The topic of this paper is Aristotle’s ‘proof by refutation’ of the Principle of Non-Contradiction (Metaphysics Γ 4, 1006a11–1007a20). I consider a worry which has often been raised in connection with this proof. The worry is that, faced with an opponent who is prepared to tolerate contradictions, the argument is dialectically powerless: it is incapable of getting them to abandon their position. In reply, I argue that the proof needs to be seen in its proper context, that is, as part (...) of Aristotle’s response to an opponent who demands a demonstration of the principle. This allows us to clarify the purpose of the argument and answer the worry about its effectiveness. (shrink)

Aristotle explicitly speaks of intelligible matter in three passages only, all from theMetaphysics, in the context of the analysis of definition as the formula that expresses the essence:Metaph.Z10, 1036 a8-11;Metaph.Z11, 1037 a5;Metaph.H6, 1045 a34-36 and 45 b1. In the case of the occurrences of Z10 and Z11, there is almost unanimous consensus that Aristotle uses the expression in a technical way, to indicate the matter of that particular type of objects that are intelligible compounds, of which mathematical objects are paradigmatic (...) instances. By contrast, there is no agreement on how to understand the expression in the case of H6. Here, ‘intelligible matter’ would denote, as stated by some interpreters, the generic element of the definition. The aim of this paper is to show that ὕλη νοητή has the same technical meaning in all the three explicit occurrences in theMetaphisics. Contrary to the interpretation that there is a shift in meaning from Z10-11 to H6, my goal is to illustrate that in both contexts, Aristotle uses the expression ‘intelligible matter’ to designate the matter of mathematical objects insofar as they are paradigmatic intelligible compounds. (shrink)

In Metaphysics Theta 3 Aristotle attributes to the Megarics and unknown others a notorious modal thesis: (M) something can φ only if it is φ-ing. Aristotle does not tell us what motivated (M). Almost all scholars take Aristotle’s report to indicate that the Megarics defended (M) as a highly counterintuitive doctrine in modal metaphysics. But this reading faces several problems. First: what would motivate the Megarics to hold such a counterintuitive view? The existing literature tries, in various ways, to motivate (...) (M) in a way neither trivial nor absurd. But, as we will argue, the main approaches end up attributing an unsustainable position to the Megarics. Second: most historical evidence for the Megaric lineage presents the group’s philosophical practice as dialectical or negative. So why think that the claim reported in Theta 3 presents a positive, and highly controversial, metaphysical claim? This paper addresses these problems by proposing a dialectical (or negative) reading of the Megarics in Theta 3. By ‘dialectical’ we here mean a mode of philosophizing that neither seeks to establish the truth or falsity of certain theses, nor takes a skeptical stance. There are different reasons why a philosopher might want to take up such a mode; in the case of the Megarics we argue that they might have wanted to put pressure on Aristotle’s idea of possibility and the ‘test’ for possibility that Aristotle mentions in several works. Reading, as we do, (M) as (part of) a paradox about possibility and actuality, we argue that the Megarics’ dialectical approach here aims to highlight a shortcoming of an intuitive conception of possibility, which underpins Aristotle’s idea of possibility and which features in his test for possibility. (shrink)

The PhD thesis advances a new approach to vagueness as dispersion, comparing it with the main philosophical theories of vagueness in the analytic tradition.

Metaphysics Θ treats potentiality (δύναμις) and actuality (ἐνέργεια), and many scholars think that Aristotle broaches these topics once he has answered his main questions in Ζ and Η. In Ζ he asked, what is primary being? After arguing in Ζ.1 that substance (οὐσία) is primary being—a being existentially, logically, and epistemologically prior to quantities and qualities and other categorial beings—he devotes the rest of the book to οὐσία itself, investigating what it is, to decide what entities count as primary substances. (...) I differ from the leading interpretative consensus that ΖΗ adequately answer the questions about primary substance, and contend instead that Metaphysics Θ continues the same investigation as ΖΗ and, using δύναμις and ἐνέργεια as tools, arrives at a striking new conception of hylomorphism, different from that in ΖΗ, which enables Aristotle to defend the substantial primacy of living organisms consisting of matter and form. (shrink)

