In a recent article, Christopher Ormell argues against the traditional mathematical view that the real numbers form an uncountably inﬁnite set. He rejects the conclusion of Cantor’s diagonal argument for the higher, non-denumerable inﬁnity of the real numbers. He does so on the basis that the classical conception of a real number is mys- terious, ineffable, and epistemically suspect. Instead, he urges that mathematics should admit only ‘well-deﬁned’ real numbers as proper objects of study. In practice, this means excluding as (...) inadmissible all those real numbers whose decimal expansions cannot be calculated in as much detail as one would like by some rule. We argue against Ormell that the classical realist account of the continuum has explanatory power in mathematics and should be accepted, much in the same way that "dark matter" is posited by physicists to explain observations in cosmology. In effect, the indefinable real numbers are like the "dark matter" of real analysis. (shrink)
This is a book review of Karen Armstrong's "The Spiral Staircase", the autobiography of a historian of religion. -/- To cite this article: Newstead, Anne. Compassion, Not Belief [Book Review] [online]. Quadrant, Vol. 49, No. 6, June 2005: 88-89. Availability: <http://search.informit.com.au/documentSummary;dn=203690937218529;res=IELLCC> ISSN: 0033-5002. [cited 06 Dec 12].
The mathematician Georg Cantor strongly believed in the existence of actually infinite numbers and sets. Cantor’s “actualism” went against the Aristotelian tradition in metaphysics and mathematics. Under the pressures to defend his theory, his metaphysics changed from Spinozistic monism to Leibnizian voluntarist dualism. The factor motivating this change was two-fold: the desire to avoid antinomies associated with the notion of a universal collection and the desire to avoid the heresy of necessitarian pantheism. We document the changes in Cantor’s thought with (...) reference to his main philosophical-mathematical treatise, the Grundlagen (1883) as well as with reference to his article, “Über die verschiedenen Standpunkte in bezug auf das aktuelle Unendliche” (“Concerning Various Perspectives on the Actual Infinite”) (1885). (shrink)
This paper is on Aristotle's conception of the continuum. It is argued that although Aristotle did not have the modern conception of real numbers, his account of the continuum does mirror the topology of the real number continuum in modern mathematics especially as seen in the work of Georg Cantor. Some differences are noted, particularly as regards Aristotle's conception of number and the modern conception of real numbers. The issue of whether Aristotle had the notion of open versus closed intervals (...) is discussed. Finally, it is suggested that one reason there is a common structure between Aristotle's account of the continuum and that found in Cantor's definition of the real number continuum is that our intuitions about the continuum have their source in the experience of the real spatiotemporal world. A plea is made to consider Aristotle's abstractionist philosophy of mathematics anew. (shrink)
G. E. M. Anscombe’s view that agents know what they are doing “without observation” has been met with skepticism and the charge of confusion and falsehood. Simultaneously, some commentators think that Anscombe has captured an important truth about the first-personal character of an agent’s awareness of her actions. This paper attempts an explanation and vindication of Anscombe’s view. The key to the vindication lies in focusing on the role of practical knowledge in an agent’s knowledge of her actions. Few commentators, (...) with the exception of Moran (2004) and Hursthouse (2000), have gotten the emphasis right. The key to a proper interpretation of Anscombe’s views is to explain her claims within the context of her teleological theory of action. The result is a theory ofintentional action that makes self-knowledge of one’s own actions the norm. (shrink)
We show how an epistemology informed by cognitive science promises to shed light on an ancient problem in the philosophy of mathematics: the problem of exactness. The problem of exactness arises because geometrical knowledge is thought to concern perfect geometrical forms, whereas the embodiment of such forms in the natural world may be imperfect. There thus arises an apparent mismatch between mathematical concepts and physical reality. We propose that the problem can be solved by emphasizing the ways in which the (...) brain can transform and organize its perceptual intake. It is not necessary for a geometrical form to be perfectly instantiated in order for perception of such a form to be the basis of a geometrical concept. (shrink)
