Modern philosophy of mathematics has been dominated by Platonism and nominalism, to the neglect of the Aristotelian realist option. Aristotelianism holds that mathematics studies certain real properties of the world – mathematics is neither about a disembodied world of “abstract objects”, as Platonism holds, nor it is merely a language of science, as nominalism holds. Aristotle’s theory that mathematics is the “science of quantity” is a good account of at least elementary mathematics: the ratio of two heights, for example, (...) is a perceivable and measurable real relation between properties of physical things, a relation that can be shared by the ratio of two weights or two time intervals. Ratios are an example of continuous quantity; discrete quantities, such as whole numbers, are also realised as relations between a heap and a unit-making universal. For example, the relation between foliage and being-a-leaf is the number of leaves on a tree,a relation that may equal the relation between a heap of shoes and being-a-shoe. Modern higher mathematics, however, deals with some real properties that are not naturally seen as quantity, so that the “science of quantity” theory of mathematics needs supplementation. Symmetry, topology and similar structural properties are studied by mathematics, but are about pattern, structure or arrangement rather than quantity. (shrink)

Aristotelian substance theory tells us that substances have structures (read: forms) as proper parts. This claim has recently been defended by Kathrin Koslicki who dubbed it the ‘Neo-Aristotelian Thesis.’ Strangely, Aristotelianism has not yet been universally embraced by philosophers – partly because some of its claims, such as the Neo-Aristotelian Thesis – are viewed by some as counterintuitive at best. In this paper, I argue for Aristotelianism by showing its philosophical usefulness: specifically, I put it to use in (...) saving the metaphysical doctrine of endurantism and some central mereological doctrines (such as Transitivity) from recent attacks. This utility gives us reason to endorse Aristotelianism. Along the way, I defend Koslicki's argument for the Neo-Aristotelian Thesis from a recent criticism, thus helping provide still more reason to endorse Aristotelianism: namely, Koslicki's vindicated argument. (shrink)

In lieu of an abstract, here is a brief excerpt of the content:The Aristotelianism of Locke's PoliticsJ. S. MaloyThose, then, who think that the positions of statesman, king, household manager, and master of slaves are the same are not correct. For they hold that each of these differs not innly in whether the subjects ruled are few or many... the assumption being that there is no difference between a large household and a small city-state.... But these claims are not (...) true.Aristotle, Politics, 1252a1The Power of a Magistrate over a Subject may be distinguished from that of a Father over his Children, a Master over his Servant, a Husband over his Wife, and a Lord over his Slave. All which distinct Powers happening sometimes together in the same Man, if he be considered under these different Relations, it may help us to distinguish these Powers one from another, and show the difference betwixt a Ruler of a Common-wealth, a Father of a Family, and a Captain of a Galley.Locke, Two Treatises of Government, 2.22 [End Page 235]When the political theory of John Locke first appeared in print in 1689, the imposing authority of Aristotle stood ready to defeat it. So believed many of Locke's critics, at any rate. After his death in 1704, when it was confirmed that the internationally renowned author of An Essay Concerning Human Understanding had also written the anonymously published Two Treatises of Government, Locke was widely taken to represent a distinctive type of political theory based on individual rights and the social contract. Learned opposition to this sort of voluntaristic account of politics has often rested on Aristotle, "the Philosopher," the ancient authority on the human instinct for sociability and the hierarchal communities arising therefrom. Within the modern academy "liberals," "communitarians," and "republicans" have again made a habit of pronouncing the names of Locke and Aristotle in tones of antagonism. In broad outline the reasons have not changed in two or three centuries ago: the first stands for natural-rights individualism and the second for an organic conception of community.3What are we to make of this conventional opposition in light of the awkward fact that the second of Locke's Two Treatises, "Of Civil Government," takes the reclamation of the Aristotelian conception of political power as its principal purpose? Locke announced in the opening chapter of that essay that his chief target, Robert Filmer, had misunderstood the nature of distinctively political relationships, mainly by ignoring the differences between authority in political society and authority within the family (L 2.1–2). Locke alleged that this basic conceptual mistake of the Filmerian theory of "absolute" and "arbitrary" government was the source of its disastrous practical ramifications, which he had summed up in the first Treatise as "Chains for all Mankind" (L 1.1). Filmer, in turn, had taken Plato's side in the debate about political and familial rule which Aristotle had joined in the opening lines of his Politics (A 1252a). Though a perceptive reader long ago noticed the Aristotelianism of Locke's response to Filmer—Locke and Algernon Sidney were the "two famous men" to whom Rousseau alluded as having defended Aristotle against Filmer's Platonic notions of power—no modern scholar has attempted a full explanation of the significance of Locke's intervention in this debate.4 [End Page 236]The analysis below will show that Aristotle was the classic source for both the principal theoretic argument of Locke's second Treatise and the method employed to pursue it, i.e. using analogies of power for conceptual comparison and distinction. But my argument for the Aristotelianism of Locke's politics will rest on contextual as well as textual grounds. Not only was Locke pursuing an evident variation on the central theme of bk. 1 of Aristotle's Politics; he was far from alone in doing so. This sort of project was by the 1680s typical of radical constitutionalist writing in Europe, including not only English Whigs like Sidney and James Tyrrell but also a long line of writers on both sides of the English Channel, stretching back at least a century, who deployed a particular interpretation of Aristotle in the service... (shrink)