I argue for the claim that for Aristotle, the content of productive understanding primarily concerns the nature of the object a craftsperson aims to bring into existence as well as its material requirements, and only derivatively things she might do with a view to producing that object. I explain why technê is a form of understanding, by considering what it shares with and how it differs from its practical and theoretical cousins. I give four arguments for my claim. The analogy (...) of craft and nature suggests that a craftsperson understands the nature of their product and the material necessities required by the product’s existence. Further evidence comes from some of Aristotle’s remarks on the practical syllogism, from considerations concerning capacities for change in general, and from his views on why it is a two-way capacity. I end by mentioning several respects in which technê goes beyond productive understanding. (shrink)

Although Aristotle’s Metaphysics received much attention in the nineteenth and the twentieth centuries, scholars and historians of science were not particularly interested in clarifying the aim of Aristotle’s appeal to astronomy in Λ 8. Read with monotheistic prejudices, this chapter was quickly abandoned by Aristotelian scholars as a gratuitous insertion, which downgrades Aristotle’s God for the sake of some supplementary principles, whose existence was dictated by celestial mechanics. On the other hand, historians of astronomy read the astronomical excursus as providing (...) a picture of Aristotle as an able astronomer, who made an important contribution to the theory of concentric celestial spheres of Eudoxus and Callippus by adding the counteracting spheres. The present article argues (a) that Aristotle purposefully turned to astronomy as the only mathematical science whose objects were correlative to the immaterial first substances or gods, the number of which had to be precisely determined by his own project of first philosophy; and (b) that he had no aspiration of improving the astronomical theory of his peers, contrary to an interpretation that first emerged with the Peripatetic exegete Sosigenes in the second century A.D. (shrink)

Glimpses into Byzantium. Its Philosophy and Arts -/- This volume contains peer-reviewed articles published by the author either in hard-copy or in electronic format between 2019 and 2021. These focus on various aspects of Byzantine and Medieval culture. -/- It is not possible to upload an entire book here, but there are copies of it in libraries and it can also be bought from Amazon.

In NE III.10, 1118b1–3, Aristotle says that the “most shared of the senses is that according to which intemperance [comes about], and it would seem justifiably to be shameful, because it inheres [in us] not insofar as we are human beings, but insofar as we are animals”. This statement appears to describe the sense of touch as shameful. This may seem like a strange position for Aristotle to hold, since elsewhere he describes human touch as the most accurate among animal (...) species, which corresponds to our superior intelligence, and as necessary for animal life. In this paper, I argue that Maimonides nevertheless succeeds in showing that Aristotle has a strong theoretical reason for maintaining that the sense of touch is shameful. Maimonides shows that, based on principles of Aristotelian psychology, human touch is indeed shameful because it obstructs intellectual activity. (shrink)

In this paper, I compare the Megarian thesis of Metaphysics IX 3 with other sources on the Megarians in order to clarify two questions: that of the unity and nature of the so-called Megarian school and that of Aristotle’s broader argument in IX 3. I first review the disputed issue of the status of the Megarian school and then examine two hypotheses regarding the identity behind Aristotle’s allusion in IX 3. Third, I explore the connection between Megarianism and Plato’s Euthydemus, (...) a task that helps us to contextualize Aristotle’s anti-Megarian polemic. Lastly, I build on the preceding argument in a re-examination of the Eleatic hypothesis with regard both to the Megarians as a whole and to the thesis that Aristotle transmits. (shrink)

Chapter Θ10 of Aristotle's Metaphysics is traditionally taken to be about the truth of intuitions, namely episodes of an immediate and sub-propositional grasp of entities. This exegesis however saddles Aristotle with a broken-backed theory of truth because in other passages of his works he claims that truth and falsehood apply only to items of a propositional nature and denies that sub-propositional items can be true or false. An alternative exegesis is preferable which takes Θ10 to be about the truth of (...) existential statements and judgements concerning simple items. (shrink)