In chapter 7 of The Varieties of Reference, Gareth Evans claimed to have an argument that would present "an antidote" to the Cartesian conception of the self as a purely mental entity. On the basis of considerations drawn from philosophy of language and thought, Evans claimed to be able to show that bodily awareness is a form of self-awareness. The apparent basis for this claim is the datum that sometimes judgements about one’s position based on body sense are immune to (...) errors of misidentification relative to the first-person pronoun 'I'. However, Evans’s argument suffers from a crucial ambiguity. 'I' sometimes refers to the subject's mind, sometimes to the person, and sometimes to the subject's body. Once disambiguated, it turns out that Evans’s argument either begs the question against the Cartesian or fails to be plausible at all. Nonetheless, the argument is important for drawing our attention to the idea that bodily modes of awareness should be taken seriously as possible forms of self-awareness. (shrink)
According to Quine’s indispensability argument, we ought to believe in just those mathematical entities that we quantify over in our best scientific theories. Quine’s criterion of ontological commitment is part of the standard indispensability argument. However, we suggest that a new indispensability argument can be run using Armstrong’s criterion of ontological commitment rather than Quine’s. According to Armstrong’s criterion, ‘to be is to be a truthmaker (or part of one)’. We supplement this criterion with our own brand of metaphysics, 'Aristotelian (...) (...) realism', in order to identify the truthmakers of mathematics. We consider in particular as a case study the indispensability to physics of real analysis (the theory of the real numbers). We conclude that it is possible to run an indispensability argument without Quinean baggage. (shrink)
It is argued that there are ways of individuating the objects of perception without using sortal concepts. The result is an moderate anti-sortalist position on which one can single out objects using demonstrative expressions without knowing exactly what sort of thing those objects are.
This paper reports on an ongoing ARC Discovery Project that is conducting design research into learning in collaborative virtual worlds (CVW).The paper will describe three design components of the project: (a) pedagogical design, (b)technical and graphics design, and (c) learning research design. The perspectives of each design team will be discussed and how the three teams worked together to produce the CVW. The development of productive failure learning activities for the CVW will be discussed and there will be an interactive (...) demonstration of the project's CVW. (shrink)
Coping with everyday life limits the extent of one’s scepticism. It is practically impossible to doubt the existence of the things with which one is immediately engaged and interacting. To doubt that, say, a door exists, is to step back from merely using the door (opening it) and to reflect on it in a detached, theoretical way. It is impossible to simultaneously act and live immersed in situation S while doubting that one is in S. Sceptical doubts—such as ‘Is this (...) really a door?’, ‘Am I really walking?’ — require a reflective withdrawal in thought from the situation at hand. Maintaining sceptical doubt while coping with everyday life requires a split consciousness, a bad faith, with one part of consciousness doubting the existing of things that the other part takes forgranted. For this reason, a sustained lived sceptical doubt is sometimes thought to be impossible. -/- In this article, I examine Wittgenstein's response to scepticism in "On Certainty". I argue that one of his responses is "the response based on action", which is (as other Wittgenstein interpreters have noted) a characteristically pragmatist response. I then evaluate the quality of this pragmatist response to scepticism, noting that actions just as much as representations are susceptible to mis-interpretation. It is argued that despite the insights contained in it, Wittgenstein's contextualism about meaning is inadequate to rescue the Wittgensteinian response to scepticism. (shrink)
G. E. M. Anscombe’s view that agents know what they are doing “without observation” has been met with skepticism and the charge of confusion and falsehood. Simultaneously, some commentators think that Anscombe has captured an important truth about the first-personal character of an agent’s awareness of her actions. This paper attempts an explanation and vindication of Anscombe’s view. The key to the vindication lies in focusing on the role of practical knowledge in an agent’s knowledge of her actions. Few commentators, (...) with the exception of Moran and Hursthouse, have gotten the emphasis right. The key to a proper interpretation of Anscombe’s views is to explain her claims within the context of her teleological theory of action. The result is a theory ofintentional action that makes self-knowledge of one’s own actions the norm. (shrink)
This paper discusses an argument for the reality of the classical mathematical continuum. An inference to the best explanation type of argument is used to defend the idea that real numbers exist even when they cannot be constructively specified as with the "indefinable numbers".
