Posterior Analytics Research Articles

Aristotle and Greek Geometrical Analysis

This paper aims to show that an examination of some passages in Aristotle’s work can contribute to the resolution of crucial problems related to the interpretation of ancient geometrical analysis. In this context, we will focus in particular on the famous passage of the Posterior Analytics in which Aristotle cryptically refers to the analysis practised by the geometers (Posterior Analytics, book I, chapter 12) and we will show the fundamental importance of this passage for a correct understanding of ancient geometrical analysis.

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

Abstract 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.

Неизданные логические сочи­нения Герасима Влаха

Gerasimos Vlachos was one of the most important Greek scholars of the 17th century, he is also known as the teacher of the brothers Leichoudes, the founders of the Slavic-Latin-Greek Academy in Moscow. The paper focuses on his unpublished student textbook on logic, which was a model for that of Sophronios Leichoudes. It appears that all the texts that make up this collection still remain unidentified. However, the catalogue of the Gerasimos Vlachos’s private library, composed by Vlachos himself in 1683, and preserved in the Hellenic Institute for Byzantine and Post-Byzantine Studies in Venice, provides us with the list of his logical writings. According to it, the whole collection comprises a com­mon “Introduction in logic”, an “Introduction in questions and answers”, as well as the paraphrases and introductions to Porhyry’s “Isagoge”, Aristotle’s “Categories”, “On Inter­pretation”, “Prior Analytics” and “Posterior Analytics”. The main objective of the present investigation, therefore, is to identify the titles of the logical writings listed in a catalogue of his private library with the logical texts, attributed to Vlachos in the manuscripts. After examining all the known witnesses that are supposed to transmit Vlachos’s texts, we con­cluded that indeed only five of eight codices contain the genuine Vlachos’s works on logic, no single codex contains the whole collection of his logical treatises but it seems that all of them survived. These preliminary investigations allow us to arrange these writings in orig­inal order and identify them with the titles of the catalogue. Finally, the data obtained from this survey authorized us to present the arguments for the selection and priority of the wit­nesses as well as for the possible structure of the future edition.

Aristotle on Geometrical Potentialities

This paper examines Aristotle's discussion of the priority of actuality to potentiality in geometry at Metaphysics Θ9, 1051a21–33. Many scholars have assumed what I call the "geometrical construction" interpretation, according to which his point here concerns the relation between an inquirer's thinking and a geometrical figure. In contrast, I defend what I call the "geometrical analysis" interpretation, according to which it concerns the asymmetrical relation between geometrical propositions in which one is proved by means of the other. His argument as so construed is ultimately based on the asymmetrical relation between the corresponding geometrical facts. Then I explore this ontological priority in geometry by drawing attention to a parallel passage, Posterior Analytics II.11, 94a24–35, where Aristotle explains the relation between the same geometrical propositions in connection to material causation.

The Supposed Material Cause in Posterior Analytics 2.11

Abstract 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.

A Teoria da Demonstração Científica de Aristóteles em Segundos Analíticos 1.2-9 e 1.13

Defendo uma interpretação do livro I dos Segundos Analíticos de Aristóteles que distingue dois projetos em diferentes trechos da obra: (i) explicar em que consiste uma dada ciência e (ii) explicar em que consiste o conhecimento propriamente científico. Exponho a teoria de Aristóteles que responde à questão ii, com especial atenção à definição de conhecimento científico em 71b9-12 e mostrando como isso se desdobra ao longo dos capítulos 1.2-9 e 1.13 em uma consistente Teoria da Demonstração Científica. O principal ponto dessa teoria é que demonstrações precisam capturar explicações relevantes. Alguns requisitos formais (como a estrutura silogística e a coextensão de termos) são desdobramentos do alvo principal, a saber, capturar e expor de forma apropriada relações causais-explanatórias relevantes.

