Understanding by Induction

I offer an interpretation of Aristotle’s account of our cognitive development, as he presents it in Posterior Analytics II.19 and Metaphysics A1. I defend an expansive reading of inductive learning as a form of cognitive progress from a range of particular truths to some universal explanation why all these truths hold. I argue that, if inductive learning is understood this way, Aristotle’s claim that we learn first principles by induction is not an implausible one—and I present some examples where Aristotle seems to be displaying just this sort of inductive progress in his own scientific works. I end by examining the notion of particularity and universality at play in his descriptions of various cognitive states, and considering what his views on induction tell us about the role perception plays as a starting point for our learning.

Aristotle on Knowledge

This chapter considers Aristotle’s epistemology, focusing on issues explored in Part I. It asks how he conceives of epistêmê in the Posterior Analytics. In particular, is it knowledge and, if so, is it knowledge as such or just a kind of knowledge? In considering this question, the chapter compares Aristotle’s account of epistêmê in the Posterior Analytics with Plato’s account of it in the Meno. It argues that, in defining epistêmê, Aristotle is defining knowledge—but just one kind of knowledge, not knowledge as such. Epistêmê counts as knowledge because it is a truth-entailing cognitive condition that is appropriately cognitively superior to mere true belief. But it isn’t knowledge as such, because Aristotle recognizes other cognitive conditions that also fall under the concept of knowledge but that do not count as epistêmê as it is defined in 1.2

Aristotle’s Two Worlds: Knowledge and Belief in Posterior Analytics 1.33

This chapter explores Posterior Analytics 1.33, asking whether it advocates some version of a Two Worlds Theory. It also compares Aristotle’s attitude to the Two Worlds Theory with Plato’s in Republic 5–7. The chapter discusses different versions of the Two Worlds Theory, distinguishing a theory about propositions from one about objects, and distinguishing a strong from a weak theory. The chapter argues that Aristotle is committed to a Weak Two Worlds Theory for Objects and, on the most plausible reading, some version of a Strong Two Worlds Theory for Propositions. This contrast with Plato, who rejects both a Weak and a Strong Two Worlds Theory for both Objects and Propositions,

Attempts by Avicenna and Ibn alNafīs to Expand the Field of the Transference of Demonstration in the Context of the Relationship Between Geometry and Medicine

This paper aims to deal with the disputes on transferring demonstration between the various sciences in the context of the medicine-geometry relationship. According to Aristotle’s metabasis-prohibition, these two sciences should be located in separate compartments due to the characteristics of their subject-matter. However, a thorough analysis of the critical passage in Aristotle’s Posterior Analytics on circular wounds forces a revision of the boundaries of the interactions between sciences, since subsequently Avicenna, on the grounds of this passage, would widen the area of the transference of demonstration. Furthermore, the fact that Avicenna and Ibn al-Nafīs continued to use geometrical demonstrations in their anatomical investigations shows the need to understand kind-crossing prohibition as a reminder to take into account the present scientific infrastructure and logical rules before proceeding onto a scientific investigation instead of accepting it as a mere nominal doctrine. Therefore, whether kind-crossing was possible or not depended on the extent to which the conclusion derived at the end of the scientific investigation, using a different method after taking into account all these reminders, had contributed to the solution of a particular proposition or the achievement of an approximate truth.

Themistius on Concept Formation

This paper reconstructs the account of concept formation developed in the 4th Century A.D. by Themistius in the most ancient extant commentary on Aristotle’s Posterior Analytics. Themistius’ account can be contrasted with two widespread modern interpretations of Aristotle. Unlike psychological empiricists, Themistius ascribes an active role in concept formation to our innate capacity of understanding (νοῦς). Unlike intuitionists, he would not be satisfied by saying that νοῦς “intuits” or “spots” concepts. Rather, the question is what makes our νοῦς capable of “finding” and “recognizing” concepts in experience, and this can only be an understanding prior to all experience. Themistius seems to be responding here to Platonist arguments against Aristotle’s epistemology: postulating a “potential νοῦς” is not enough, for one can apply Meno’s dilemma to it and ask how it can recognize that it has found what it was looking for. But, contrary to the judgment of some modern scholars, Themistius never embraced the theory of recollection either (he rejects it decisively). He argued that both empiricism and Platonist innatism are wrong and developed a middle path marked by a strong interdependence between the perceptive and the rational capacity. This holds for all rational learning, and concept formation is its first stage: to form a concept means to learn something genuinely new, but also to recognize it as falling, e. g., under one of the ten categories. While being presented as a mere “paraphrasis” of Aristotle’s words, Themistius’ account is a well-advised and original response to the epistemological debates of his time.

