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.

I argue that Topics VI does not contain any serious theory about definitions, but only a collection of advices for formulating definitions in a dialectical context, namely, definitions aiming to catch what the opponent means. Topics VI is full of inconsistencies that can be explained away by this approach: the inconsistencies reflect "acceptable opinions about definitions" that distinct groups of interlocutors accept. I also argue that the "topoi" need not be pieces of serious theory Aristotle is commited to. The "topoi" (...) must also be considered as "endoxa", namely, as accepted opinions about how it is legitimate to draw an inference. (shrink)

Aristotle contrasts episteme and doxa through the key notions of universal and necessary. These notions have played a central role in Aristotle’s characterization of scientific knowledge in the previous chapters of APo. They are not spelled out in APo I.33, but work as a sort of reminder that packs an adequate characterization of scientific knowledge and thereby gives a highly specified context for Aristotle’s contrast between episteme and doxa. I will try to show that this context introduces a contrast in (...) terms of explanatory claims: on the one hand, episteme covers those claims which capture explanatory connections that are universal and necessary and thereby deliver scientific understanding; on the other hand, doxa covers the explanatory attempts that fail at doing so. (shrink)

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)

I discuss the exact meaning of the thesis according to which the object of scientific knowledge is necessary. The thesis is expressed by Aristotle in the Posterior Analytics, in his definition of scientific knowledge. The traditional interpretation understands this definition as depending on two parallel and independent requirements, the causality requirement and the necessity requirement. Against this interpretation, I try to show, through the examination of several passages that refer to the definition of scientific knowledge, that the necessity requirement specifies (...) more exactly the causality requirement: what cannot be otherwise is the explanatory relation between the explanandum and the cause by which it is what it is. (shrink)

A novel theoretical formulation of Categorical Logic based on two properties of categorical propositions and three simple axioms has been introduced recently. This formulation allowed for the suppression of the distinction between immediate and mediate inferences, and also provided a theoretical framework to study opposition relations, thus restoring the theoretical unity of traditional Aristotelian logic. By using this approach, it has been reported that a total of 3072 conclusive syllogistic moods can be found when including indefinite terms in classical syllogistic, (...) but this result has yet to be proven. This paper presents an overview of the recently proposed theoretical formulation of Categorical Logic, along with the derivation of the 48 canonical syllogistic moods that are capable of generating the 3072 conclusive moods previously reported. (shrink)

Resumen En esta nota presento la teoría unificada de las oraciones copulativas propuesta por Andrea Moro, quien sostiene que el verbo ser no es más que un soporte para la flexión verbal, independientemente de las peculiaridades gramaticales y semánticas de las oraciones adscriptivas, identificativas y existenciales en que aparece. Primero contextualizo la propuesta de Moro; después explico la manera en que Moro aclara una anomalía sintáctica que parece corroborar la supuesta polisemia del verbo ser. Por último, comento algunas omisiones de (...) relevancia filosófica en la historia del verbo ser contada por Moro.In this note I present the unified theory of copular sentences proposed by Andrea Moro, who maintains that the verb to be is nothing more than a support for verbal inflection, regardless of the grammatical and semantic peculiarities of the ascriptive, equative, and existential sentences in which it appears. First, I contextualize Moro's proposal. Then, I explain how Moro clarifies a syntactic anomaly that seems to corroborate the alleged polysemy of the verb to be. Lastly, I comment on some omissions of philosophical relevance in the history of the verb to be told by Moro. (shrink)

This is a brief note that looks at the problem presented by the traditional rendering of the modal syllogism Disamis XLL. In two recent articles, I argue that we should not attribute Disamis XLL to Aristotle. The purpose of this note is to provide textual support for my claim.

The ways in which the Aristotelian sciences are related to each other has been discussed in the literature, with some focus on the subalternate sciences. While it is acknowledged that Aristotle, and Plato as well, was concerned as well with how the arts were related to one another, less attention has been paid to Aristotle's views on relationships among the arts. In this paper, I argue that Aristotle's account of the subalternate sciences helps shed light on how Aristotle saw the (...) art of rhetoric relating to dialectic and politics. Initial motivation for comparing rhetoric with the subalternate sciences is Aristotle's use of the language of boundary transgression, germane to the Posterior Analytics, when discussing rhetoric’s boundaries, as well as the language of "over" and "under" found in APo. First, I discuss three passages in Rhetoric Book I and argue that Garver's (1988) account cannot be correct. Second, I look to the subalternate sciences, especially focusing on optics and the distinction between "unqualified" optics and mathematical optics. Third, I discuss rhetoric's dependence on both dialectic and politics. (shrink)

This chapter discusses the first part of Aristotle's Posterior Analytics A-33, 88b30-89a10. I claim that Aristotle is not concerned with an epistemological distinction between knowledge and belief in general. He is rather making a contrast between scientific knowledge (which is equivalent to explanation by the primarily appropriate cause) and some explanatory beliefs that falls short of capturing the primarily appropriate cause.