ARISTOTLE, POSTERIOR ANALYTICS 2.1, 89B25–6 ΕΙΣ ΑΡΙΘΜΟΝ ΘΕΝΤΕΣ

In the opening sentences of Book 2 of Posterior Analytics, Aristotle defines the four types of question that one can pose within the demonstrative science. In the edition by William D. Ross, the text reads as follows (89b23–31): τὰ ζητούμενά ἐστιν ἴσα τὸν ἀριθμὸν ὅσαπερ ἐπιστάμεθα. ζητοῦμεν δὲ τέτταρα, τὸ ὅτι, τὸ διότι, εἰ ἔστι, τί ἐστιν. ὅταν μὲν γὰρ πότερον τόδε ἢ τόδε ζητῶμεν, εἰς ἀριθμὸν θέντες, οἷον πότερον ἐκλείπει ὁ ἥλιος ἢ οὔ, τὸ ὅτι ζητοῦμεν. σημεῖον δὲ τούτου· εὑρόντες γὰρ ὅτι ἐκλείπει πεπαύμεθα· καὶ ἐὰν ἐξ ἀρχῆς εἰδῶμεν ὅτι ἐκλείπει, οὐ ζητοῦμεν πότερον. ὅταν δὲ εἰδῶμεν τὸ ὅτι, τὸ διότι ζητοῦμεν, οἷον εἰδότες ὅτι ἐκλείπει καὶ ὅτι κινεῖται ἡ γῆ, τὸ διότι ἐκλείπει ἢ διότι κινεῖται ζητοῦμεν.The things we seek are equal in number to those we understand. We seek four things: the fact, the reason why, if it is, what it is. For when we seek whether it is this or this, putting it into a number (e.g. whether the sun is eclipsed or not), we seek the fact. Evidence for this: on finding that it is eclipsed we stop; and if from the start we know that it is eclipsed, we do not seek whether it is. When we know the fact we seek the reason why (e.g. knowing that it is eclipsed and that the earth moves, we seek the reason why it is eclipsed or why it moves).

Circular Demonstration and the Necessity of Minor Premises

In the Prior Analytics Aristotle famously endorses the validity of the mixed modal syllogism Barbara lxl, but in the Posterior Analytics we appear to find Aristotle arguing that since demonstrations are only of what cannot be otherwise, both premises need to be necessary. One would almost think that Aristotle had forgotten what he said about mixed modal syllogisms were it not for the fact that he also appears to refer to it directly in Posterior Analytics i.6. This is puzzling. In this paper I will consider evidence for and against taking both premises to be necessary and conclude that, in accordance with Barbara lxl, the major premise of a demonstration needs to be necessary but the minor premise need not be, and this because the minor term – which denotes the object of inquiry and that to which the demonstrator is trying to demonstrate that something belongs necessarily – may be an accidental term. In particular, I will be offering an original interpretation of Aristotle’s arguments against circular demonstration in Posterior Analytics i.3, which only makes sense if the minor premise is not necessary.

An early stage in the evolution of Aristotle's physics

Aristotle's Physics V and VI deal with the same concepts: motion, change and continuity. The two books, however, employ altogether different approaches to the study of these concepts, thus presenting different orders of conceptualization. Abraham Edel (1982, 42) claims that Aristotle is a systematic philosopher “not in the sense of [i] one who pursues a deductive system … but in the sense of [ii] one who has a well-constructed and fairly clearly analyzed conceptual network that he uses with considerable power in field after field of human inquiry.” Truly, [ii] is more typical of Aristotle, but in the Physics both approaches are present. Books VI and V (respectively) are good examples. It is commonly taken for granted that Physics V prepares for VI, because of the order in which they appear in the corpus, and because V includes the definitions of the main concepts that are used in VI. A closer look at the texts, however, reveals that the definitions of V are not used in VI. I argue that the definitions of V were not only unknown when VI was written, but are actually incompatible with the spirit of Physics VI and with the main thesis underlying it. Physics VI is close in method, conceptual basis and in its radical formal approach to the Posterior Analytics, and a part of it (the early stratum) looks like a mathematical exercise. The mathematical-logical approach was abandoned, and gave way to the more mature Aristotelian style, which is already dominant in Physics V.