Does Cantorian set theory alter our intuitive conception of number? Yes. In particular, Cantorian set theory revises our intuitive conception of when two sets have the same size (cardinal number). Consider a variant of Galileo’s Paradox, which notes that the members of the set of natural numbers, N, can be put in one-to-one correspondence with the members of the set of even numbers, E.
Does mathematical practice require the existence of actual infinities, or are potential infinities enough? Contrasting points of view are examined in depth, concentrating on Aristotle’s arguments against actual infinities, Cantor’s attempts to refute Aristotle, and concluding with Zermelo’s assertion of the primacy of potential infinity in mathematics.
This thesis proposes that an account of first-person reference and first-person thinking requires an account of practical knowledge. At a minimum, first-person reference requires at least a capacity for knowledge of the intentional act of reference. More typically, first-person reasoning requires deliberation and the ability to draw inferences while entertaining different 'I' thoughts. Other accounts of first-person reference--such as the perceptual account and the rule-based account--are criticized as inadequate. An account of practical knowledge is provided by an interpretation of GEM (...) Anscombe's account in her landmark monograph "Intention". (shrink)
This paper presents the intelligent virtual animals that inhabit Omosa, a virtual learning environment to help secondary school students learn how to conduct scientific inquiry and gain concepts from biology. Omosa supports multiple agents, including animals, plants, and human hunters, which live in groups of varying sizes and in a predator-prey relationship with other agent types (species). In this paper we present our generic agent architecture and the algorithms that drive all animals. We concentrate on two of our animals to (...) present how different parameter values affect their movements and inter/intra-group interactions. Two evaluations studies are included: one to demonstrate the effect of different components of our architecture; another to provide domain expert validation of the animal behavior. (shrink)
Over the past decade, teaching and learning in virtual worlds has been at the forefront of many higher education institutions around the world. The DEHub Virtual Worlds Working Group (VWWG) consisting of Australian and New Zealand higher education academics was formed in 2009. These educators are investigating the role that virtual worlds play in the future of education and actively changing the direction of their own teaching practice and curricula. 47 academics reporting on 28 Australian higher education institutions present an (...) overview of how they have changed directions through the effective use of virtual worlds for diverse teaching and learning activities such as business scenarios and virtual excursions, role-play simulations, experimentation and language development. The case studies offer insights into the ways in which institutions are continuing to change directions in their teaching to meet changing demands for innovative teaching, learning and research in virtual worlds. This paper highlights the ways in which the authors are using virtual worlds to create opportunities for rich, immersive and authentic activities that would be difficult or not possible to achieve through more traditional approaches. (shrink)
Anne Conway rejects the view that creatures are essentially members of any natural kind more specific than the kind 'creature'. That is, she rejects essentialism about species membership. This chapter provides an analysis of one of Anne Conway's arguments against such essentialism, which (as I argue) is drawn from metaethical rather than metaphysical premises. In her view, if a creature's species or kind were inscribed in its essence, that essence would constitute a limit on the creature's potential to (...) participate in the divine good. It is this consideration that ultimately leads her to reject essentialism about species membership. The chapter concludes with an examination of some of the metaethical consequences of Conway's view as well as a lesson it can teach us about ideal adviser accounts of the good. (shrink)
In chapter IX of the Principles, Anne Conway claims that her metaphysics is diametrically opposed to those of Descartes and Spinoza. Scholars have analyzed her rejection of Cartesianism, but not her critique of Spinoza. This paper proposes that two central points of Conway’s metaphysics can be understood as direct responses to Spinoza: (1) the relation between God, Christ, and the creatures in the tripartite division of being, and (2) the individuation of beings in the lowest species. I will argue (...) that Conway, in criticizing Spinoza’s identification between God and nature, defends a paradoxical monism, and that her concept of individuation is a reductio ad absurdum of Spinoza’s criterion of identity in the individuation of finite modes. (shrink)
In her book, Moral Status, Mary Anne Warren defends a comprehensive theory of the moral status of various entities. Under this theory, she argues that animals may have some moral rights but that their rights are much weaker in strength than the rights of humans, who have rights in the fullest, strongest sense. Subsequently, Warren believes that our duties to animals are far weaker than our duties to other humans. This weakness is especially evident from the fact that Warren (...) believes that it is frequently permissible for humans to kill animals for food. Warren’s argument for her view consists primarily in the belief that we have inevitable practical conflicts with animals that make it impossible to grant them equal rights without sacrificing basic human interests. However, her arguments fail to justify her conclusions. In particular, Warren fails to justify her beliefs that animals do not have an equal right to life and that it is permissible for humans to kill animals for food. (shrink)
A scholarly edition of letters by Anne, Viscountess Conway, Henry More, and their friends. The edition presents an authoritative text, together with an introduction, commentary notes, and scholarly apparatus.
