Aristotle: Posterior Analytics

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)

Nos Segundos Analíticos I. 14, 79a16-21 Aristóteles afirma que as demonstrações matemáticas são expressas em silogismos de primeira figura. Apresento uma leitura da teoria da demonstração científica exposta nos Segundos Analíticos I (com maior ênfase nos capítulo 2-6) que seja consistente com o texto aristotélico e explique exemplos de demonstrações geométricas presentes no Corpus. Em termos gerais, defendo que a demonstração aristotélica é um procedimento de análise que explica um dado explanandum por meio da conversão de uma proposição previamente estabelecida. (...) Em uma estrutura silogística, a proposição previamente estabelecida é a premissa maior e o termo mediador deve ser comensurado ao explanandum. O conjunto da premissa maior e da premissa menor (o explanans) é coextensivo ao explanandum, mas há uma assimetria intensional entre o explanans e o explanandum, de modo que apenas o primeiro explique o último. Por fim, defendo que o elemento identificado no termo mediador deve ser o mais apropriado para explicar precisamente o que certo explanandum é. (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)

I defend an interpretation of Aristotle’s Posterior Analytics Book I which distinguishes between two projects in different passages of that work: (i) to explain what a given science is and (ii) to explain what properly scientific knowledge is. I present Aristotle’s theory in answer to ii, with special attention to his definition of scientific knowledge in 71b9-12 and showing how this is developed on chapters I.2-9 and I.13 into a solid Theory of Scientific Demonstration. The main point of this theory (...) is that demonstrations need to capture relevant explanations. Some formal requirements of the demonstration (as the syllogistic structure and coextension between terms) are unfoldings of the main project, i.e., to capture and present properly relevant causal-explanatory relations. (shrink)

In this paper I argue against rationalist readings of Aristotle's epistemology, on which our scientific understanding is justified on the basis of certain demonstrative first principles that are themselves justified only by some brute form of rational intuition. I then investigate the relationship between our intuition of principles and the broadly perceptual knowledge from which it derives. I argue that, for Aristotle, perceptual knowledge helps justify our intuition of principles, and also serves as an authority against which these principles and (...) their consequences must be assessed. I end by considering how we should understand the justificatory role played by perception, and sketching the nuanced, empirically-minded sort of foundationalism I take Aristotle to endorse. (shrink)

how does one inquire into the truth of first principles? Where does one begin when deciding where to begin? Aristotle recognizes a series of difficulties when it comes to understanding the starting points of a scientific or philosophical system, and contemporary scholars have encountered their own difficulties in understanding his response. I will argue that Aristotle was aware of a Platonic solution that can help us uncover his own attitude toward the problem.Aristotle's central problem with first principles arises from the (...) fact that they cannot be demonstrated in the same way as other propositions. Since demonstrations proceed from prior and better-known principles, if the principles themselves were in need of... (shrink)

according to aristotle's posterior analytics, scientific expertise is composed of two different cognitive dispositions. Some propositions in the domain can be scientifically explained, which means that they are known by "demonstration", a deductive argument in which the premises are explanatory of the conclusion. Thus, the kind of cognition that apprehends those propositions is called "demonstrative knowledge".1 However, not all propositions in a scientific domain are demonstrable. Demonstrations are ultimately based on indemonstrable principles, whose knowledge is called "comprehension".2 If the knowledge (...) of all scientific propositions were... (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)

Aristotelian commenters have long noted an apparent contradiction between what Aristotle says in Posterior Analytics I.2 and Physics I.1 about how we obtain first principles of a science. At Posterior 71b35–72a6, Aristotle states that what is most universal (καθόλου) is better-known by nature and initially less-known to us, while the particular (καθ’ ἕκαστον) is initially better-known to us, but less-known by nature. At Physics 184a21-30, however, Aristotle states that we move from what is better-known to us, which is universal (καθόλου), (...) to what is better-known absolutely, which is particular (καθ’ ἕκαστον). This paper turns to two of Aristotle’s most notable medieval commentators—Albertus Magnus and Thomas Aquinas—to resolve this apparent contradiction. The key to Thomas and Albert’s solutions, we will argue, is a twofold distinction between a sense-perceptive and scientific universal, and the particulars as sensed individuals and as differentiating attributes. Our Synthetic treatment of these distinctions contributes to the ongoing scholarly effort to understand the Stagyrite’s complex theory of knowledge. (shrink)

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.