In the first book of the Prior Analytics, Aristotle sets out, for the first time in Greek philosophy, a logical system. It consists of a deductive system (I.4-22), meta-logical results (I.23-26), and a method for finding and giving deductions (I.27-29) that can apply in “any art or science whatsoever” (I.30). After this, Aristotle compares this method with Plato’s method of division, a procedure designed to find essences of natural kinds through systematic classification. This critical comparison in APr I.31 raises an (...) interpretive puzzle: how can Aristotle reasonably juxtapose two methods that differ so much in their aims and approach? What can be gained by doing so? Previous interpreters have failed to show how this comparison is legitimate or what important point Aristotle is making. The goal of this paper is to resolve the puzzle. In resolving this puzzle we not only learn more about the relationship be- tween division and the syllogistic in Aristotle. We will also learn something about the motivation for the syllogistic itself, by seeing the role that it plays in his philosophy of science. (shrink)

I argue that these inconsistencies in wording and practice reflect the existence of two distinct Aristotelian views of inquiry, one peculiar to the Posterior Analytics and the other put forward in the Physics and practiced in the Physics and in other treatises. Although the two views overlap to some degree (e.g. both regard a rudimentary understanding of the subject as an essential first stage), the view of the syllogism as the workhorse of scientific investigation and the related view of inquiry (...) as a search for the ‘missing middle terms’ turn out to be ideas peculiar to the Analytics. Conversely, the techniques of analysis and differentiation highlighted in the Physics account receive only cursory attention in the Analytics. However, when we consider the character of Aristotle’s own inquiries, on both scientific and philosophical topics, it becomes clear that it is the Physics rather than the Posterior Analytics that gives us Aristotle’s considered view the path to knowledge. (shrink)

In Prior Analytics I.30, Aristotle seems too much optmistic about finding out the principles of sciences. For he seems to say that, if our empirical collection of facts in a given domain is exhaustive or sufficient, it will be easy for us to find out the explanatory principles in the domain. However, there is a distance between collecting facts and finding out the explanatory principles in a given domain. In this paper, I discuss how the key expression in the sentence (...) at 46a25 should be interpreted: “the true characteristics of things” (“τῶν ἀληθῶς ὑπαρχόντων τοῖς πράγμασιν”). I argue that, on a more accurate interpretation of the expression, Aristotle’s point would cease to look like a piece of naïve or even silly optimism. (shrink)

Este livro marca o início da Série Investigação Filosófica. Uma série de livros de traduções de textos de plataformas internacionalmente reconhecidas, que possa servir tanto como material didático para os professores das diferentes subáreas e níveis da Filosofia quanto como material de estudo para o desenvolvimento pesquisas relevantes na área. Nós, professores, sabemos o quão difícil é encontrar bons materiais em português para indicarmos. E há uma certa deficiência na graduação brasileira de filosofia, principalmente em localizações menos favorecidas, com relação (...) ao conhecimento de outras línguas, como o inglês e o francês. Tentamos, então, suprir essa deficiência, ao introduzirmos traduções de textos importantes ao público de língua portuguesa, sem nenhuma finalidade comercial e meramente pela glória da filosofia. O presente volume é constituído de três traduções de verbetes importantes sobre lógica, da Enciclopédia de Filosofia da Stanford: (1) A Lógica de Aristóteles, (2) Lógica Clássica, (3) Lógica Modal. (shrink)