In this second of a 2-part survey of Aristotle’s epistemology, I present an overview of Aristotle’s views on technē (craft or excellent productive reason) and phronēsis (practical wisdom or excellent practical reason). For Aristotle, attaining the truth in practical matters involves actually doing the right action. While technē and phronēsis are rational excellences, for Aristotle they are not as excellent or true as epistēmē or nous because the kinds of truth that they grasp are imperfect and because they are excellent (...) states for humans, not simply speaking. I then discuss why Aristotle takes sophia (wisdom), understanding and scientific knowledge of the best things, to be its own excellence. While this is the best cognitive state for human beings, I argue that Aristotle thinks divine cognitive activity is different in kind and more perfect than any human activity. (shrink)

Philosophy Compass, Volume 17, Issue 1, January 2022.

Discussions of Aristotle’s Metaphysics Z tend to treat it either as an independent treatise on substance and essence or as preliminary to the main conclusions of the Metaphysics. I argue instead that Z is central to Aristotle’s project of first philosophy in the Metaphysics: the first philosopher seeks the first causes of being qua being, especially substances, and in Z, Aristotle establishes that essences or forms are the first causes of being of perceptible substances. I also argue that the centrality (...) of Z to first philosophy is compatible with its status as theology. (shrink)

Kind representations, concepts like table, triangle, dog, and planet, underlie generic language. Here, we investigate the formal structure of kind representations—the structure that distinguishes kind representations from other types of representations. The present studies confirm that participants distinguish generic‐supporting properties of individuals (e.g., this watch is made of steel) and accidental properties (e.g., this watch is on the nightstand). Furthermore, work dating back to Aristotle establishes that only some generic‐supporting properties bear a principled connection to the kind, that is, are (...) true of an individual by virtue of its being a member of a specific kind (e.g., telling time for a watch). The present studies tested the hypothesis that principled connections are part of the formal structure of kind representations. Specifically, they tested whether they structure a newly learned kind representation. Experiment 1 found that introducing a property of a newly encountered novel kind in any one of four linguistic frames that provide evidence that a property has a principled connection to a kind (e.g., “It has fur because it is a blick”) led participants to infer a different conceptual consequence of principled connections (i.e., “There is something wrong with this blick, which does not have fur”) for which they had no direct evidence. Two introduction frames that provided no evidence for principled connections (e.g., “Almost all blicks have fur”) did not generate the same consequence. Experiment 2 found that all of the targeted properties were generic licensing, irrespective of the introduction frame. That the distinction between properties that bear principled connections to their kinds, and merely generic‐supporting properties structures novel kind representations, provides strong evidence that this distinction is part of the formal structure of kind representations. (shrink)

Aristotle's notion of matter has been seen either as unintelligible, it being some mysterious potential entity that is nothing in its own right, or as simply the notion of an everyday object. The latter is the common assumption in contemporary approaches to hylomorphism, but as has been pointed out, especially by scholars with a background in ancient philosophy, if we conceive of matter as an object itself we cannot account for the unity of hylomorphic substances. Thus, they assume that a (...) hylomorphic substance is an essential unity and matter not a constituent at all. This solution to the problem of unity, however, brings us back to the mysterious notion of matter. For these reasons, I will revisit Aristotle's conception of matter in this paper. I will argue that an understanding of form as a cause of being requires that matter be an independent constituent of the individual substance. However, I agree that the conception of matter as an individual object with an essence makes it impossible to solve the problem of unity. We therefore need to take seriously Aristotle's assertion that matter is nothing in its own right and not an individual. By denying that matter is an individual, Aristotle does not introduce a mysterious entity, nor does he deny that it can be identified independently of the whole; instead, matter for Aristotle is an irreducible plurality, and this explains why it is not an individual and has no essence. I will conclude with some observations on how this gives rise to two competing versions of hylomorphic constitution. (shrink)

