Aristotle: Principles

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)

I discuss a short string of five sentences in Metaphysics V.5, 1015b6-9 relating demonstration to necessity. My proposal is that Aristotle focuses his attention on the demonstration as a demonstration. Other interpretations reduce the necessity in question to the modality of the component sentences of the demonstrations (the conclusion and the premises). My view does not deny that the modality of the component sentences is important, but takes seriously the idea that a demonstration itself should be understood as necessary—as not (...) capable of being otherwise. A demonstration cannot be different from what it is in the sense that [i] its components cannot be different from what they are, [ii] its components must be related to each other exactly in the way they are related. Demonstrations aim at the fully appropriate explanation of a given explanandum—and each demonstration is individuated by the explanandum it takes. Thus, the basic idea is that, for the target explanandum that individuates a given demonstration, the premises delivering the fully appropriate explanation cannot be replaces with different ones. I show how this proposal, which explains Aristotle’s language in 1015b6-9 accurately, does not make demonstrations ‘melt down into conditional necessity’, first, because the modality of the component sentences is still importantly involved, second, because the explanatory relation expressed in a demonstration is a necessary fact in the real world, so that the demonstration itself is also necessary (in the way I have explained) inasmuch as it captures that fact. (shrink)

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

Aristotle maintains that defining nous requires first defining its activity, which requires first having considered its objects, intelligible beings. This chapter is about the nature of these objects: what about them makes them intelligible? My principal proposals will be that what makes them intelligible is that they are separate or unmixed, and that because, insofar as they are intelligible, they are, in their essence, activity. I am not unaware that this makes it sound as though Aristotle takes intelligibility to consist (...) in some kind of nous. But he himself virtually says as much, when he claims that nous is the form of its objects (lit. εἶδος εἰδῶν); besides it is a result he is committed to by the doctrines that nous is intelligible and that there is something that intelligible objects all are in common; for the alternative, as he himself says, is to suppose that nous “will have something mixed-in, which makes it intelligible just like the rest.” The challenge, then, is not to steer clear of this result, but to make sense of it. My proposal will be that the key lies in realizing that and why Aristotle thinks intelligibility is a creature of nous. (shrink)

I discuss the argument Aristotle ascribes to Parmenides at Physics 186a23-32. I discuss (i) the reasons why Aristotle considers it as eristic and inconclusive and (i) the solution (lusis) Aristotle proposes against it.

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)

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. (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)

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)

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)

Some of Aristotle’s statements about the indemonstrability of the Principle of Non-Contradiction (PNC) in Metaphysics Γ 4 merit more attention. The consensus seems to be that Aristotle provides two arguments against the demonstrability of the PNC, with one located in Γ 3 and the other found in the first paragraph of Γ 4. In this article, I argue that Aristotle also relies upon a third argument for the same conclusion: the argument from truth. Although Aristotle does not explicitly state this (...) argument, it is the best argument that he could use to defend some of his statements in the second paragraph of Γ 4. Since the argument relies on only a few of Aristotle’s core views about truth, I propose that it is faithful to his considered position throughout his corpus, and it may be the strongest argument he could offer for the indemonstrability of the PNC. (shrink)

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)

In his Metaphysics Γ.4, Aristotle defends the principle of non-contradiction (PNC). The PNC says that all contradictions are false. So if some contradictions are true, then PNC is false. Even if PNC’s contrary is false, PNC’s contradictory might still be true. But it’s been noted in the literature for over a century that Aristotle seems to be exclusively interested in attacking PNC’s contrary (‘All contradictions are true’) rather than PNC’s contradictory (‘Some contradictions are true’). So his defense of PNC seems (...) to fail. This would be a surprising error from the inventor of formal logic. It is especially puzzling because we have plenty of evidence showing that Aristotle is keenly aware of the distinction between contraries and contradictories, and because Aristotle distinguishes between PNC’s contradictory and PNC’s contrary in Γ.4. I defend Aristotle against these charges: (1) I explain that one important reason for Aristotle’s focus on PNC’s contrary is that he took it to be deeply connected to views held by thinkers such as Anaxagoras, Cratylus, Democritus, Empedocles, Heraclitus, Parmenides, Protagoras, and Xenophanes; (2) Aristotle’s defense of PNC must be a particular kind of indirect defense rather than a direct demonstration; (3) I argue that if Aristotle’s defense of PNC is read as centering around his argument for what counts as a thing that is determinate, Aristotle demonstrates the reliance of coherent communication on non-contradiction. Read this way, he gives a fairly compelling case to reject not just PNC’s contrary but also PNC’s contradictory. (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)