This volume is dedicated to Prof. Dag Prawitz and his outstanding contributions to philosophical and mathematical logic. Prawitz's eminent contributions to structural proof theory, or general proof theory, as he calls it, and inference-based meaning theories have been extremely influential in the development of modern proof theory and anti-realistic semantics. In particular, Prawitz is the main author on natural deduction in addition to Gerhard Gentzen, who defined natural deduction in his PhD thesis published in 1934. The book opens with an (...) introductory paper that surveys Prawitz's numerous contributions to proof theory and proof-theoretic semantics and puts his work into a somewhat broader perspective, both historically and systematically. Chapters include either in-depth studies of certain aspects of Dag Prawitz's work or address open research problems that are concerned with core issues in structural proof theory and range from philosophical essays to papers of a mathematical nature. Investigations into the necessity of thought and the theory of grounds and computational justifications as well as an examination of Prawitz's conception of the validity of inferences in the light of three “dogmas of proof-theoretic semantics” are included. More formal papers deal with the constructive behaviour of fragments of classical logic and fragments of the modal logic S4 among other topics. In addition, there are chapters about inversion principles, normalization of proofs, and the notion of proof-theoretic harmony and other areas of a more mathematical persuasion. Dag Prawitz also writes a chapter in which he explains his current views on the epistemic dimension of proofs and addresses the question why some inferences succeed in conferring evidence on their conclusions when applied to premises for which one already possesses evidence. (shrink)

This is a translation, made by myself, of the paper to be published in Portuguese in the journal Discurso, 2020, in honour of the late professor Oswaldo Porchat. I discuss what Aristotle was trying to encode when he said that the object of scientific knowledge is necessary, or that what we know (scientifically) cannot be otherwise etc. The paper is meant as a continuation of previous papers—orientated towards a book on the Posterior Analytics—and thus does not discuss in much detail (...) key passages, as the very definition of scientific knowledge in APo I.2, or passages from APo I.4 and I.6 (for these, I refer to my previous papers). This paper is mainly focused on Aristotle’s references to his notion of scientific knowledge both in other passages from the APo and in other treatises. I intend to show that there is a progressive, intrinsic relation between the two requirements by which scientific knowledge is defined. It is not true that each of these requirements stems from a different source. The Causal-Explanatory requirements gives Aristotle the general heading. Then, the Necessity Requirement ranges over the explanatory relation between explanans and explanandum and thereby specifies what sort of cause is sctricly required for having scientific knowledge of a given explanandum. Now, Aristotle was also concerned with the necessary truth of the elemental predications that constitute a demonstration. My claim that the Necessity Requirement ranges over the explanatory relation does not ignore that concern, and does not deny it. My claim is that Aristotle’s main focus, and main concern, consists in stressing that the explanatory factor to be captured in scientific knowledge of a given explanandum is such that cannot be otherwise. (shrink)

At some point in the Incessu Animalium, Aristotle appeals to some geometrical claims in order to explain why animal progression necessarily involves the bending (of the limbs), and this appeal to geometrical claims might be taking as violating the recommendation to avoid “kind-crossing” (as found in the Posterior Analytic). But a very unclear notion of kind-crossing has been assumed in most debates. I will argue that kind-crossing in the Posterior Analytics does not mean any employment of premises from a discipline (...) other than that to which the explanandum belongs. Kind-crossing was meant to cover a specific sort of employment of premises from a different discipline, namely, the case in which premises from a discipline X are taken as the most important explanatory factor that delivers the fullest appropriate explanation of an explanandum within discipline Y. If this is so, the employment of geometrical premises in the Incessu Animalium is not an instance of the prohibited kind-crossing, but something that is in line with the theory of the Posterior Analytics. (shrink)

Through a detailed analysis of the various modes of argumentation employed by Aristotle throughout his natural scientific works, I aim to contribute to the growing scholarship on the relation between Aristotle’s theory of science and his actual scientific practice. I challenge the standard reading of Aristotle as a methodological empiricist and show that he permits a variety of non-empirical arguments to support controversial theses in properly scientific contexts. Specifically, I examine his use of logical (logikôs) argumentation in the discussion of (...) mule sterility in Generation of Animals II 8, rational (kata ton logon) argumentation in his discussion of cardiocentrism throughout the biological works, and the method of division in Posterior Analytics II 13. (shrink)