This article argues for an emendation in Aristotle's Metaphysics A 10, 993a13–15. The emendation is based on a hitherto overlooked reading preserved in Alexander of Aphrodisias’ commentary on A 7. First, the article problematizes the reading of the Metaphysics manuscripts in terms of syntax, diction and content. Second, it shows that Alexander's reading is free of all three problems. Third, it argues for the originality of Alexander's reading according to the principle utrum in alterum abiturum erat? and based on the (...) fact that the new reading reveals a subtle didactic link between A 7 and A 10 that sheds new light on the argumentative architecture of Metaphysics Book A. (shrink)

This paper offers an interpretation of Aristotle’s concepts of dynamis and energeia (commonly translated as potentiality and actuality), and of the thematic progression of Metaphysics IX. I first raise the question of where motion fits in Aristotle’s categories and argue that the locus of motion in the system of categories are the categories of doing and suffering, in which case dynamis and energeia in respect of motion can also be understood as the dynamis and energeia of doing and suffering. Next, (...) I argue that the analogy that Aristotle draws in IX.6 is an analogy between the dynamis and energeia of doing and suffering and the dynamis and energeia of substance. Finally, I try to show that it is this analogy between the kinetic and non-kinetic variants of dynamis and energeia—and not the distinction between end-inclusive and end-exclusive activities—that provides the key to understanding the structure of Metaphysics IX. (shrink)

In several of his writings Hegel suggests an identification of his absolute idea/spirit with Aristotle's God in theMetaphysics. This suggestion is remarkable since it indicates that Hegel regarded his philosophy in line with classical positions in ancient metaphysics. Although there is increasing discussion of the relation between Hegel and Aristotle it is still doubtful what it was that Hegel seemed to find at the highest point of Aristotle's philosophy. To clarify this relation within the realm of first philosophy I will (...) first give a short reconstruction of Aristotle's conception of God in order, second, to confront this conception with the absolute idea/spirit in Hegel. Against Ferrarin, I will not primarily discuss the conception of actuality/activity and infinite subjectivity; rather I will focus on Aristotle's and Hegel's ontological understanding of truth. The new thesis in my paper is that Hegel can relate his theory of the absolute idea/spirit to Aristotle's God on the basis of their shared understanding of truth. This understanding allows both of them to find the highest realization and thus the fulfillment of truth in the self-thinking thinking of God (Aristotle) or the self-thinking thinking of the absolute idea/spirit (Hegel). When Hegel seems to return to Aristotle at the end of his system, this return has its systematic link in the idea of a fulfilled truth which is God or the Absolute in the sense of self-thinking thinking. Although Hegel's return to Aristotle's theology has a certain plausibility, it is also limited by the fact that for Aristotle God's self-thinking thinking is not a process of self-determination, as Hegel finds it to be and which leads him to miss a crucial feature of Aristotle's theology. (shrink)

This chapter is a work in applied metaphysics. Recent discussions of monism and metaphysical dependence are deployed to develop a view—the doctrine of divine priority (DDP)—that is a viable alternative to the doctrine of divine simplicity (DDS). DDS and the traditional motivation for it are discussed, then DDP is introduced by way of an analogy involving Jonathan Schaffer’s distinction between two forms of monism. It is argued that DDP is an alternative to DDS by showing that it is consistent with (...) the traditional motivation for the latter view, and argued that DDP is a viable alternative by showing that objections to its peculiar implications rest on assumptions that can reasonably be rejected. In the concluding section, the findings of the main discussion are summarized and DDP’s potential theological import is illustrated with a brief discussion of a possible solution to the Problem of the Trinity it affords. (shrink)