This essay provides some historical background for, and considers the philosophical importance of, the collection of Anne Berkeley’s letters to Adam Gordon. The primary philosophical significance of the letters is her arguments against the so-called “free thinkers.” She discusses the philosophical view and the behavior of five prominent free-thinkers: Shaftesbury, Bolingbroke, Voltaire, Rousseau, and Hume. Her discussion of Shaftesbury is particularly illuminating and can be read as a commentary on Alciphron III.13-14. Because the work of the other four were (...) published mainly after the Bishop’s death, the letters also show Anne ’s independent lifelong interest in matters theological, philosophical, and moral. (shrink)
American Indian Thought is a contemporary collection of twenty-two essays written by Indigenous persons with Western philosophical training, all attempting to formulate, and/or contribute to a sub-discipline of, a Native American Philosophy. The contributors come from diverse tribal, educational, philosophical, methodological, etc., backgrounds, and there is some tension among aspects of the collection, but what is more striking is the harmony and the singularity of the collection’s intent. Part of this singularity may derive from the solidarity among its authors. In (...) addition to the fact that all belong to Indigenous tribes, there is also a striking sensitivity to the interconnection between distinct Western disciplines—particularly between philosophy and poetry. I take the latter to be a thread which can be strategically woven into the center of the anthology’s weave. In this book discussion, I aim to draw out the poetic aspects of five of the anthology’s essays, which deal with philosophy, metaphysics, epistemology, ethics and aesthetics, respectively. In this way, I hope to illuminate a poetic quality at the heart of the collection, and thus also of the burgeoning field of Native American or Indigenous philosophy in general. In the process, I will also consider ways in which Indigenous philosophy resonates with the Western philosophical traditions of phenomenology and American pragmatism. With the latter tradition in particular this connection has become more fully appreciated, especially through the work of Bruce Wilshire and Scott Pratt. (shrink)
ABSTRACTWhat follows is an interview with William Damon and Anne Colby, pioneers in the fields of moral psychology and education. Throughout their careers, they have studied, moral identity, moral ideals, positive youth development, purpose, good work, vocation, character development in higher education, and professional responsibility. In their words, they are interested in the ‘best of humankind’—not only the competencies, but also the character necessary for living a good life—not only for the sake of the individual, but also for society. (...) They have received numerous academic and civic awards and honors. Their publications include Some Do Care, Greater Expectations, Educating Citizens, The Path to Purpose, and most recently, The Power of Ideals—in addition to editing, for example, New Directions for Child and Adolescent Development and The Handbook of Child Psychology. As a married couple, their vocational journeys have mostly been separate, but have always complemented each other and sometimes converged. This interview asks about reflections on their careers, their own sense of purpose, their greatest contributions, current needs in our field, and advice to emerging scholars. (shrink)
ABSTRACTMany scholars have drawn attention to the way that elements of Anne Conway’s system anticipate ideas found in Leibniz. This paper explores the relationship between Conway and Leibniz’s work with regard to time, space, and process. It argues – against existing scholarship – that Conway is not a proto-Leibnizian relationist about time or space, and in fact her views lie much closer to those of Henry More; yet Conway and Leibniz agree on the primacy of process. This exploration advances (...) our understanding of Conway’s system, and the intellectual relationships between Conway, More, and Leibniz. (shrink)
In the contemporary debate on moral status, it is not uncommon to find philosophers who embrace the the Principle of Full Moral Status, according to which the degree to which an entity E possesses moral status is proportional to the degree to which E possesses morally relevant properties until a threshold degree of morally relevant properties possession is reached, whereupon the degree to which E possesses morally relevant properties may continue to increase, but the degree to which E possesses moral (...) status remains the same. One philosopher who has contributed significantly to the contemporary debate on moral status and embraces the Principle of Full Moral Status is Mary Anne Warren. Warren holds not only that it is possible for some entities to possess full moral status, but that some entities actually do, e.g., normal adult human beings. I argue that two of Warren’s primary arguments for the Principle of Full Moral Status—the Argument from Pragmatism and the Argument from Explanatory Power—are significantly flawed. (shrink)