I present Aristotle’s theory of causation in a way that privileges a comparison with contemporary discussion on causation. I do so by selecting in Aristotle’s theory points that are interesting to contemporary discussion and by translating Aristotle in the contemporary philosophical terminology. I compare Aristotle’s views with Mackie’s (1993/1965) and Sosa’s (1993/1980). Mackie is a humean regularist regarding the metaphysics of causal necessity, but his theory postulates some formal aspects of the causal relation which are similar to the Aristotelian theory. (...) By introducing the notion of causal field as a third causal relatum – a sample in which the cause must be picked out as a explanation coextensive to the effect –, Mackie holds a point very similar to Aristotle, inasmuch as both defend that the causal relation is triadic and both have the extensional desideratum. Sosa (1993/1980) defends that every cause necessitates its effect, arguing against classical Humeanism, and he also proposes a causal pluralism. Both these theses are clearly Aristotelian. Aristotle comprehends that the causal relation has three relata: a subjacent C, a property of that subjacent A and a cause B that explains why such property is attributed to that subjacent. The subjacent is similar to Mackie’s notion of causal field, for in regard to it the cause must be coextensive to the property. But Aristotle also says that for each explanandum (property attributed to a subjacent of which one aims to investigate a cause) there is only one cause, which necessitates it. Sosa and Aristotle are similar because both develop a causal pluralism from a theory of causes as having intrinsic necessitation. For Aristotle, causes/explanations [aitiai] are central for attaining scientific knowledge, and its triadic structure determines the syllogistic structure of scientific demonstrations. Aristotle’s theory of causation also involves comprehending the actualisation of capacities (dispositional properties of objects) affirming that the causal relation is resultant from intrinsic properties of the objects, and the cause B is the essence of the explanandum. (shrink)

This dissertation explores Aristotle’s use of teleology as a principle of explanation, especially as it is used in the natural treatises. Its main purposes are, first, to determine the function, structure, and explanatory power of teleological explanations in four of Aristotle’s natural treatises, that is, in Physica (book II), De Anima, De Partibus Animalium (including the practice in books II-IV), and De Caelo (book II). Its second purpose is to confront these findings about Aristotle’s practice in the natural treatises with (...) the theoretical picture of the structure of teleological explanations gained from Aristotle’s theory of scientific demonstration. For this purpose a new interpretation of Analytica Posteriora II.11 is presented. This study thereby contributes to recent scholarship on the relation between Aristotle’s philosophy of science and his philosophy of nature, while at the same time adding to our knowledge of Aristotle’s notion of teleology in terms of its explanatory merits and limits. (shrink)

Although there are many questions to be asked about philosophy of mathematics, the fundamental questions to be asked will be questions about what the mathematical object is in view of being and what the mathematical reasoning is in view of knowledge. It is clear that other problems will develop in parallel within the framework of the answers to these questions. For this rea­ son, when we approach Aristotle's philosophy of mathematics over these two basic problems, we come up with the (...) concept of abstraction. In our work, I will try to explain the mathematical abstraction that Aristotle has developed to understand mathematical philosophy. (shrink)

I review David Bronstein's "Aristotle on Knowledge and Learning: The Posterior Analytics".

I argue that Aristotle’s account of scientific demonstrations in the Posterior Analytics is centred upon formal causation, understood as a demonstration in terms of essence (and as innocent of the distinction between form and matter). While Aristotle says that all four causes can be signified by the middle term in a demonstrative syllogism, and he discusses at some length efficient causation, much of Aristotle’s discussion is foremost concerned with the formal cause. Further, I show that Aristotle had very detailed procedures (...) for identifying the formal cause, and that he is aware of several problems which might lead one to erroneously identify the wrong form as the cause of a property. Finally, I show that Aristotle’s account can easily be adapted to material causation, and through some modifications (introduction of process universals related through parthood), hinted at in II 11-12 and 16-17, to efficient and final causation. (shrink)

The concept of “necessity of thought” plays a central role in Dag Prawitz’s essay “Logical Consequence from a Constructivist Point of View” (Prawitz 2005). The theme is later developed in various articles devoted to the notion of valid inference (Prawitz, 2009, forthcoming a, forthcoming b). In section 1 I explain how the notion of necessity of thought emerges from Prawitz’s analysis of logical consequence. I try to expound Prawitz’s views concerning the necessity of thought in sections 2, 3 and 4. (...) In sections 5 and 6 I discuss some problems arising with regard to Prawitz’s views. (shrink)

Epicureans and Stoics reject the independent existence of the Platonic Ideas. This paper assesses what both schools put forward as substitutes for universals. Both Epicureans and Stoics appeal to an a posteriori mental capacity for generalisation but that is where their shared commitments end. the divergences are mapped out, against a tendency in historiography to assimilate the two strategies, and both theories are then analysed independently.