ArgumentThe aim of this paper is two-fold: to offer an interpretation that preserves the natural reading ofPhysicsII 1 – that Aristotle is drawing a stark distinction between what is natural and what is artificial; and to show how there is logical room for atertium quid– a category for things that are products of both nature and art. This aim is attained by highlighting two important qualifications Aristotle makes about the products of art in relation to an innate internal principle of (...) change and pointing out that the proper understanding of the significance of the essential-accidental distinction that Aristotle draws must be viewed in the context where he identifies two kinds of nature – form and matter. Based on these analyses, the following three logical categories are shown to be consistent with the passage: 1) purely natural things; 2) essentially artificial objects; and 3) essentially natural things with artificial aspects. (shrink)

The issue of the justification of the laws of logic has been under discussion since the end of the nineteenth century. However, in many works devoted to this problem Ajdukiewicz’s achievements are left unmentioned. It can be shown that in certain periods of the development of his views, he tried to present various attempts at solving the problem of the justification of the laws of logic.

Contemporary platonism has been conditioned in large part by two dogmas. One is the belief in a fundamental cleavage between intelligible but invisible Platonic forms that are real and eternal, and perceptible objects whose confinement to spacetime constitutes an inferior existence and about which knowledge is impossible. The other dogma involves a kind of reductionism: the belief that Plato’s unhypothetical first principle of the all is identical to the form of the good. Both dogmas, I argue, are ill-founded.

Recent interpreters portray Aristotle as a Protagorean antirealist, who thinks that colors and other perceptibles do not actually exist apart from being perceived. Against this, I defend a more traditional interpretation: colors exist independently of perception, to which they are explanatorily prior, as causal powers that produce perceptions of themselves. They are not to be identified with mere dispositions to affect perceivers, or with grounds distinct from these qualities, picked out by their subjective effect on perceivers (so-called “secondary qualities”). Rather, (...) they are intrinsic qualities of objects, which are in reality just as they appear to be. At the same time, Aristotle rejects any “simple theory of color” according to which the essence and nature of colors is fully revealed in experience. Although the character of perceptibles as they are experienced is “better known to us,” their essence and nature only comes to be known through a correct theory. (shrink)

This dissertation is a collection of essays exploring the role of metaphor in Aristotle’s scientific method. Aristotle often appeals to metaphors in his scientific practice; but in the Posterior Analytics, he suggests that their use is inimical to science. Why, then, does he use them in natural science? And what does his use of metaphor in science reveal about the nature of his scientific investigations? I approach these questions by investigating the epistemic status of metaphor in Aristotelian science. In the (...) first essay, I defend an interpretation of metaphor as a type of heuristic reasoning: I claim that Aristotle uses metaphor to express conditions an explanation in natural science must meet if it is to explain regular, ordered change. These conditions specify the kinds of causes—particularly unmoved efficient causes—which the inquirer into nature is seeking. In the second essay, I look to Aristotle’s use of certain endoxa or common beliefs as explanatory principles in science, and show that his use of these principles is similar to his use of metaphor. In the final essay, I present a historical study of the analogy of art and nature, and I suggest that by looking to how the Greeks understood the role of inquiry in the arts, we can shed some light on Aristotle’s views concerning the method of inquiry he thinks the natural scientist should adopt. (shrink)

The opening argument in the Metaphysics M.2 series targeting separate mathematical objects has been dismissed as flawed and half-hearted. Yet it makes a strong case for a point that is central to Aristotle’s broader critique of Platonist views: if we posit distinct substances to explain the properties of sensible objects, we become committed to an embarrassingly prodigious ontology. There is also something to be learned from the argument about Aristotle’s own criteria for a theory of mathematical objects. I hope to (...) persuade readers of Metaphysics M.2 that Aristotle is a more thoughtful critic than he is often taken to be. (shrink)