In general historical treatments, one often encounters the idea that Kepler’s and Newton’s discovery of elliptical planetary orbits marked a decisive break with tradition and definitively undermined any possibility of an Aristotelian approach to physics and astronomy. Although Aristotle had no understanding of gravity, I want to demonstrate that elliptical orbits were a refinement of earlier models and that one can produce an Aristotelian account of elliptical orbits once one corrects his crucial mistake about gravity. One interesting side-effect of this (...) straightforwardly Aristotelian approach is that it eliminates the empty, second focal point around which any elliptical system revolves. I should emphasize that the present paper is not intended to contradict, oppose, or replace any aspect of contemporary mathematical physics or astronomy. The point is not to propose a new scientific theory—we all know that planetary orbits are elliptical—but to demonstrate that metaphysical Aristotelianism is more versatile than is generally supposed. (shrink)

William Gilbert’s 1600 book, De magnete, greatly influenced early modern natural philosophy. The book describes an impressive array of physical experiments, but it also advances a metaphysical view at odds with the soon to emerge mechanical philosophy. That view was animism. I distinguish two kinds of animism – Aristotelian and Platonic – and argue that Gilbert was an Aristotelian animist. Taking Robert Boyle as an example, I then show that early modern arguments against animism were often effective only against Platonic (...) animism. In fact, unacknowledged traces of Aristotelian animism can be found in Boyle’s mechanical account of nature. This was Gilbert’s legacy. (shrink)

In recent years virtue theory, which is derived from Aristotle’s moral philosophy, has become increasingly popular as an alternative both to deontological theories such as Kant’s and to consequentialism such as Mill’s utilitarianism. Here Rosalind Hursthouse (1943– ) sketches the main features of such virtue theory or neo-Aristotelianism, bringing out its distinctive approach. Neo-Aristotelians are interested not just in particular actions, but in the flourishing of individuals over a lifetime; they are concerned with character traits rather than duties. The (...) essential question for a neo-Aristotelian is not ‘Which actions are right or wrong?’ but rather ‘How am I to live well?’ (From Rosalind Hursthouse, Beginning Lives, 1987). (shrink)

