the chapter 19, which seems to confirm that the acquisition of the principles is reached by a process of empirical observation. We examine the method, proposed in chapters 13 to 17, for the right formulation of definitions, which seems (...) to attribute to dialectics the task of finding the principles. Aristotle seems to indicate two different methods ? on one hand, the empirical observation followed by intelligence, on other, the dialectics ? for the apprehension of the principles. Our purpose is to study possible solutions for the problem of the concurrence between these two methods in order to refute as much a strictly empiricist interpretation as a strictly dialectical one. (shrink)

Aristotle's theory of demonstration, developed in the Posterior Analytics, is not restricted to determining the formal requirements for formulating probative arguments that establish properly the results of scientific investigation. To the probative aspect of demonstration it shall be added its primarily explanatory character, orientated by theses of strong ontological and metaphysical content and involving notions like substance, essence and causation. We shall analyze the relation between those two ranges of Aristotle's philosophy of science and investigate how the formal features of (...) demonstration maintain an affinity with the metaphysical background to which scientific activity is conditioned. (shrink)

En este artículo se discute la relación entre silogismo y demostración con respecto al concepto aristotélico del conocimiento científico formulado en los Analíticos segundos. La argumentación sigue tres líneas principales: (i) se ofrecen razones para rechazar la relegación de la sistematización silogística a la instancia postrera de justificación y exposición didáctica del conocimiento previamente adquirido. Como respuesta alternativa, (ii) se muestra que una explicación aristotélica necesita la silogística en virtud del papel que desempeña la causa como término medio silogístico. En (...) consecuencia, debería estar en condiciones de (iii) sostener que no resulta factible establecer firmemente los principios propios como premisas explicativas sin construir silogismos. This article focuses on the relation between syllogism and demonstration, as related to Aristotle's concept of scientific knowledge in his Posterior Analytics. Three main lines of argumentation are followed: (i) reasons are given to reject that syllogistic systematization plays a unique role as a skill for justification and didactic proof of a body of knowledge previously acquired. Alternatively, (ii) it is showed that an Aristotelian explanation requires syllogistic as to the role of cause as middle syllogistic term. Thus, it should be feasible (iii) to sustain that it is not possible to firmly establish proper principles as explanative premises without constructing syllogisms. (shrink)