In one of the unpublished parts of his manuscript titled the Spicilegia, Arthur Schopenhauer presents an uncharacteristically sympathetic reading of an Aristotelian text. The text in question, De anima III. 5, happens to include the only occurrence of arguably the most controversial idea in Aristotle, namely the distinction between active and passive nous. Schopenhauer interprets these two notions as corresponding to his own notions of the ?will? and the ?intellect? or ?subject of knowledge?, respectively. The result is a unique interpretation, (...) according to which Aristotle's active nous is in fact non-intellectual: it is devoid of any interaction with intelligible objects, and hence lacks any intellectual activity. I show that this interpretation, though counterintuitive, is tenable, and that it may contribute to our understanding of Aristotle even if we do not adopt Schopenhauer's metaphysics. (shrink)

A standard thesis of contemporary Aristotelian virtue ethics and some recent Heideggerian scholarship is that virtuous behavior can be performed immediately and spontaneously without engaging conscious processes of deliberative thought. It is also claimed that phronēsis either enables or is consistent with this possibility. In the Nicomachean Ethics, however, Aristotle identifies phronesis as the excellence of the calculative part of the intellect, claims that calculation and deliberation are the same and that it is the mark of the phronimos to be (...) able to deliberate well. He also insists that for an action to count as virtuous it must issue from rational choice, which he characterizes as determined by deliberation. It thus seems that any exegetically respectable attempt to explain virtuous action within an Aristotelian framework would need to integrate with some account of deliberative choice. This creates a tension in Aristotelian scholarship. In this paper, I shall formalize this tension in terms of an apparently inconsistent triad of claims and shall examine the merits of at least one prominent interpretation of phronesis with respect to its reconciliation. (shrink)

This article seeks to provide an answer as to why Metaphysics, Lam ends not with the justly famous account of the divine nous with which this book of the treatise is always associated, but with an aporetic account of the living and dying of everything mortal. This surprising moment, I argue, is a manifestation of Aristotle's conviction—quite alien to the mainstream understanding of philosophy as a discipline today—that even the purest moments of theoretical speculation are the work of a human (...) soul always in touch with its materiality and its subsistence in the world. A soul that only is at all when it is at work in living well, which is to say when the soul enacts itself in praxis. This means: the best understanding of the aporetic conclusion to Metaphysics, Lam is the one that asks us to recall that Aristotle's project of first philosophy—however much its most proper subject matter is the unchanging and immaterial—proceeds as part of a human life lived a certain way, and not as part of an academic discipline. (shrink)

Like many realists about causation and causal powers, Aristotle uses the language of necessity when discussing causation, and he appears to think that by invoking necessity, he is clarifying the manner in which causes bring about or determine their effects. In so doing, he would appear to run afoul of Humean criticisms of the notion of a necessary connection between cause and effect. The claim that causes necessitate their effects may be understood—or attacked—in several ways, however, and so whether the (...) view or its criticism is tenable depends on how we understand the necessitation claim. In fact, Aristotelian efficient causation may be said to involve two distinct necessary connections: one is a relation between causes considered as potential, while the other relates them considered as active. That is, the claims that (1) what has the power to heat necessarily heats what has the power to be heated, and that (2) a particular flame which is actually under a pot necessarily heats it, both of which appear to be true for Aristotle, involve distinct notions of necessity. The latter kind of necessity is based on the facts, as Aristotle sees them, about change, whereas the former is based in the nature of properties. Though different, both kinds of necessity are instances of what contemporary philosophers would call metaphysical necessity, and together they also amount to a theory of causal determination. (shrink)

Both literalism, the view that mathematical objects simply exist in the empirical world, and fictionalism, the view that mathematical objects do not exist but are rather harmless fictions, have been both ascribed to Aristotle. The ascription of literalism to Aristotle, however, commits Aristotle to the unattractive view that mathematics studies but a small fragment of the physical world; and there is evidence that Aristotle would deny the literalist position that mathematical objects are perceivable. The ascription of fictionalism also faces a (...) difficult challenge: there is evidence that Aristotle would deny the fictionalist position that mathematics is false. I argue that, in Aristotle's view, the fiction of mathematics is not to treat what does not exist as if existing but to treat mathematical objects with an ontological status they lack. This form of fictionalism is consistent with holding that mathematics is true. (shrink)

In this paper I ask whether in Aristotle's metaphysical system the form of a non-living sensible substance, such as the form of this house, is or is not universal. I argue that his position as it stands is self-contradictory, and then try to give some account of the pressures that led to this central contradiction in Aristotle's metaphysical thought.