Alasdair MacIntyre is an Aristotelian critic of communitarianism, which he understands to be committed to the politics of the capitalist and bureaucratic nation-state. The politics he proposes instead is based in the resistance to managerial institutions of what he calls ‘practices’, because these are schools of virtue. This shares little with the communitarianism of a Taylor or the Aristotelianism of a Gadamer. Although practices require formal institutions. MacIntyre opposes such conservative politics. Conventional accounts of a ‘liberal-communitarian debate’ in political (...) philosophy face the dilemma that Alasdair MacIntyre, often identified as a paradigmatic communitarian, has consistently and emphatically repudiated this characterization. Although neo-Aristotelianism is sometimes seen as a philosophical warrant for communitarian politics, MacIntyre’s Aristotelianism is opposed to communitarianism. This paper explores the rationale of that opposition. (shrink)

In Studies on Early Modern Aristotelianism Paul Richard Blum shows that Aristotle’s thought remained the touchstone of modern philosophy; for it was the philosophy taught at universities. The concept of philosophy at Jesuit schools forms the first part of this book. Their impact on the sciences and mathematics in combination with Renaissance ideas of nature is the topic of the second part. The transformation of Aristotelian metaphysics and theology under the influence of the Renaissance is the third area of (...) this book. Surprising continuity from the late Middle Ages into modernity and the radical difference of subject centered modern philosophy from ‘teachable’ school philosophy are innovative in these studies. (shrink)

This chapter contains section titled: I Aristotle and Early Modern Philosophy II Medieval Thought in Early Modern Scholasticism III The Philosophical Textbook IV Conclusions.

This paper examines whether Giordano Bruno’s philosophy should be considered pantheist or immanentist—two philosophies that scholars regard as partly equivalent. However, this paper distinguishes them and argues that Bruno either identified the whole of nature with God or recognized a primary principle that is immanent, yet distinguishable, from matter. In terms of Bruno’s interpretation of the Aristotelian notions of form and matter, the difference between an immanentist view and a pantheist one lies in the role that form (or act) assumes (...) with regard to matter (or potency). This paper maintains that Bruno interpreted and adapted Aristotle’s philosophy to find his own immanentist metaphysics, which is built on the traditional Aristotelian system. This argument was based on the reconstruction of how he used Aristotelian thought as an instrument to subvert Aristotelianism. In particular, Bruno attested that intellect exists within nature, but it is not co-extensive with the whole nature. Finally, the paper highlights how Bruno applied Aristotle’s language, method, and themes to criticize the fundamentals of Aristotelian philosophy and the related traditions. (shrink)

The view that dominated the last century claims that ethical thought requires thinking of some things – e.g. pleasure, knowledge, virtue – as good “full stop,” or good simpliciter . Traditional Consequentialists, for instance, argue that moral evaluations of acts, motives, etc . are grounded in facts about the simple goodness of that which those things bring about. Similarly, some rational intuitionists think that claims about what one has reason to do are grounded in facts about what is good simpliciter (...) . Such a view gives rise to a set of semantic, metaphysical, and epistemological puzzles about the nature of good simpliciter . I argue that an Aristotelian approach to ethics reveals that ethical thought does not requires good simpliciter , that Aristotelian positions avoid charges of metaphysical and epistemological queerness, and that it gives a straightforward semantic analysis of key moral terms, e.g. morally good/bad and morally right/wrong. I then distinguish between two varieties of Aristotelianism. (shrink)

Minimalism and Trivialism are two recent forms of lightweight Platonism in the philosophy of mathematics: Minimalism is the view that mathematical objects arethinin the sense that “very little is required for their existence”, whereas Trivialism is the view that mathematical statements have trivial truth‐conditions, that is, that “nothing is required of the world in order for those conditions to be satisfied”. In order to clarify the relation between the mathematical and the non‐mathematical domain that these views envisage, it has recently (...) been proposed that both Linnebo's notion of sufficiency and Rayo's “just is”‐operator can, or even should, be interpreted in terms of metaphysicalgrounding. This interpretation makes Minimalism and Trivialism akin to Aristotelianism in the philosophy of mathematics, according to which mathematical entities depend for their existence and their properties on non‐mathematical ones. In this paper we raise a general objection to this interpretation. We highlight a tension – a “Big Picture” Problem – between the metaphysical picture underlying both Minimalism and Trivialism, on the one side, and the metaphysics of Platonism and Aristotelianism on the other. We then consider various ways in which Linnebo and Rayo could respond. We finally argue that Minimalism and Trivialism are closer to Aristotelianism than to Platonism; however, even though these positions are not forms of traditional Platonism, they are not standard forms of Aristotelianism either. (shrink)