The issue on whether knowledge can be possibly transmitted and in which order from the teacher to his students has been a hot topic since ancient Greece. Plato and Aristotle, Augustine and Thomas Aquinas, just to mention two of the most famous philosophical “couples” apparently dissented from each other on this point. In this paper, I analyze the Conimbricenses’ thought on this topic by interpreting their commentary to the first lines of the Posterior Analytics. Assessing the Conimbricenses’ thought on this (...) topic provide further insights on the general attitude of Jesuit philosophers toward their philosophical binding authorities, namely Aristotle and Thomas Aquinas. (shrink)

: In APo II 3-7 Aristotle discusses a series of difficulties concerning definition, deduction, and demonstration. In this paper I focus on two interrelated but distinct questions: firstly, what are exactly the difficulties emerging from or alluded to in the discussion in II 3-7; secondly, whether and in what sense the discussion in II 3-7 can be considered an aporetic discussion with a specific role to play in the development of the argument in APo II.

This article sketches, and works to motivate, a controversial approach to Posterior Analytics II.19. But its primary goal is to recommend a novel solution to one particular interpretive aporia that’s especially vexed recent scholars working on Post. An. II.19. The aporia concerns how to understand the enigmatic "ē ek pantos" ( “or from all...”) in the genealogical account of foundational knowledge at II.19 100a3-9. Our proposed solution to the aporia is discussed in connection with a number of larger philosophical issues (...) concerning Aristotle’s theory of epistēmē. (shrink)

The paper examines Posterior Analytics II 11, 94a20-36 and makes three points. (1) The confusing formula ‘given what things, is it necessary for this to be’ [τίνων ὄντων ἀνάγκη τοῦτ᾿ εἶναι] at a21-22 introduces material cause, not syllogistic necessity. (2) When biological material necessitation is the only causal factor, Aristotle is reluctant to formalize it in syllogistic terms, and this helps to explain why, in II 11, he turns to geometry in order to illustrate a kind of material cause that (...) can be expressed as the middle term of an explanatory syllogism. (3) If geometrical proof is viewed as a complex construction built on simpler constructions, it can in effect be described as a case of purely material constitution. (shrink)

Aristotle claims that "although we perceive particulars, perception is of universals; for instance of human being, not of Callias-the-human-being" (APo II.19 100a16-b1). I offer an interpretation of this claim and examine its significance in Aristotle's epistemology.

In their pioneering, masterly research and survey on Bartolomeo Fonzio’s manuscripts, published in 1974, Stefano Caroti and Stefano Zamponi informed the reader that the Ms. Ricc. 152 of the Riccardiana Library in Florence was a huge amount of notebooks with notes taken by Fonzio while attending the Studium in Florence. Among them Caroti and Zamponi called the reader’s attention to the notes Fonzio took when he went to Argyropoulos’ lessons on the Posterior Analytics. In this essay the reader finds a (...) transcription of those notes, preceded by some comments on the sources from which the outstanding commentator is likely to have drawn and which can be picked out from the fragmentary notes, that is John Philoponus and Paul of Venice. (shrink)

I discuss an important feature of the notion of cause in Post. An. 1. 13, 78b13–28, which has been either neglected or misunderstood. Some have treated it as if Aristotle were introducing a false principle about explanation; others have understood the point in terms of coextensiveness of cause and effect. However, none offers a full exegesis of Aristotle's tangled argument or accounts for all of the text's peculiarities. My aim is to disentangle Aristotle's steps to show that he is arguing (...) in favour of a logical requirement for a middle term's being the appropriate cause of its explanandum. Coextensiveness between the middle term and the attribute it explains is advanced as a sine qua non condition of a middle term's being an appropriate or primary cause. This condition is not restricted either to negative causes or to middle terms in second‐figure syllogisms, but ranges over all primary causes qua primary. (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)

In Posterior Analytics II 16-17, Aristotle seems to claim that there cannot be more than one explanans of the same scientific explanandum. However, this seems to be true only for “primary-universal” demonstrations, in which the major term belongs to the minor “in itself” and the middle term is coextensive with the extremes. If so, several explananda we would like to admit as truly scientific would be out of the scope of an Aristotelian science. The secondary literature has identified a second (...) problem in II 16-17: the middle term of a demonstration is sometimes taken as the definition of the minor term (the subject), other times as the definition (or the causal part of the definition) of the major (the demonstrable attribute). I shall argue that Aristotle’s solution to the first problem involves showing that certain problematic attributes, which appear to admit more than one explanation, actually fall into the privileged scenario of primary-universal demonstrations. In addition, his solution suggests a conciliatory way-out to our second problem (or so I shall argue): the existence of an attribute as a definable unity depends on its subject having the essence it has, which suggests that both the essence of subjects and the essence of demonstrable attributes can play explanatory roles in demonstrations. (shrink)