So begins "For Anne Gregory," published by W. B. Yeats in 1933. It is surely one of his most charming poems.1 The poem's lilting rhythm and affectionate tone effectively soften—even disguise—what is arguably a dark and dismaying message. Anne is destined to be loved not for herself alone, but for an accidental physical attribute—her blond hair. Why do I claim that the poem's message is dark? Why should it dismay Anne if she is loved for the beauty (...) of her hair? Is that not better, after all, than not being loved in the first place? And what would it be to love Anne for herself "alone"? Love Anne for her sweet disposition; for her ability always to say the right thing; for her kindness; but for her yellow hair? .. (shrink)
As for Avicenna the human soul is a complete substance which does not inhere in the body nor is imprinted in it, asserting its survival after the death of the body seems easy. Yet, he needs the body to explain its individuation. The paper analyzes Avicenna's arguments in the De anima sections, V, 3 & 4, of the Shifā ' in order to explore the exact causal relation there is between the human soul and its body and confronts these arguments (...) with relevant passages in the Metaphysics. It argues that the causal relation between body and soul remains obscure and that, though Avicenna claims that there is a personal immortality and that the disembodied soul remains individuated, he does not provide a satisfactory ontological account for it. (shrink)
This 2004 book was the first intellectual biography of one of the very first English women philosophers. At a time when very few women received more than basic education, Lady Anne Conway wrote an original treatise of philosophy, her Principles of the Most Ancient and Modern Philosophy, which challenged the major philosophers of her day - Descartes, Hobbes and Spinoza. Sarah Hutton's study places Anne Conway in her historical and philosophical context, by reconstructing her social and intellectual milieu. (...) She traces her intellectual development in relation to friends and associates such as Henry More, Sir John Finch, F. M. van Helmont, Robert Boyle and George Keith. And she documents Conway's debt to Cambridge Platonism and her interest in religion - an interest which extended beyond Christian orthodoxy to Quakerism, Judaism and Islam. Her book offers an insight into both the personal life of a very private woman, and the richness of seventeenth-century intellectual culture. (shrink)
Anne Conway argues that all substances are spiritual. Yet, she also claims that all created substance has some type of body. Peter Loptson has argued that Conway didn’t carefully consider her view that all created beings have bodies for it seems God could have created only disembodied spirits. There are several reasons to think Loptson is right. First, Conway holds that God is all‐good and will do the best for his creation. She also holds that spirit is better than (...) body. So, how is it that creatures always have bodies? Second, although she maintains that incorporation is punishment for sin, Conway holds that some creatures can fall without acquiring visible corporality. I argue that when we examine these views more closely, we will see that not only did Conway give them careful consideration, but that there is no inconsistency. Finally, I show that Conway’s views concerning the nature and function of body provides further evidence of her carefully crafted system. Conway holds that bodies play an important role in a finite beings’ ability to change and interact with others. Even more surprising is Conway’s view that the body is the repository of thoughts, memories, and knowledge. (shrink)
This paper considers the conception of the Triune God, soteriology and eschatology in Anne Conway’s metaphysics. After outlining some of the key features of her thought, including her account of a timeless God who is nevertheless intimately present in creation, I will argue that her conception of the Trinity offers a distinctive role for Christ and the Holy Spirit to play in her philosophical system. I also propose an interpretation of Conway’s eschatology, in which time is understood as grounded (...) in a never-ending soteriological process of the overall movement of creatures towards perfection and a state of spirituality. (shrink)