In lieu of an abstract, here is a brief excerpt of the content:Journal of the History of Ideas 62.2 (2001) 211-232 [Access article in PDF] Aristotelianism and the Soul in the Arabic Plotinus Peter Adamson It is common for historians of medieval thought to note that the influence of Aristotle on Islamic philosophy was tinged with Neoplatonism, thanks to a text known as the "Theology of Aristotle." It is now known that the "Theology" is in fact not a work (...) of Aristotle's but rather a paraphrase of parts of Plotinus's Enneads. Certainly, the misattribution of this work to Aristotle facilitated the spread of Neoplatonism as an aspect of Islamic peripateticism, as represented by such authors as al-Kindi, al-Farabi, and Ibn Sina (Avicenna). Some efforts have been made to assess its influence on particular philosophers, most notably Ibn Sina whose notes on the "Theology" have come down to us and who may have doubted its authenticity. 1 Until recently the attention paid to the "Theology" itself has tended more towards philological than philosophical analysis, focusing in particular on possible sources of the text. 2 Yet the differences between the original writings of Plotinus and its Arabic paraphrase are of considerable philosophic interest. In recent years research into the "Theology" has begun to pay more attention to the philosophical issues raised by the paraphrase. 3 Here I hope to further this trend by suggesting that, although the author [End Page 211] of this paraphrase was not Aristotle, his own thought was suffused with Aristotelianism.First, we should note that the so-called "Theology of Aristotle" is itself only a part of an original, larger paraphrase of the Enneads. It is now usually thought that this paraphrase was authored by a member of al-Kindi's circle in ninth- century Baghdad. 4 The original Arabic Plotinus has been preserved in three separate texts. The first is the "Theology" (hereafter Th.A) which is itself subdivided into a prologue, a series of "headings" (ru'us), and ten chapters, each called a mimar, meaning "chapter" in Syriac. 5 This is by far the longest of the three texts. We also have the so-called Letter on Divine Science, formerly attributed to al-Farabibut shown by Kraus to belong to the Arabic Plotinus materials. 6 Finally, there are the Sayings of the Greek Sage, a set of fragments collected from various sources by Rosenthal and Lewis which also paraphrases Plotinus in Arabic. 7 As argued by F. W. Zimmermann, these three sources all derive originally from a lost, perhaps much more extensive, paraphrase of Plotinus. 8 They are united both by writing style and philosophical content. I will call them, collectively, AP; and since I cannot here provide conclusive arguments as to the identity of their author, I will call him the Adaptor.One of the major goals of al-Kindi and his circle seems to have been the synthesis of available Greek texts into a coherent philosophy. Thus al-Kindi himself produced doxographical works (for example, his Discourse on the Soul) and a survey of the Aristotelian corpus. 9 If the Adaptor worked in such a milieu, he may well have been influenced by other philosophical sources in making a paraphrase of Plotinus. Zimmermann has suggested that such an influence is at [End Page 212] work in mimar III, where the Adaptor may have drawn on Aristotle's De Anima in order to "reconcile" Plotinus with an Aristotelian theory of the soul as the entelechia of the body. 10 Here I will examine the relationship of soul and body in AP and expand on Zimmermann's thesis in an effort to show that the Adaptor was, in this respect at least, an Aristotelian interpreter of Plotinus. I will close by examining the relationship between AP and a contemporaneous work, the paraphrase of the De Anima produced in al-Kindi's circle. Mimar III and the Question of entelechiaStudents of Aristotle are familiar with his thesis that soul is the form of the body. In the De Anima Aristotle explains this further by claiming that the soul is the "perfection" or entelechia of... (shrink)

Central to the western theistic understanding of divine providence is the conviction that God is the sovereign Lord of nature. He created the physical universe and continually conserves it in existence. What's more, He is always and everywhere active in it by His power. The operations of nature, be they minute or catastrophic, commonplace or unprecedented, are the work of His hands, and without His constant causal influence none of them would or could occur.