I examine the difficulties involved in the Aristotelian proposal to identify the knowledge of “what it is” and “why it is”, in order to better understand the outlines that delimit it. I propose that the connections by which Aristotle links definition and explanation, and hence essence and cause, depend on the mutual convertibility between nominal expressions and predicative sentences.

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

ABSTRACT This is a review of David Bronstein's book "Aristotle on Knowledge and Learning: The Posterior Analytics".

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)

David Bronstein sheds new light on Aristotle's Posterior Analytics--one of the most important, and difficult, works in the history of western philosophy--by arguing that it is coherently structured around two themes of enduring philosophical interest: knowledge and learning. He argues that the Posterior Analytics is a sustained examination of scientific knowledge, an elegantly organized work in which Aristotle describes the mind's ascent from sense-perception of particulars to scientific knowledge of first principles. Bronstein goes on to highlight Plato's influence on Aristotle's (...) text, and argues against current orthodoxy that Aristotle is committed to the Socratic Picture of inquiry, according to which one should seek what a thing's essence is before seeking its demonstrable attributes and their causes. (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)

I review Michael T. Ferejohn's "Formal Causes: Definition, Explanation, and Primacy in Socratic and Aristotelian Thought".

For Aristotle, demonstrative knowledge is the result of what he calls ‘intellectual learning’, a process in which the knowledge of a conclusion depends on previous knowledge of the premises. Since demonstrations are ultimately based on indemonstrable principles (the knowledge of which is called ‘νοῦς’), Aristotle is often described as advancing a foundationalist doctrine. Without disputing the nomenclature, I shall attempt to show that Aristotle’s ‘foundationalism’ should not be taken as a rationalist theory of epistemic justification, as if the first principles (...) of science could be known as such independently of their explanatory connections to demonstrable propositions. I shall argue that knowing first principles as such involves knowing them as explanatory of other scientific propositions. I shall then explain in which way noetic and demonstrative knowledge are in a sense interdependent cognitive states – even though νοῦς remains distinct from (and, in Aristotle’s words, more ‘accurate’ than) demonstrative knowledge. (shrink)

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)

Aristotle rejected the idea of a single, overarching super-science or “theory of everything”, and he presented a powerful and influential critique of scientific unity. In theory, each science observes the facts unique to its domain, and explains these by means of its own proper principles. But even as he elaborates his prohibition on kind-crossing explanations (Posterior Analytics 1.6-13), Aristotle points out that there are important exceptions—that some sciences are “under” others in that they depend for their explanations on the principles (...) of a superior (more architectonic) science. In this paper, I explore how subordination relations and architectonic structures apply to Aristotle’s scientific practice—including not only the works of theoretical philosophy, which have already been discussed in this connection, but also in and between these and the practical and productive sciences. (shrink)