A Companion to Giles of Rome ed. by Charles F. Briggs and Peter S. Eardley

Reviewed by: A Companion to Giles of Rome ed. by Charles F. Briggs and Peter S. Eardley Chris Jones Briggs, Charles F., and Peter S. Eardley, eds, A Companion to Giles of Rome (Brill’s Companions to the Christian Tradition, 71), Leiden, Brill, 2016; e-book; pp. xii, 319; R.R.P. US$194.00, €157.00; ISBN 9789004315396. Giles of Rome has never quite made the A-list. Machiavelli, typecast as the Eminem of medieval political thought, enjoys instant name recognition alongside a reputation for being occasionally offensive. Aquinas, on the other hand, remains an enigmatic Beyoncé-esque figure; even those who have not dived deeply into his back catalogue recognize both his genius and his influence. If constructing a taxonomy of late medieval celebrity, Giles, however, would be a Lloyd Cole-like figure. This is, in part, because, despite a semi-dramatic shift in style late in his career, his work is marked by strong underlying themes. In the context of this slightly stretched metaphor, however, the most important point is that, beyond a devoted and knowledgeable fan-base, his name is likely to invoke hazy recollection among some over-forties while leaving most to reach for Google. While this Companion is unlikely to change that, it is not only a welcome addition to the shelves of those interested in late medieval thought, but a notable reminder of Giles’s influence among his contemporaries. Today, Giles is probably best-known as a so-called papal hierocrat. His De ecclesiastica potestate sits alongside the work of James of Viterbo as the intellectual underpinning of Pope Boniface VIII’s ultimately disastrous attempt to pit papal theory against the reality of Capetian power at the start of the fourteenth century. A few decades earlier, Giles wrote what would become the most influential mirror of princes in the Middle Ages for the man who became Boniface’s most implacable foe, King Philip IV. At the same time, Giles was the [End Page 182] dominant intellectual force within the Augustinian order, a university master, an archbishop, and a voice in favour of suppressing the Templars. As one of the editors, Charles Briggs, explains in the first chapter, the last thirty years have seen a renewed interest in Giles and his work. This entry in Brill’s Companions to the Christian Tradition series capitalizes and builds on this research to provide a rounded introduction. Following Briggs’s overview of Giles’s life, works, and legacy, seven chapters explore his approach to, respectively, theology; natural philosophy; metaphysics; cognition; ethics and moral psychology; logic, rhetoric, and language; and political thought. Overall, the chapters are of an extremely high quality, written by leading experts in the field. Together, they draw attention to two questions: the degree to which Giles’s thought was shaped by Aristotle, Augustine, and Aquinas, and the extent to which Giles himself stepped beyond his influences. They nuance our understanding while underlining strongly, as Roberto Lambertini highlights (p. 273), that drawing a simplistic dichotomy between Augustinianism and Aristotelianism is highly misleading. Generally speaking, the editorial quality is high. The book is equipped with excellent bibliographies and a comprehensive index. I spotted only one obvious typo (p. 13, n. 31: the date should read 1293, not 1393) and two cases of repeated words in Chapter 6. Nevertheless, it should be said that the formal introduction (pp. 1–5) is perfunctory; it is little more than a series of abstracts. Further, while most chapters include the Latin source material in their notes, Richard Cross’s discussion of Giles’s theology (Chapter 2) does not. Editorial intervention here would have ensured greater consistency. Constantino Marmo’s contribution (Chapter 7), while drawing attention to Giles as the first medieval commentator on Aristotle’s Rhetoric and offering analysis of his much-neglected commentary on the Posterior Analytics, like Chapter 2, ends abruptly without any summing up. This seems out of step with the volume as a whole. It is also unclear why Chapter 5 (Giorgio Pini’s ‘Cognition’) restricts itself to Giles’s mature thought, while Chapter 6 (Peter Eardley’s ‘Ethics and Moral Psychology’) takes a—welcome—longer view. Inevitably, specialists will find points of contention in individual...