The paper examines the influence of aristotelianism on the explanation of action by Thomas Aquinas and Raymund Lullus. The main focus is on the basic elements of this influence, on the originality of the thought of Thomas Aquinas and Raymund Lullus, on their different interpretations of action in comparison with aristotelianism, and on reasons leading to different ways of accepting aristotelianism.

The volume collects the most important papers Pierluigi Donini wrote in the last three decades with the aim of promoting a better assessment of post-hellenistic philosophy. The philosophical relevance of post-hellenistic philosophy is now widely (though not yet universally) recognized. Yet much remains to be done. The common practice of focusing each single school in itself detracts from a balanced assessment of the strategies exploited by many philosophers of the period. On the assumption that debates among schools play a major (...) role in the philosophy of the commentators, Donini concentrates on the interaction between leading Aristotelians and Platonists and demonstrates that the developments of both systems of thought were heavily influenced by a continuous confrontation between the two schools.And whereas in cases such as Alcinous and Aspasius this is basically uncontroversial, for other authors such us Alexander, Antiochus and Plutarch the pioneering work of Donini paves the way for a better understanding of their doctrines and definitely confirms the intellectual importance of the first imperial age, when the foundations were laid of versions of both Aristotelianism and Platonism which were bound to influence the whole history of European thought, from Late Antiquity onwards. (shrink)

In this paper I would like to establish the priority of Aristotle in the thought of George Frederick Holmes (1820-1897), the South's leading philosopher of the nineteenth century. Accompanying this aim is the possibility of an improved understanding of the historical "Mind of the South" and its particular orientation to the ongoing rise of modern civilization. Holmes copiously presented a firmly articulated "metaphysics" in a myriad of articles over a period stretching from the early 1840's until the end of the (...) 1870's. Holmes spent much of his philosophical energy struggling with such then influential moderns as Comte, Spencer and Darwin. But for all that the basis of his thought remained Aristotelian in nature. If it be allowed that Aristotle can make a "comeback" under today's conditions perhaps George Frederick Holmes is also entitled to be viewed once again as a "live option" given the fundamentally Aristotelian nature of his thought. (shrink)

'dealing with a special problem and limited in its proof. . .shows how Aristotelian Bacon was in his methodology'; Vickers 1992, 505 dislikes intensely.

Chakravartty claims that science does not imply any specific metaphysical theory of the world. In this sense, science is consistent with both neo-Aristotelianism and neo-Humeanism. But, along with many others, he thinks that a neo-Aristotelian outlook best suits science. In other words, neo-Aristotelianism is supposed to win on the basis of an inference to the best explanation (IBE). I fail to see how IBE can be used to favour neo-Aristotelianism over neo-Humeanism. In this essay, I aim to (...) do two things. Firstly, I explain why this failure is not idiosyncratic: it should be there even by Chakravartty's lights. Secondly, I raise some critical worries about Chakravartty's semirealism, especially in connection with the concept of a 'concrete structure' and the detection/auxiliary distinction. The essay ends with a dilemma: an exclusive disjunction encapsulated in its title. (shrink)

This volume deals with the development of moral and political philosophy in the medieval West. Professor Nederman is concerned to trace the continuing influence of classical ideas, but emphasises that the very diversity and diffuseness of medieval thought shows that there is no single scheme that can account for the way these ideas were received, disseminated and reformulated by medieval ethical and political theorists.