This dissertation deals with an important topic in the history of the theory of scientific knowledge, a theory which became the paradigm for science for the next two millennia. It is well known that Aristotle characterized scientific knowledge with two conditions: first, it must be necessary; and secondly, knowledge is only scientific if the reason or cause of what we know is revealed. To give an example, the theorem that the interior angle-sum of a triangle is 180° is a necessary (...) truth. In order to show why the triangle necessarily has this angle-sum, we have to conduct a demonstration that reveals why the triangle’s angle-sum is necessarily 180°. Large parts of the first book of the Posterior Analytics are concerned with the foundations and conditions of such demonstrations. One of these conditions has been called the metabasis-prohibition. It demands that a demonstration does not cross from one γένος into another or from one discipline into another. But despite the fact that Aristotle provides a number of examples for such illicit crossings, it is not clear what Aristotle understands under a γένος and why precisely metabasis is problematic for scientific knowledge. Previous attempts to shed light on this question maintained that Aristotle considered each discipline to be concerned with a specific range or realm of objects and that the word γένος refers to this realm. This notion of a γένος, its demarcation and internal structure, has been seen as explanatory for the metabasis-prohibition by almost every interpreter in this and the last century. However, making the notion of γένος as the domain of a science explanatory for the metabasis-prohibition leads to severe problems and therefore has to be abandoned. A textual problem for the domain-interpretation can be found in Posterior Analytics I.7, where Aristotle says that demonstrations prove the per se attributes of a γένος, but that this is not possible in a demonstration that crosses from one γένος to another. But Aristotle’s theory of per se predication, as exhibited by the foregoing chapters of the Posterior Analytics, does not allow for a realm of objects to have per se attributes. Perhaps this problem could be solved by allowing the term γένος to be used ambiguously in the respective passage. However, there are more pressing, systematic problems. One of these problems is the following. According to the domain-interpretation, metabasis signifies the crossing from one domain of a science to another and hence the question how a domain is being demarcated has dominated the previously proposed explanations of the metabasis-prohibition. According to the majority of the interpreters, the domain is demarcated by the most general term or terms of the science, which subsume the other terms of the science. A different interpretation holds that instead of such a class-inclusion system, Aristotle thinks of the domain of a science as a network, in which subjects and attributes are linked to a term or a class of terms that demarcate the domain. Both interpretations are faced with a serious problem when the proposed relations between the subjects of the science and their respective highest terms are scrutinized. For if the science of geometry is demarcated by the term magnitude, which subsumes all other subjects by way of class-inclusion, then there does not seem to be a non-ad hoc way of preventing the postulation of a more encompassing science whose highest term is quantity. Quantity, however, would subsume both discreet quantity as well as extended quantity in the same way as magnitude subsumes triangle and hence in this science there would be, according to the domain-interpretation’s assumption, no metabasis between arithmetic and geometry, a result that is plainly in contradiction with Aristotle’s claim. The alternative network-interpretation can be shown to suffer from the same problem. The only way out, embraced but at least one interpreter, is to accept that the domains of sciences are stipulated and hence to accept that whether or not metabasis obtains is a question of stipulation. However, since Aristotle introduces the metabasis-prohibition as a condition for the possibility of scientific knowledge, this is not a viable option. My thesis provides a new interpretation to help understand Aristotle’s metabasis problem. I argue that Aristotle clearly indicates that the metabasis-prohibition is a consequence of his investigation of per se or essential properties and that we therefore have to explain metabasis with reference to this investigation. A property is essential for an object if the object were not what it is if it did not have this property. For example, a triangle is only a triangle if it is a figure bound by three straight lines with an interior angle-sum of 180°. The properties ‘figure’, ‘bound by three straight lines’ and ‘having an interior angle-sum of 180°’ are all essential properties of the triangle. Aristotle’s way of expressing this is to say that the triangle is a figure in itself or qua itself, i.e. in what it is by itself, or in virtue of itself. But not all essential properties are equal. Aristotle distinguishes between basic essential properties, on the one hand, and those essential properties that are dependent on them, on the other. In the case of the triangle, ‘figure’ and ‘bound by three straight lines’ are examples of basic properties, while ‘having an interior angle-sum of 180°’ is an example of a dependent essential property. While basic properties enter into the definition of the object, the dependent properties have to be demonstrated to belong to the object by reference to the basic properties. This is the case because the basic properties are the reason or cause why the dependent properties belong to the object, and revealing why a property belongs to an object is the mark of science in Aristotle’s understanding. I argue that pseudo-demonstrations committing metabasis do so precisely because they do not conduct the demonstration from the essential properties of the object of which they attempt to show that it has a certain property essentially. Such a demonstration, then, will not reveal the reason why a given property belongs to an object. Hence, the kind of knowledge produced by such demonstrations