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)
Abstract The aim of the paper is to reassess the role of British Aristotelianism within the history of early modern logic between the sixteenth and seventeenth centuries, as a crucial moment of cultural transition from the model of humanistic rhetoric and dialectic to that of facultative logic, that is, a logic which concerns the study of the cognitive powers of the mind. The paper shows that there is a special connection between Paduan Aristotelianism and British empiricism, through the (...) mediation of British Aristotelianism. British Aristotelians took the ideas of the Paduan Aristotelian tradition and carried them to an extreme, gradually removing them from the original Aristotelian context in which they were grounded and developing what would later become the fundamental ideas of British empiricism. (shrink)
To read Adorno as a negativist Aristotelian was always going to be controversial. It is, thus, unsurprising that the common critical concern running through the three reviews assembled here is the Aristotelianism I ascribe to Adorno. I am immensely grateful for these generous and thoughtful contributions, and in what follows I will try to do justice to the concerns they raise. I focus on the ascription of Aristotelianism as the major concern, but I also discuss related and wider (...) comments, regarding immanent critique, negativism, the role of social theory in Adorno?s work, and the danger of being co-opted. Elsewhere, I have clarified the structure of the book and the aims of the different parts of it, and readers of this current reply might find it helpful to consult this other text first. (shrink)
The aim of this article is to pinpoint some of the features that do—or should—make Aristotelianism attractive to current moral educators. At the same time, it also identifies theoretical and practical shortcomings that contemporary Aristotelians have been overly cavalier about. Section II presents a brisk tour of ten of the ‘pros’: features that are attractive because they accommodate certain powerful and prevailing assumptions in current moral philosophy and moral psychology—applying them to moral education. Section III explores five versions of (...) the view that Aristotle's position is somehow anachronistic and out-dated. As none of those bears scrutiny, Section IV addresses ten features of Aristotelianism that do not seem to sit well with contemporary moral philosophy and psychology: the genuine ‘cons’ of Aristotelianism. It is subsequently argued that if we want to avoid acquiring Aristotelianism on the cheap, those less attractive features need to be engaged head-on: reinterpreted, revised or simply rejected. (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)
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)
The essays in this collection explore the implications of Alasdair MacIntyre's critique of liberalism, capitalism, and the modern state, his early Marxism, and the complex influences of Marxist ideas on his thought. A central idea is that MacIntyre's political and social theory is a form of revolutionary--not reactionary--Aristotelianism. The contributors aim, in varying degrees, both to engage with the theoretical issues of MacIntyre's critique and to extend and deepen his insights. The book features a new introductory essay by MacIntyre, (...) "How Aristotelianism Can Become Revolutionary," and ends with an essay in which MacIntyre comments on the other authors' contributions. It also includes Kelvin Knight's 1996 essay, "Revolutionary Aristotelianism," which first challenged conservative appropriations of MacIntyre's critique of liberalism by reinterpreting his Aristotelianism through the lens of his earlier engagement with Marx. "This is an excellent collection. Its particular strength is its sustained focus on Alasdair MacIntyre's political thought, in particular MacIntyre's complicated relation and indebtedness to Marxism. In their introduction, the co-editors say that the reception of MacIntyre within political philosophy has largely been reductive and one-sided, namely, that he is simply viewed as a conservative communitarian. In focusing on MacIntyre's radical heritage, this volume helps correct that simplistic misperception. --_Keith Breen, Queen's University Belfast_. (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)
To read Adorno as a negativist Aristotelian was always going to be controversial. It is, thus, unsurprising that the common critical concern running through the three reviews assembled here is the Aristotelianism I ascribe to Adorno. I am immensely grateful for these generous and thoughtful contributions, and in what follows I will try to do justice to the concerns they raise. I focus on the ascription of Aristotelianism as the major concern, but I also discuss related and wider (...) comments, regarding immanent critique, negativism, the role of social theory in Adorno’s work, and the danger of being co-opted. Elsewhere, I have clarified the structure of the book and the aims of the different parts of it, and readers of this current reply might find it helpful to consult this other text first. (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)