Averroes defended philosophy by returning to the true Aristotle. For this purpose, Aristotle's book in which he explained the eternity, uniqueness and movement of the universe, occupied a place of special importance. But the Aristotelian philosopher had a hard time holding his own in the face of contradictions within the book and with respect to Aristotle's later works. In his early Compendium, later Paraphrase, and final Long Commentary of De Caelo, Ibn Rushd continued the efforts of the Hellenistic commentators in (...) order to integrate all the elements of his doctrine into a unified system, to harmonize his early cosmology with his later Metaphysics and to uphold his models of homocentric planetary spheres against the mathematical paradigm of Ptolemaic astronomy. By insisting throughout on demonstrative arguments based on rational principles, he asserted the philosophers' claim to irrefutable truth. (shrink)

In this paper I offer a reading of one of Plato's later works, the Sophist, that reveals it to be informed by principles comparable on the face of it with those that have emerged recently in the field of critical thinking. As a development of the famous Socratic method of his teacher, I argue, Plato deployed his own pedagogical method, a ‘mid‐wifely’ or ‘maieutic’ method, in the Sophist. In contrast to the Socratic method, the sole aim of this method is (...) not to disabuse the reader or learner of her false opinions. Rather, its purpose is to supply her with the skills and dispositions as well as the claims and counter‐claims she needs to critically evaluate a view, and so facilitate knowledge acquisition, for herself. But the text does not merely teach critical thinking in this indirect manner. One of the strategies its author employed was to encourage the reader/learner to consider under what conditions a claim or idea would be false. To the extent that it achieves this, the Sophist provides both a model and an application of that particular kind of critical thinking in the learning environment that Jonathan Baron has described as ‘active open‐mindedness’. (shrink)

Aristotle’s classification of ideal number in Metaphysics M 6 has often been considered an unfair presentation of Plato’s actual views. I take another look at the passage and argue that Aristotle is a more careful critic than has been usually recognised. In particular, I argue that much of the scholarly discussion on the passage has failed to take account of Aristotle’s deeper concern, namely, the conditions necessary for numbers to be ordinal. I then set Aristotle’s critique within the broader context (...) of his concern to separate Form from Number, and thus to separate metaphysical questions from mathematical ones. The latter half of the article shows some of the consequences of mixing mathematics with metaphysics from a systematic and historical point of view. (shrink)

Aristotle offers apparently inconsistent explanations for paronymous expressions derived from matter: on the received picture, derived from Metaphysics Θ.7, such expressions are used in all and only cases of substantial change, because predicating the matter directly of a substance would be false; on the error picture, derived from Metaphysics Z.7, the same expressions are used in all and only cases of change from an unclear and nameless privation, because ordinary language users conflate such privations with matter. I propose a resolution: (...) the received picture explains why the usage is fitting, but the error picture explains how the usage originated. (shrink)

In Metaphysics Λ, Aristotle appeals to the prime mover: an unmoved mover that is the first moving cause of the world. Elsewhere, he calls the science concerned with the prime mover ‘theology’ (Meta. E.1, 1026a19). But what is the point of this science? On a common view, its purpose is to give an account of the prime mover itself, and especially to prove its existence. By contrast, I argue that Aristotle’s theology in Metaphysics Λ is ‘nature-bound’: it ultimately aims at (...) explaining facts about the perceptible world, in particular the motion of heavenly bodies and the cycle of generation of perishable substances. (shrink)