Między tęczą a kryształem. Echo u Macieja Kazimierza Sarbiewskiego jako gatunek odbicia w świetle jego komentarza do Summy teologicznej Akwinaty

Between the Rainbow and the Crystal Glass: Echo in Maciej Kazimierz Sarbiewski as a Species of Refraction in the Light of His Commentary on Summa theologica by Thomas Aquinas The aim of this essay is to highlight an important gap in the research into the works of Maciej Kazimierz Sarbiewski (1595–1640), Jesuit neo-Latin poet and philosopher, namely the fact that his still unpublished lectures on one God in three persons and on angels, held in Vilnius Academy in the years 1631–1633, have remained largely unexplored by researchers so far. The main thesis is that these thomistic commentaries can considerably deepen our understanding of the dialectical and theological context of Sarbiewski’s poetry. For example, they shed new light on his Marian imagery (inter alia, the usage of the invocation ‘purum sine fraude vitrum’), or on his way of avoiding the danger of the infinite regress of concepts as being similar to mirror reflections. The argument concentrates on the figure of echo in two poems: the praise of Jan Karol Chodkiewicz and the ode Secunda leuca seu Vaca as influenced by a new version of the Litany of Loreto (Litaniae Deiparae Virginis Mariae). It makes use of the definition of echo as taught in the Coimbra Jesuit Aristotelian courses. The phenomenon of echo is taken together with other species of refraction: the rainbow and reflection (Aristotle, Posterior Analytics, 98a.24–29), and set against the background of new technologies, such as the production of crystal mirrors.

The Supposed Material Cause in Posterior Analytics 2.11

Aristotle presents four causes in Posterior Analytics 2.11, but where we expect matter we find instead the confusing formula, ‘what things being the case, necessarily this is the case’, and an equally confusing example. Some commentators infer that Aristotle is not referring to matter, others that he is but in a non-standard way. I argue that APo. 94a20-34 presents not matter, but determination by general features or facts, including facts about something’s genus. The closest connection to matter is Aristotle’s view that the relation between genus and species is analogous to that between matter and a hylomorphic compound.

Pistis, Persuasion, and Logos in Aristotle

The core sense of pistis as understood in Posterior Analytics, De Anima, and the Rhetoric is not that of a logical relation in which cognitively grasped propositions stand in respect to one another, but the result of an act of socially embedded interpersonal communication, a willing acceptance of guidance offered in respect to action. Even when pistis seems to have an exclusively epistemological sense, this focal meaning of pistis is implicit; to have pistis in a proposition is to willingly accept that proposition as a basis for some kind of activity (albeit possibly theoretical) as a result of some kind of communicative act. This is in accordance with Aristotle’s understanding of argumentation as a social practice, entered into in order lead others to certain actions, for certain ends. Understanding pistis in this way allows us to understand how it is that pistis admits of quantitative variation.

Demonstration By Reductio Ad Impossibile In Posterior Analytics 1. 26

In Posterior Analytics 1. 26, Aristotle states that direct demonstrations are better than demonstrations by reductio ad impossibile. The former, he argues, proceed from premisses that are prior in nature to the conclusion, whereas the latter proceed from premisses that are posterior in nature to the conclusion. While Aristotle’s thesis in Posterior Analytics 1. 26 has been widely influential, his argument for it has proved difficult to understand and is often taken to be incoherent. I argue that Aristotle’s thesis relies on a deductive framework in which the only direct demonstrations are those that derive a universal conclusion. The relevant relation of priority in nature is determined by the order of terms in acyclic chains of immediate universal affirmations. Given this characterization of priority in nature, Aristotle’s argument in Posterior Analytics 1. 26 can be shown to be coherent and successful.

Oxford Studies in Ancient Philosophy, Volume 58

Oxford Studies in Ancient Philosophy provides, twice each year, a collection of the best current work in the field of ancient philosophy. Each volume features original essays that contribute to an understanding of a wide range of themes and problems in all periods of ancient Greek and Roman philosophy, from the beginnings to the threshold of the middle ages. From its first volume in 1983, OSAP has been a highly influential venue for work in the field, and has often featured essays of substantial length as well as critical essays on books of distinctive importance. Volume LVIII contains: a close reading of Plato’s argument for the unity of the political arts in the Statesman; a new interpretation of the lowest part of the Divided Line in Plato’s Republic, based on the perception of value properties; an analysis of Plato’s treatment of belief attribution in the Theaetetus, the Gorgias, and the Meno; a reconstruction of Aristotle’s argument for why direct demonstrations are superior to those which argue by reduction ad impossibile in Posterior Analytics 1. 26; an interpretation of Aristotle’s conception of spontaneous generation that emphasizes the role of putrefaction; a sceptical reading of Cicero’s Tusculan Disputations; a comprehensive survey of Sextus Empiricus’ attitude towards religious belief and practice; and a review essay of Miriam Griffin’s collected papers, which discusses not only the question of how precisely philosophy affected statesmen in Rome, but also larger methodological questions about the history of philosophy.