This paper comes out of a panel honoring the work of Anne Donchin (1940-2014), which took place at the 2016 Congress of the International Network on Feminist Approaches to Bioethics (FAB) in Edinburgh. My general aim is to highlight the contributions Anne made to feminist bioethics, and to feminist reproductive ethics in particular. My more specific aim, however, is to have a kind of conversation with Anne, through her work, about whether reproductive justice could demand insurance coverage (...) for in vitro fertilization. I quote liberally from Anne’s work for this purpose, but also to shower the reader with her words, reminding those of us who knew her well what a wonderful colleague she was. (shrink)
The main aim of the present paper is to use a proof system for hybrid modal logic to formalize what are called false-belief tasks in cognitive psychology, thereby investigating the interplay between cognition and logical reasoning about belief. We consider two different versions of the Smarties task, involving respectively a shift of perspective to another person and to another time. Our formalizations disclose that despite this difference, the two versions of the Smarties task have exactly the same underlying logical structure. (...) We also consider the Sally-Anne task, having a more complicated logical structure, presupposing a “principle of inertia” saying that a belief is preserved over time, unless there is belief to the contrary. (shrink)
The work of Spinoza, Descartes and Leibniz is cited in an attempt to develop, both expositorily and critically, the philosophy of Anne Viscountess Conway. Broadly, it is contended that Conway's metaphysics, epistemology and account of the passions not only bear intriguing comparison with the work of the other well-known rationalists, but supersede them in some ways, particularly insofar as the notions of substance and ontological hierarchy are concerned. Citing the commentary of Loptson and Carolyn Merchant, and alluding to other (...) commentary on the Cambridge Platonists whose work was done in tandem with Conway's, it is contended that Conway's conception of the "monad" preceded and influenced Leibniz's, and that her monistic vitalism was in many respects a superior metaphysics to the Cartesian system. It is concluded that we owe Conway more attention and celebration than she has thus far received. (shrink)
La filosofía de Anne Finch, Viscondesa de Conway ha sido estudiada desde la perspectiva del papel crítico de su monismo vitalista frente a la filosofía de sus contemporáneos, así como en la valoración de su papel en la historia de la filosofía. No obstante, la atención que han recibido sus tesis epistemológicas ha sido escasa en razón del carácter fragmentario de sus Principios de la más antigua y moderna filosofía. El presente artículo parte de la idea de que es (...) posible sistematizar la filosofía de esta autora moderna, lo cual, implica la reconstrucción de sus tesis epistemológicas a través de los conceptos de percepción sensible e imaginación. Lo anterior, nos permitirá no sólo comprender estas tesis bajo la lógica de su correlación con la ontología y la filosofía moral de Conway, también permite acceder a una propuesta original alterna a los modelos mecanicistas imperantes en la época. (shrink)
This article is an expansion of comments I was honored to present at a celebration of the life and work of Anne Donchin at the June 2016 meeting of the International Network on Feminist Approaches to Bioethics in Edinburgh. It is obviously far from comprehensive, but I hope it gives readers a glimpse of an Anne of whose depths many of us were not fully aware. One of the most difficult parts of talking about someone who has died (...) is highlighting the positive without overdoing it to the extent that their friends and loved ones find themselves rolling their mental eyes a bit, since most of us—no matter how wonderful—are a little less than perfect. But my problem here is that the more I have found out... (shrink)
Consider the significance of Anne Frank's horse chestnut tree. During her years of hiding in the secret annex, Anne thought of the tree as a symbol of freedom, happiness, and peace. As a stand-in for all of Nature, Anne saw the tree as that part of the universe that could not be destroyed by human evil. In this essay, I use Anne's tree as a starting point for a discussion of the domination of both nature and (...) humanity. I connect the concept of domination to the policy of ecological restoration, to national and historical narratives of the connection to forest landscapes, and to the environmental policies of the Third Reich, the specific evil entity that confronted Anne Frank. Domination is also intertwined with the idea of the “paradox of progress,” viz., that human progress cannot be separated from acts and policies of domination. (shrink)