This article presents a skeleton of a potential paradigm of human flourishing and happiness in a free society. It is an exploratory attempt to construct an understanding from various disciplines and to integrate them into a clear, consistent, coherent, and systematic whole. Holding that there are essential interconnections among objective ideas, the article specifically emphasizes the compatibility of Aristotelianism, Austrian Economics, Positive Psychology, and Ayn Rand’s Objectivism arguing that particular ideas from these areas can be integrated into a paradigm (...) of human flourishing and happiness based on the nature of man and the world. Such a paradigm will help people to understand the world and to survive and flourish in it. It is hoped that the paradigm will grow and evolve as scholars engage, question, critique, interpret, and extend its ideas. Our goal is to have a paradigm that accords with reality and there is always more to learn from reality. (shrink)
In Quodlibet XV q.13, Henry of Ghent considers whether the Virgin Mary was immaculately conceived. He argues that she was not, but rather possessed sin only at the first instant of her existence. Because Henry’s defense of this position involves an elaborate discussion of motion and mutation, his discussion marks an important contribution to medieval discussions of Aristotelian natural philosophy. In fact, a number of scholars have identified Henry’s discussion as the source of an unusual fourteenth-century theory of change referred (...) to as “quasi-Aristotelianism” (so-called because the account purports to be Aristotelian but is not). My aim in the paper is two-fold: first, to show that Henry's position is not quasi-Aristotelian in the sense that scholars have supposed; second, to show that, even so, his discussion in q. 13 does involve a novel interpretation of Aristotle’s account of instantaneous change. (shrink)
In this volume, thirteen distinguished scholars consider the impact of Aristotelianism on modern philosophy. Spanning the last five centuries, the articles examine Aristotelian issues present in the writings of late scholastic, Renaissance, and early modern philosophers, such as: Vernia, Barbaro, Cajetan, Nifo, Piccolomini, Zabarella, Galileo, Campanella, Semery, Leibniz, Rousseau, Kant, Hegel, Nietzsche, Husserl, Heidegger, Wittgenstein, and Gadamer. The contributors pay particular attention to the role of the five intellectual virtues set forth by Aristotle in book VI of the Nicomachean (...) Ethics-art, prudence, science, wisdom, and intellect-in modern philosophy. (publisher, edited). (shrink)
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 elementarymathematics: 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)
Aristotelianism remained the dominant influence on the course of natural philosophy taught at the University of Paris until the 1690s, when it was swiftly replaced by Cartesianism. The change was not one wanted by church or state and it can only be understood by developments within the wider University. On the one hand, the opening of a new college, the Collège de Mazarin, provided an environment in which the mechanical philosophy could flourish. On the other, divisions within the French (...) Catholic Church between Austinians and Molinists led to Cartesianism finding support within an important section of the faculty of theology, which was the traditional guardian of philosophical orthodoxy. The conversion of the University of Paris to Cartesianism had important consequences. It encouraged similar changes to the natural philosophical curriculum throughout France and affected the structure and raison d'être of the Académie des Sciences. (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 Quodlibet XV q.13, Henry of Ghent considers whether the Virgin Mary was immaculately conceived. He argues that she was not, but rather possessed sin only at the first instant of her existence. Because Henry’s defense of this position involves an elaborate discussion of motion and mutation, his discussion marks an important contribution to medieval discussions of Aristotelian natural philosophy. In fact, a number of scholars have identified Henry’s discussion as the source of an unusual fourteenth-century theory of change referred (...) to as “quasi-Aristotelianism” . My aim in the paper is two-fold: first, to show that Henry's position is not quasi-Aristotelian in the sense that scholars have supposed; second, to show that, even so, his discussion in q. 13 does involve a novel interpretation of Aristotle’s account of instantaneous change. (shrink)
Can one both be an Aristotelian in ethics and a negativist, whereby the latter involves subscribing to the view that the good cannot be known in our social context but that ethical guidance is nonetheless possible in virtue of a pluralist conception of the bad? Moreover, is it possible to combine Aristotelianism with a thoroughly historical outlook? I have argued that such combinations are, indeed, possible, and that we can find an example of them in Adorno's work. In this (...) paper, I reply to three critics who cast doubt on this proposal. I also reply to other concerns they raise, regarding immanent critique, negativism, the role of social theory in Adorno's work, and the danger of being co-opted. I stress the holism of Adorno's position, and, amid some more deflationary moves, insist on the distinctiveness of the Aristotelian position that results. (shrink)
New Perspectives on Aristotelianism and Its Critics traces Aristotelian influences in modern and pre-modern discourses on knowledge, rights, and the good life. The contributions offer new insights on contemporary discussions on life in its cognitive, political, and ethical dimensions.
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.
This book emphasizes the compatibility of Aristotelianism, Austrian economics, and Ayn Rand's Objectivism, arguing that particular ideas from these areas can be integrated as a potential paradigm of human flourishing and happiness in a free society. It constructs an understanding from various disciplines into a clear, consistent, and systematic whole.