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

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)

This work attempts to respond to Tomas Aquinas' Cosmological Argument in a way that combines Set Theory with the idea of the ‘Book of Change’. The study defines the ith Cause Set on which to operate on, which leads to the ontological commitment of austerity that the ‘First Cause's Compromise with emergence’ cannot be avoided. It is argued in the present paper that the concept that ‘emergence only consists of Synchronic Emergence and Diachronic Emergence’ should be extended to a broader (...) notion of emergence, which is made up of the two discussed elements and a third one ‘No-Boundary Emergence’ (beyond the time dimension). The article defines the concept of No-Boundary Emergence, proves why it is a type of emergence that differs from the traditional two types, and asserts that it underlies the bottom layer of the cosmos. This study describes the common feature of all emergence as communication protocols between layers. The assemblage of all emergences behaves similar to a distributed system that cannot be restricted by Gödel's theorem. The paper provides evidence (in Big Bang Cosmology, Conformal Cyclic Cosmology, Superstring Theory, Quantum Gravity) for this point of view, and notes that emergence (in the context of No-Boundary Emergence) is not only a simple scientific theory but also a progressive scientific research programme that can spontaneously grow from scientific theory based on Platonism at the expense of a degenerating shift to the ontological commitment of austerity. This paper proposes an improved model of Schrödinger Cat that provides a new explanation for quantum measurement and argues that there must be a forbidden zone of thought experiments. The study also introduces the implications of ancient Chinese thoughts (namely, the ‘Book of Change’ and Confucius). The paper comes to the conclusion that emergence (crossing the gap between ‘being’ and ‘nothing’, while ignoring the forbidden zone of thought experiments) relieves ‘cosmological insufficiency’ in the sense of Neo-Aristotelism. (shrink)

Aristotle uses two kinds of material cause in his analysis of biological organisms: compositional matter, which persists through their birth and death;and functional matter, which consists of the organs and functional parts out of which biological organisms are made while they are alive. These two kinds of material cause, it has been argued, have quite different explanatory roles: functional matter is required by biological organisms to perform their essential functions,but compositional matter contributes nothing necessary to them and is only responsible (...) for their accidental properties. Against this view, I argue that biological organisms are systematically dependent upon their compositional matter and the latter is responsible for many of their necessary attributes. (shrink)

Aristotelian causal theories incorporate some philosophically important features of the concept of cause, including necessity and essential character. The proposed formalization is restricted to one-place predicates and a finite domain of attributes (without individuals). Semantics is based on a labeled tree structure, with truth defined by means of tree paths. A relatively simple causal prefixing mechanism is defined, by means of which causes of propositions and reasoning with causes are made explicit. The distinction of causal and factual explanation are elaborated, (...) and examples of cyclic and convergent causation are given. Soundness and completeness proofs are sketched. (shrink)

This article is intended to examine the structure and scope of the argumentation drawn in Metaphysics Γ 4, 1006a18-b34. As we shall see, though this passage does not bring a complete proof of the Principle of Non-Contradiction, it corresponds to its first step, which consists in determining the conditions of meaning necessary for discourse. That passage encloses in nuce the reasons which underlie Aristotelian conviction con- cerning the conventional nature of names and also brings to light the way this conven- (...) tional nature of names must be understood according to Aristotle. (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)

According to a long interpretative tradition, Aristotle holds that the formal cause is the ultimate object of induction when investigating perceptible substances. For, the job of induction is to find the essential nature common to a set of individuals, and that nature is captured solely by their shared formal cause. Against this view, I argue that Aristotle understands perceptible individuals as irreducibly composite objects whose nature is constituted by both their formal and their material cause. As a result, when investigating (...) perceptible objects, the job of induction is to discover their composite, formal and material nature. The process by which universal claims about this composite nature are justified, I argue, is similar to what we now know as mathematical induction. In particular, such claims are grounded in a non-enumerative, but replicable process in which things are resolved into their simplest components. As a result, the observation of past uniformities has, at most, a heuristic function in scientific inquiry. (shrink)