The Elements of Avicenna's Physics: Greek Sources and Arabic Innovations by Andreas Lammer

Reviewed by: The Elements of Avicenna's Physics: Greek Sources and Arabic Innovations by Andreas Lammer Bilal Ibrahim Andreas Lammer. The Elements of Avicenna's Physics: Greek Sources and Arabic Innovations. Scientia Graeco-Arabica, 20. De Gruyter, 2018. Pp. xx + 594. Cloth, $149.99. In this timely and outstanding contribution, Andreas Lammer tackles central concepts and problems in Avicenna's Physics of the Healing. The analysis provides a wide-ranging but cohesive study of Avicenna's approach and ideas. The philological and philosophical analysis of the historical context of Avicenna's arguments pays dividends. Avicenna's—often radical—reworking of Aristotle's approach in the Physics critically engages a long tradition of Peripatetic and Neoplatonic philosophy in Greek and Arabic. Lammer's contribution, based on his doctoral dissertation, lays fertile ground for future work. Given the limitations of this review, I focus in the following on the results and fruitful questions raised by chapters 2, 3, and 4. Despite their importance, I set aside chapter 5, which treats Avicenna's defense of Aristotle view of place, and chapter 6, which deals with his attempt to unify Aristotle's reductive view of time with a Platonist view of it as a stable magnitude. Chapter 1 assesses the translation history of Aristotle's Physics and the status of related commentarial material. Lammer sets the boundaries of what we presently know about Avicenna's sources, which is rather little in terms of direct evidence. Subsequent chapters proceed by piecing together the larger context of ideas that Avicenna would have engaged. In chapter 2, Lammer assesses Avicenna's method in the exposition of concepts in his Physics, I.1. The central argument of the chapter is a significant one: Avicenna does not set out a method of inquiry into the principles of natural things, which is the dominant understanding of Aristotle's Physics I.1 among ancients and moderns. Rather, Avicenna adopts a mode of instruction. Aristotle begins I.1 with the advice that we start from what is "more knowable and clear to us" and proceed to what is more knowable by nature (which corresponds to the instruction of Posterior Analytics I.2). However, he also states in I.1 that we proceed from the universals (καθόλου) to the particulars. The ancient Greek commentators resolve this tension by reading καθόλου not as natural-kinds universals but as "indiscriminate particulars." Here, Avicenna conspicuously departs. He offers a more "literal" reading of Aristotle, in which 'universal' means what is most "common" in nature and better known to [End Page 168] the intellect. Notably, Avicenna's use of "common things" (al-umūr al-'āmma) corresponds to generic universals, which are better known to the intellect but are not better known "by nature" (a complication of Aristotle's two-part view). Lammer convincingly concludes that Avicenna does not describe a method of scientific research here. However, it remains unclear what mode of instruction means and how it relates to demonstrative proof qua proof. Just as interpreters have attenuated the stronger claim suggested by Barnes that demonstrative method is a purely didactic tool, the above will raise fruitful questions regarding instruction, proof, and the acquisition of first principles in Avicenna. Is the problem one of method versus instruction, or is it one that turns on the status of the acquisition of first principles vis-à-vis the methods of demonstrative science? In chapter 3, Lammer turns to the subject-matter and principles of physics as discussed in I.2. In contrast to Aristotle, Avicenna does not think we begin with an inquiry into change to arrive at an account of the principles. Rather, he "sets out" or posits form, matter, and privation as the principles of natural things. In fact, Avicenna "decouples" the analysis of body and its essential constituents, as that which undergoes change, from the external or accidental items in virtue of which the body undergoes change (e.g. privation). All this confirms Lammer's point, mentioned above, that Avicenna does not employ a method of discovery of principles. Here, Lammer offers two important revisions that should be highlighted. Regarding the nature of body, Lammer argues against the predominant reading of Avicenna, in which corporeality is viewed as...

The role of induction in the cognition of non-demonstrable principles in Aquinas

The analysis of the 20th lectio of the second book of the Aquinas?s Commentary on the Posterior Analytics shows that he recognizes four types of non-demonstrable principles: axioms, definitions, hypotheses and so-called causal principles. The comparison of the axioms and the causal principles shows that the induction is necessary for the cognition of later ones; the interpretation that induction has the role in the cognition of all types of non-demonstrable principles is dismissed. The article makes the distinction between broad sense of induction (all cognition with the basis in sensed singulars) and strict sense of induction (the inductive process described in the Second Analytics). In the strict sense, the induction has no role in the cognition of the axioms; nevertlheless, in wider sense of the repeated sensations its role is to provide sensory information on the basis of which the intellect can apprehend the meaning of the terms used in the axiom.