This paper focuses on 3 features of Freyenhagen's Aristotelian version of Adorno. It challenges the strict negativism Freyenhagen finds in Adorno. If we have morally relevant interests in ourselves, it is implicit that we have a standard by which to understand what is both good and bad for us. Because strict negativism operates without reference to what is good, it seems to be detached from real interests too. Torture, it is argued, is, among other things, a violation of those interests. (...) Freyenhagen identifies the “impulse” in Adorno as an untutored yet moral reaction to morally demanding situations. The plausibility of this primitivism and its compatibility with Adorno's general worries about immediacy are considered. The disruptive character of Adorno's version of the categorical imperative, its willingness to complicate action through wholesale reflection on the norms of what we are committing ourselves to, is set in contrast with Freyenhagen's Aristotelian claim that certain notions, such as “humanity,” cannot be intelligibly questioned. (shrink)
The rise in the recent Western pattern of surrogate decision making is not a necessary result of an increase in the number of elderly with decreased competence; it may rather manifest the dominant Western vision of human life and relations. From a comparative philosophical standpoint, the Western pattern of medical decision making is individualistic, while the Chinese is familistic. These two distinct patterns may reflect two different comprehensive perspectives on human life and relations, disclosing a foundational difference that can be (...) seen in the Aristotelian account of friendship and the Confucian account of humanity. The contemporary development of surrogate decision making in the West may illustrate a general tendency toward the Aristotelian account, while the Chinese approaches are congruent with the Confucian view. Also explored are some merits of the Chinese approach to family decision making for health care. (shrink)
Once the reality of properties is admitted, there are two fundamentally different realist theories of properties. Platonist or transcendent realism holds that properties are abstract objects in the classical sense, of being nonmental, nonspatial, and causally inefficacious. By contrast, Aristotelian or moderate realism takes properties to be literally instantiated in things. An apple’s color and shape are as real and physical as the apple itself. The most direct reason for taking an Aristotelian realist view of properties is that we perceive (...) them. We perceive an individual apple, but only as a certain shape, color, and weight, because it is those properties that confer on it the power to affect our senses. It is in virtue of being blue that a body reflects certain light and looks blue. Since “causality is the mark of being,” the properties that confer causal power are real. And that means a reality, not in a Platonic and acausal world of “abstract objects,” but in the ordinary concrete world in which we live. On an Aristotelian view, it is the business of science to determine which properties there are and to classify and understand the properties we perceive, and to find the laws connecting them. (shrink)
Philosophers of mathematics agree that the only interpretation of arithmetic that takes that discourse at 'face value' is one on which the expressions 'N', '0', '1', '+', and 'x' are treated as proper names. I argue that the interpretation on which these expressions are treated as akin to free variables has an equal claim to be the default interpretation of arithmetic. I show that no purely syntactic test can distinguish proper names from free variables, and I observe that any semantic (...) test that can must beg the question. I draw the same conclusion concerning areas of mathematics beyond arithmetic. This paper is a greatly extended version of my response to Stewart Shapiro's paper in the conference 'Structuralism in physics and mathematics' held in Bristol on 2–3 December, 2006. (shrink)
Early modern commentaries on Aristotle’s Metaphysics contain a lively debate on whether experience is ‘rational’, so that it may count as ‘proto-knowledge’, or whether experience is ‘non-rational’, so that experience must be regarded as a primarily perceptual process. If experience is just a repetitive apprehension of sensory contents, the connection of terms in a scientific proposition can be known without any experiential input, as the ‘non-rational’ Scotists state. ‘Rational’ Thomists believe that all principles of scientific knowledge must rely on experiential (...) data, because experience consists in an apprehension of facts rather than objects. And it is only apprehension of facts that can justify knowledge of principles. In this context, the role of mathematical knowledge is special, because it is self-evident. So Thomists must either show that mathematical principles do rely on experience, or that they do not express knowledge claims. (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.
Since the 1980’s, a key issue in political philosophy has been the debate between communitarian philosophers, such as Alasdair MacIntyre, Michael Sandel, Michael Walzer and Charles Taylor, and those who support forms of liberal individualism, such as that found in Rawls’s Theory of Justice. In this debate, reference has quite often been made to Aristotle. This is particularly so in the case of Alasdair MacIntyre, who is frequently seen as presenting a neo-Aristotelian view. Nevertheless, it is not clear whether MacIntyre (...) always presents a plausible interpretation of Aristotle’s arguments. What is most important concerns the historical foundations of the concept of the Aristotelian tradition. If, as I argue in this paper, MacIntyre articulates an unhistorical view of what he calls the ‘Aristotelian tradition’, then his is a forced view of methodology that must fail. However, if this ‘embedded’, historicist methodology fails, then MacIntyre’s argument loses its strength. He would have to support it by using rationalistic methodology, since all his historicist methodology is unhistorical, but this would mean using argumentative resources that he does not have, since he has rejected the possibility that philosophical theory must be based on recognised first principles available to us all. (shrink)
The group of writings entitled De motu constitutes Galileo's earliest writings on dynamics. These manuscripts are usually dated to the years 1589 to 1592, when Galileo taught mathematics at the University of Pisa. Among their characteristics, the application of dynamic principles of Archimedean hydrostatics to the problem of motion stands out, as does their anti-Aristotelian tone. This paper tries to embed these writings within the cultural context in which they were created by documenting their link to the debate over the (...) motion of the elements between Girolamo Borro and Francesco Buonamici, the two most celebrated Pisan Aristotelians of the late sixteenth century. (shrink)
After 25 centuries, Aristotle's influence on our society's moral thinking remains profound and he continues to be a very important contributor to contemporary debates in philosophical ethics. This collection showcases some of the best new writing on the Aristotelian notion of virtue of character, which remains central to much of the most interesting work in ethical theory.