Although the theory of the assertoric syllogism was Aristotle's great invention, one which dominated logical theory for the succeeding two millenia, accounts of the syllogism evolved and changed over that time. Indeed, in the twentieth century, doctrines were attributed to Aristotle which lost sight of what Aristotle intended. One of these mistaken doctrines was the very form of the syllogism: that a syllogism consists of three propositions containing three terms arranged in four figures. Yet another was that a syllogism is (...) a conditional proposition deduced from a set of axioms. There is even unclarity about what the basis of syllogistic validity consists in. Returning to Aristotle's text, and reading it in the light of commentary from late antiquity and the middle ages, we find a coherent and precise theory which shows all these claims to be based on a misunderstanding and misreading. (shrink)

This article outlines a method of collaboration that will manifest a high probability of cumulative and progressive results in science. The method will accomplish this through a division of labour grounded in the order of occurrence of human cognitional operations. The following article explores the possibility of a method known as functional specialization, distinct tasks presently operative in neuroscience. Functional specialization will enhance collaboration within a science as well as initiate implementation of generalized empirical method. Implementation of generalized empirical method (...) will be achieved through the focus of individual specialties on specific mental operations. (shrink)

Aristotle's General Definition of the Syllogism may be taken as consisting of two parts: the Inferential Conditions and the Final Clause. Although this distinction is well known, traditional interpretations neglect the Final Clause and its influence on syllogistic. Instead, the aforementioned tradition focuses on the Inferential Conditions only. We intend to show that this neglect has severe consequences not just on syllogistic but on the whole exegesis of Aristotle's Prior Analytics I. Due to these consequences, our objective is to analyse (...) the General Definition's Final Clause and its consequences on syllogistic. We propose a reading of the Final Clause as an additional criterion for distinguishing some arguments as properly syllogistic ones and as a main theme which connects all parts of the Prior Analytics I into one coherent piece of work. (shrink)

We can now recognize Aristotle's many accomplishments in logical theory, not the least of which is treating the deduction process itself as a subject matter and thus establishing the science of logic. Aristotle took logic to be that part of epistemolo gy used to establish knowledge of logical consequence. Prior Analytics is a metalogical treatise on his syllogistic system in which Aristotle modelled his deduction system to demonstrate certain logical relationships among its rules. Aristotle's n otion of substitution distinguishes logical (...) syntax from semantics and enabled him to distinguish validity from deducibility sufficiently to note the completeness of his logic. (shrink)

Aristotle's cognitive ideal is a form of understanding that requires a sophisticated grasp of scientific first principles. At the end of the Analytics, Aristotle tells us that we learn these principles by induction. But on the whole, commentators have found this an implausible claim: induction seems far too basic a process to yield the sort of knowledge Aristotle's account requires. In this paper I argue that this criticism is misguided. I defend a broader reading of Aristotelian induction, on which there's (...) good sense to be made of the claim that we come to grasp first principles inductively, and show that this reading is a natural one given Aristotle's broader views on scientific learning. (shrink)

In the Meno there is a paradox claiming that research and therefore learning is impossible; because we know a something or not. If there is knowledge, we don't need to research and if there isn't, we cannot search; because we haven't any idea of a subject-matter. Plato resolves the paradox by the theory of Anamnesis: knowledge/learning is recollection. This theory presupposes the pre-existence of the soul and its transmigration. In the Posterior Analytics Aristotle discusses the paradox and resolves it by (...) separation between previous universal knowledge and the particular knowledge of things. Al-Farabi in the treatise Harmonization between the opinions of Plato and Aristotle, tries to reconcile their principal views which one of them is on the paradox of Meno. He relates their views from Plato's Phaedo and Aristotle's Posterior Analytics and then harmonizing them. Al-Farabi as a Muslim philosopher has no attention to the theory of soul transmigration in the Phaedo and looks at the arguments of the immortality of the soul as a witness that Plato uses in answering the problem of knowledge/learning. Because of this interpretation and his focusing on the essence of recollection theory, Al-Farabi eventually reconciles the recollection theory with the theories of deduction and induction. (shrink)

Aristotle studies syllogistic argumentation in Sophistical Refutations and Prior Analytics. In the latter he focuses on the formal and syntactic character of arguments and treats the sullogismoi and non-sullogismoi as argument patterns with valid or invalid instances. In the former Aristotle focuses on semantics and rhetoric to study apparent sullogismoi as object language arguments. Interpreters usually take Sophistical Refutations as considerably less mature than Prior Analytics. Our interpretation holds that the two works are more of a piece than previously believed (...) and, indeed, that Aristotle's treatment of fallacious reasoning presupposes the results of the formal theory. (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)

A discussão nos livros dos Tópicos giram em torno dos debates dialéticos e seus elementos. Aristóteles discorre sobre os gêneros, as propriedades e os chamados acidentes e suas relações predicativas em categorias. Interessa-nos, sobretudo, compreender o papel desempenhado pela Definição e qual sua relação com os demais instrumentos para a dialética.