On the Pre-demonstrative (hoti) Conception of Lunar Eclipse in Posterior Analytics B 8

My aim is to show that, in Posterior Analytics B 8, the conception of lunar eclipse brought about by pre-demonstrative knowledge (hoti) is deeply vague and radically different from the one obtained by demonstrative knowledge (dioti).

AVOIDING INFINITE REGRESS: POSTERIOR ANALYTICS I 22

This article offers a reconstruction of an argument against infinite regress formulated by Aristotle in Posterior Analytics I 22. I argue against the traditional interpretation of the chapter, according to which singular terms and summa genera, in virtue of having restrict logical roles, provide limits for predicative chains, preventing them from proceeding ad infinitum. As I intend to show, this traditional reading is at odds with some important aspects of Aristotle’s theory of demonstration. More importantly, it fails to explain how his proof is connected to a defence of the existence of ultimate explanations, a connection that must be the case if I 19-22 is advancing a foundationalist way-out to a sceptical challenge raised in I 3.

CAN THERE BE A SCIENCE OF PSYCHOLOGY? ARISTOTLE’S DE ANIMA AND THE STRUCTURE AND CONSTRUCTION OF SCIENCE

Abstract This article considers whether and how there can be for Aristotle a genuine science of ‘pure’ psychology, of the soul as such, which amounts to considering whether Aristotle’s model of science in the Posterior Analytics is applicable to the de Anima.

POSTERIOR ANALYTICS II.11, 94b8-26: FINAL CAUSE AND DEMONSTRATION

Abstract I present the text at Posterior Analytics (=APo) II.11, 94b8-26, offer a tentative translation, discuss the main construals offered in the literature, and argue for my own interpretation. Some of the general questions I discuss are the following: 1. What is the nature of the explanatory syllogisms offered as examples, especially in the case of the moving and the final cause? Are they scientific demonstrative explanations? In the case of the final cause, are they practical syllogisms? Are they productive? 2. Are we to read into such examples Aristotle’s requirements from APo I.4-6 that demonstrative premisses and conclusions are universal, per se, and necessary? If so, in what way? If such requirements do not apply here, what are the implications for question 1? 3. What, if any, is the advantage of one type of causal explanation over another (e.g., of final over efficient) in cases in which there is causal competition between complementary explanations? 4. What is the relation between the thesis of this chapter, especially the section dedicated to the final cause, and the argument of II.8-10? How is essence (the what-it-is) related to causes? How is explanation/demonstration-based definition related to causal explanation in terms of the four causes?

ARISTOTLE ON PREDICATION AND DEMONSTRATION

Abstract I argue against the standard interpretation of Aristotle’s account of ‘natural predication’ in Posterior Analytics 1.19 and 1.22 according to which only substances can serve as subjects in such predications. I argue that this interpretation cannot accommodate a number of demonstrations Aristotle sanctions. I propose a new interpretation that can accommodate them.

THEORETICAL NOUS IN THE POSTERIOR ANALYTICS

Abstract According to Aristotle's definition of episteme (understanding) in the Posterior Analytics, you have episteme of the proposition that P when you know why P, and you know that it is necessary that P. Episteme is therefore only available for propositions which have an explanation, i.e. the theorems of the science. It is a demanding cognitive state, since knowing the explanation of a proposition in a science requires being able to demonstrate or prove it. Aristotle occasionally refers to the counterpart notion to episteme which applies to propositions which lack an explanation, i.e. the first principles of a science. This counterpart notion is nous, or non-demonstrative understanding. Aristotle never defines it, but it should turn out to be an equally demanding cognitive state to achieve. This paper proposes that you have nous of the proposition that P when you know that nothing explains why P, you know the various ways in which the proposition that P features in explanations in the science, and you know that it is necessary that P.