is not scientific knowledge. One immediate consequence of this interpretation is that metabasis can happen within one and the same discipline; previous explanations held that metabasis only happens between disciplines like geometry and arithmetic. But that is not the case, because a discipline comprises many different objects and the basic essential properties of one such object will not be the reason or cause why certain properties belong to another object. Because of its emphasis on the relations between essential properties of a kind, I call my interpretation the essence-interpretation. In this interpretation, then, the term γένος primarily signifies the respective kinds the demonstration is about and which the demonstration shows to possess certain properties in virtue of the kinds’ basic properties. Apart from the above-mentioned passage in Posterior Analytics I.7, in which Aristotle explicitly says that a demonstration shows that a γένος possesses certain properties – and which turned out to be problematic for the domain-interpretation – there are further passages in I.4-6, which corroborate this use of the word γένος. However, the essence-interpretation does not deny that Aristotle had a notion of a domain of a discipline and that he intended the metabasis-prohibition to also restrict crossings from one such domain to another. However, such domains are not explanatory for the metabasis-prohibition; rather, a crossing between two such domains is seen to be derivative, since, if we suppose, e.g., a genus-species ordering the various kinds of reality, a crossing between domain will be a crossing between kinds. This interpretation can be shown to deal much better with the above-mentioned problems. A possible change in the meaning of the term γένος can be explained with reference to the primary-derivative relation that I just pointed out. The problem of the expansion of domains and the related problem of stipulation can also be avoided: since metabasis can also happen within a discipline, an expansion of the domain of a science does not, in the essence-interpretation, validate a demonstration previously seen to be invalid because of metabasis. And since this is not the case, stipulating what kinds a given discipline deals with does no longer affect the conditions of the possibility of knowledge. Moreover, as I try to show in the remainder of the first part of the thesis, none of the passages of the Posterior Analytics that have a direct relation to the metabasis-prohibition is incompatible with my interpretation, and often we gain an exegetical advantage and a better understanding of the text. The examples that Aristotle mentions in I.7 and I.9 are now open to better, often straightforward explanations. Furthermore, two claims that stand in a direct relation with the metabasis-prohibition, and which take a central place in the Posterior Analytics, can be better explained from the viewpoint of the essence-interpretation, namely the claim about so-called subordinate sciences and the claim that the principles of a science cannot be demonstrated. Especially the former posed great problems to the domain-interpretation; the genus-species and network-interpretation have a hard time showing why subordination proofs are exempt from the metabasis-prohibition, as Aristotle says. The essence-interpretation, on the other hand, can explain the exception with reference to the fundamental requirements of scientific knowledge, as they are stated by Aristotle in the beginning of the Posterior Analytics and drawn out in his theory of essential belonging. I finally consider two of Aristotle’s treatises on natural science and show that he appeals to the metabasis-prohibition in his criticisms of certain demonstrations of his fellow natural scientists. In the Generation of Animals, we find Aristotle criticising a certain proof about the sterility of mules and he unequivocally points out that the problem of this proof is metabasis. According to the domain-interpretation, this proof should somehow violate the borders of the domain of the science of biology or zoology by crossing over from another domain of a science. However, in Aristotle’s own description of the offending proof, this does not seem to be the case: all terms are zoological and there is no mention of a different science. Rather, the problem of the proof is that it did not show why the property ‘sterile’ belongs to mules from the basic essential properties of the kind to which sterility belongs. A similar result can be drawn from the analysis of a number of passages of the De Caelo. Hence, the essence-interpretation proves to be superior to the previous explanations of metabasis here, too. In the second part of the dissertation, I turn to the ancient legacy of the metabasis-prohibition. There are two reasons for this. First, by considering the two texts that deal directly with the Posterior Analytics, namely a paraphrase written by Themistius and a commentary written by Philoponus, I show that there are reasons to believe that both authors understood the metabasis-prohibition along lines similar to the essence-interpretation. Secondly, it appears that the metabasis-prohibition poses a problem for the late ancient philosophers. This comes especially to the fore in the works of Proclus, who refers to the metabasis-prohibition in his Commentary on Plato’s Timaeus and in his Commentary on Euclid’s Elements. While Proclus explicitly agrees with the metabasis-prohibition in some passages, he appears to violate it in others. This is evident when he, for instance, claims that demonstrations in natural philosophy employ theological premises and when he says that the automorphism of the numbers 5 and 6 has to be demonstrated with reference to the circle. One particular area of importance in this respect is Proclus’ doctrine of ‘geometrical atomism’, which is part of his natural philosophy. This doctrine states that the elements out of which all material reality is constructed are certain geometrical bodies and that the properties of the elements depend on the geometrical properties of these geometrical bodies. Here again it seems that we have an obvious case of metabasis. Moreover, in some sense one should even expect Proclus to violate and indeed to