Aristotle’s epistemology has sometimes been associated with foundationalism, the theory according to which a small set of premise-beliefs that are deductively valid or inductively strong provide justification for many other truths. In contemporary terms, Aristotle’s foundationalism could be compared with what is sometimes called “classical foundationalism”. However, as I will show, the equivalent to basic beliefs in Aristotle’s epistemology are the so-called first principles or “axiómata”. These principles are self-evident, but not self-justificatory. They are not justified by their act of (...) understanding, but by the arguments that satisfactorily prove them. In addition, these principles are intellectual, rather than perceptual, so that no basic belief that is about our immediate experience or sensory data is apt to provide the required foundation of knowledge. In spite of this, I argue that Aristotle’s foundationalism has no givens, and that his epistemology resists the objections usually leveled against givens. (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.

Exploring what two foundational figures, Plato and Aristotle, have to say about the nature of human awareness and understanding, Aryeh Kosman concludes that ultimately the virtues of thought are to be found in the joys and satisfactions that come from thinking philosophically, whether we engage in it ourselves or witness others' participation.

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

Essa dissertação de mestrado cuida do problema do conhecimento dos primeiros princípios em Aristóteles, mais precisamente, das vias de acesso adequadas a provê-lo. Dada a primordialidade de um tal conhecimento, erige-se a questão de método: por qual via estaria garantido o acesso àquilo que constitui todo o fundamento e “razão para” do edifício do conhecimento filosófico e científico? Aristóteles, nos Segundos Analíticos, atribui à indução (epagoge) e à inteligência (nous) este papel, mas nos Tópicos o filósofo menciona que a dialética (...) é util aos primeiros princípios. O propósito maior desta pesquisa está não tanto no conciliar estes métodos, procurando atribuir alguma significação tanto aos Segundos Analíticos quanto aos Tópicos, mas no procurar viabilizar alguma fala da dialética no que concerne ao conhecimento dos primeiros princípios, sem, contudo, extrapolar o que parece estar autorizado a partir da leitura dos textos aristotélicos. Neste intento, propõe-se a análise da diaporemática de que cuida Aristóteles em Metafísica Β, visando investigar se esta de algum modo excede a dialética nos limites com as quais esta se debate. (shrink)

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

Translation of Aristotle's Metaphysics I-III into Portuguese, with a few notes and introduction. The translation, which was made at 2007, is preliminary and its publication was intended to provide a didactic tool for courses as well as a provisional resource in research seminars. It needs some revision. I am currently working (slowly...) on the revision of the translation and a new revised one will surely appear at some point.

I examine Aristotle’s definition of scientific knowledge in Posterior Analytics 71b 9-12 and try to understand how it relates to the sophistical way of knowing and to "kata sumbebekos knowledge". I claim that scientific knowledge of p requires knowing p by its appropriate cause, and that this appropriate cause is a universal (katholou) in the restricted sense Aristotle proposes in 73b 26-27 ff., i.e., an attribute coextensive with the subject (an extensional feature) and predicated of the subject in itself (an (...) intensional feature). Kata sumbebekos knowledge, on the other hand, can occur even when the predicate of a conclusion is coextensive with its subject and is proved by a convertible meson which is not the most appropriate from an explanatory standpoint. (shrink)

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

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

I discuss the issue whether Aristotle's philosophy of science allows the use of mathematical premises or mathematical tools in general for explanaing phenomena in the natural sciences. I thereby discuss the concept of "metabasis eis allo genos" as it appears in Posterior Analytics I.7.

In Aristotle's cosmology, the nature of the elements is defined by their place in the Totality. Their cosmic motions keep the whole in motion, and this is their nature. Thus, the cosmos is an organized whole, a single substance directed to the good; this body constitutes together with its Prime Mover a composite substance that can be regarded as a self-mover.

Argues that Aristotle regarded the universe, or Totality, as a single substance with form and matter, and that he regarded this substance together with the Prime Mover as a self-mover.