This paper argues that the discussion in which Aristotle engages in Metaphysics ΖΗ has the same starting-point as natural science: the principles of changing substances. These inquiries are nonetheless distinct because natural science uses these principles in its detailed investigations into natural substances, whereas ΖΗ reflect on the principles themselves. ΖΗ are an integral part of Aristotle’s inquiry into the principles of all substances, changing and unchanging: they are not merely preliminary to an inquiry into the latter kind. They are (...) also an integral part of Aristotle’s ‘first philosophy’, alongside theology’s study of the nature and activity of unchanging substances. (shrink)

Aristotle's inquiry into the definitional question “what is substance?” in the central books of the Metaphysics is constrained by the unity requirement. Roughly, a particular hylomorphic compound substance, such as this human, ought to be a unified whole and not just a heap of material parts and form. A similar claim applies to the substance‐kind, human, which Metaphysics ΖΗΘ characterises as a hylomorphic compound taken universally. I raise the following question about this picture of unity: Is a compound's unity basic (...) or is it derived from the form's unity? Reading closely Metaphysics Z.12 and H.6, I argue that the form is explanatorily basic for the compound's unity. (shrink)

This study is concerned with a crucial passage in Metaphysics Z.11. After having established that only the formal parts of an object are stated in its definition and thus constitute its essence, Aristotle warns us against the process of separating the formal from the material parts. In doing so, he rejects the comparison proposed by Socrates the Younger. Mathematicals cannot be equated to natural objects because some material parts must be included in accounting for the latter but not in accounting (...) for the former. The goal of this article is to understand to what extent matter is essential to an object by examining the content of Aristotle’s criticism. My reconstruction shows that Aristotle is still committed to a formalist view. Socrates’ comparison is rejected because it removes matter not from the definitions of the subjects of metaphysics, but from the definitions of their attributes. (shrink)

Zusammenfassung Zur aristotelischen Unterscheidung von Herstellen und Handeln gibt es zwei konkurrierende Interpretationen: nach der einen betrifft der Unterschied zwei verschiedene Aspekte an Handlungen, nach der anderen verschiedene Typen von Handlungen. Für eine Entscheidung dieser Frage sind systematische und exegetische Gesichtspunkte zu trennen: zwar bietet die aristotelische Textbasis Belege für beide Seiten, allerdings zeigt die systematische Untersuchung, dass eine zwei-Typen-Lesart sachlich verfehlt ist. Handlungen lassen sich nicht sinnvoll unterteilen in solche, die ihr Ziel lediglich außer sich, aber kein Ziel in (...) sich haben und umgekehrt. Stattdessen sind sie notwendig von einer doppelten Zielsetzung geleitet, bei welcher der Vollzug der Handlung in deren Vollendung münden soll. (shrink)

We critically reconsider an old hypothesis of the role of the dekad in Pythagorean philosophy. Unlike Zhmud, we claim that: 1) the dekad did play a role in Philolaus’ astronomical system, and 2) Aristotle did not project Plato’s theory of the ten eidetic numbers onto the Pythagoreans. We claim that the dekad, as the τέλειος ἀριθμός, should be understood in Philolaus’ philosophy as completeness and the basis of counting in Greek – as in most other languages – in a decimal (...) system. Additionally, we argue that the number ten is not even a candidate for the τέλειος ἀριθμός in Plato’s philosophy. As a final result of our discussion, we compare and contrast Philolaus’, Plato’s, and Speusippus’ accounts of completeness in relation to numbers. (shrink)

The position on the question of divine providence of the Aristotelian commentator Alexander of Aphrodisias (fl. c. A.D. 200) is of particular interest. It marks an attempt to find avia mediabetween the Epicurean denial of any divine concern for the world, on the one hand, and the Stoic view that divine providence governs it in every detail, on the other.2As an expression of such a middle course it finds a place in later classifications of views concerning providence.3It is also of (...) topical interest: Alexander's fullest discussion, in his treatiseDe providentia (On Providence)(surviving only in two Arabic versions), has only recently been edited and translated,4although some aspects of his position had long been known from other texts preserved in Greek.5. (shrink)