reject the metabasis-prohibition, for the Neoplatonists emphasize that reality and knowledge about reality possess a great pervasive unity. In seeking to solve the tension in Proclus’ view of metabasis – accepting the prohibition but also apparently violating it – my analysis came to the following conclusion. Since the ultimate justification of the metabasis-prohibition lies in the theory of essential properties, one should expect that the demonstrations that appear to be guilty of metabasis somehow violate the strictures of this metaphysical background theory. However, it turns out that this is not the case. For Proclus’ theory of essential properties, and in particular his theory of dependence of properties, differs from that of Aristotle. The way certain objects come to possess properties can be described from two directions. From the point of view of the object, it can be said that an object possess a property because it participates in a reality that is, in the hierarchy of Neoplatonic reality, higher than itself. This is the bottom-up perspective. The same relation can also be described from a top-down perspective: every part of reality derives its being from a procession from higher realities with the One, the highest Neoplatonic principle, which is located at the top of this hierarchy. One distinctive feature of this metaphysical system is that the higher element from which a lower element receives one of its properties does not have to possess this same property itself. Rather, what this higher element possesses is the power to bring about the respective property of a lower element, or even this very element itself. Building on this metaphysical background theory, Proclus aims to show how certain objects a given science deals with receive their identities and properties from higher elements of reality. In the Euclid Commentary, he outlines how demonstrations of these relations should be conceived. For instance, the automorphism of the numbers 5 and 6 has its cause in the circle and hence a demonstration why these numbers are automorphic has to start from the essence of the circle. This appears, from an Aristotelian perspective, to be a metabasis-demonstration, and indeed one of the crossings that Aristotle explicitly forbids in the Posterior Analytics. Proclus, however, argues that automorphism is a form of circularity and that the geometrical circle is likewise a form of circularity. Both the numbers 5 and 6 as well as the geometrical circle receive their respective properties of circularity from a higher principle that neither belongs to arithmetic nor to geometry, but possess circularity in the purest way. Since Proclus holds that the circularity of the geometrical circle and the circularity of the numbers 5 and 6 have their cause in this higher principle, a demonstration revealing this relation takes the form of a subordination demonstration and is not guilty of metabasis. On the contrary, the relations that these properties have to their higher principle demand that a demonstration, if it aims at obtaining the highest form of scientific knowledge, does make the respective reference. This result suggests that the metabasis-prohibition should be understood as a purely formal theorem. The prohibition is, in accordance with the analysis of Aristotle’s argument for it, a consequence of the theory of essential properties. The concrete effects of the prohibition, i.e. the question which demonstrations are seen to be violating it, depend on the given theory of essential properties. Since Proclus’ theory differs from Aristotle’s, the two philosophers will see different demonstrations as violating the metabasis-prohibition. However, even taking into account the competing theories of essential properties, there still remains room for differing views on the question which demonstrations violate the metabasis-prohibition. For two philosophers who agree on the theory of essential properties might still give different answers to the question what the basic essential properties of a given object are. For instance, it is not at all self-evident that light propagates along straight lines, as Aristotle held. For this reason, according to Aristotle, demonstrations about the propagation of light need to refer to the geometrical properties of straight lines. But a different philosopher could, while agreeing with Aristotle’s theory of essential properties, hold that light propagates along curved lines and hence he would see demonstrations about the propagation of light that make references to straight lines as committing metabasis. The metabasis-prohibition, then, is formal. The effects of its application are determined by two factors: one, the theory of essential properties; and the other, the particular views a given scientist takes towards the essence or identity of the objects he wants to conduct demonstrations about. (shrink)

This chapter argues in favour of three interrelated points. First, I argue that demonstration (as expression of scientific knowledge) is fundamentally defined as knowledge of the appropriate cause for a given explanandum: to have scientific knowledge of the explanandum is to explain it through its fully appropriate cause. Secondly, I stress that Aristotle’s notion of cause has a “triadic” structure, which fundamentally depends on the predicative formulation (or “regimentation”) of the explanandum. Thirdly, I argue that what has motivated Aristotle to (...) choose the syllogism as a demonstrative tool was precisely the fact that syllogisms are apt to express causal relations in their triadic structure. Instead of complaining against Aristotle’s preference for the syllogisms as demonstrative tools, I argue that Aristotle was fully aware of the advantages of regimenting the explanandum into a predication. One of these advantages is to abandon a purely extensional standpoint and to highlight the importance of the notion of relevancy in explanation. (shrink)

Collective volume with papers by alumni and students from the Campinas Aristotle Group.

Discussão sobre o papel da silogística e sua relação com as noções de dedução correta e explicação apropriada na concepção aristotélica de ciência.

Discussão dos sentidos de "per se" em Aristóteles, com foco especial em Segundos I.4.