Since the discovery of incommensurability in ancient Greece, arithmeticism and geometricism constantly switched roles. After ninetieth century arithmeticism Frege eventually returned to the view that mathematics is really entirely geometry. Yet Poincaré, Brouwer, Weyl and Bernays are mathematicians opposed to the explication of the continuum purely in terms of the discrete. At the beginning of the twenty-first century ‘continuum theorists’ in France (Longo, Thom and others) believe that the continuum precedes the discrete. In addition the last 50 years witnessed (...) the revival of infinitesimals (Laugwitz and Robinson—non-standard analysis) and—based upon category theory—the rise of smooth infinitesimal analysis and differential geometry. The spatial whole-parts relation is irreducible (Russell) and correlated with the spatial order of simultaneity. The human imaginative capacities are connected to the characterization of points and lines (Euclid) and to the views of Aristotle (the irreducibility of the continuity of a line to its points), which remained in force until the ninetieth century. Although Bolzano once more launched an attempt to arithmetize continuity, it appears as if Weierstrass, Cantor and Dedekind finally succeeded in bringing this ideal to its completion. Their views are assessed by analyzing the contradiction present in Grünbaum’s attempt to explain the continuum as an aggregate of unextended elements (degenerate intervals). Alternatively a line-stretch is characterized as a one-dimensional spatial subject, given at once in its totality (as a whole) and delimited by two points—but it is neither a breadthless length nor the (shortest) distance between two points. The overall aim of this analysis is to account for the uniqueness of discreteness and continuity by highlighting their mutual interconnections exemplified in the nature of a line as a one-dimensional spatial subject, while acknowledging that points are merely spatial objects which are always dependent upon an extended spatial subject. Instead of attempting to reduce continuity to discreteness or discreteness to continuity, a third alternative is explored: accept the irreducibility of number and space and then proceed by analyzing their unbreakable coherence. The argument may be seen as exploring some implications of the view of John Bell, namely that the “continuous is an autonomous notion, not explicable in terms of the discrete.” Bell points out that initially Brouwer, in his dissertation of 1907, “regards continuity and discreteness as complementary notions, neither of which is reducible to each other.”. (shrink)

This is a close scrutiny of "De Anima II 5", led by two questions. First, what can be learned from so long and intricate a discussion about the neglected problem of how to read an Aristotelian chapter? Second, what can the chapter, properly read, teach us about some widely debated issues in Aristotle's theory of perception? I argue that it refutes two claims defended by Martha Nussbaum, Hilary Putnam, and Richard Sorabji: (i) that when Aristotle speaks of the perceiver becoming (...) like the object perceived, the assimilation he has in mind is ordinary alteration of the type exemplified when fire heats the surrounding air, (ii) that this alteration stands to perceptual awareness as matter to form. Claim (i) is wrong because the assimilation that perceiving is is not ordinary alteration. Claim (ii) is wrong because the special type of alteration that perceiving is is not its underlying material realisation. Indeed, there is no mention in the text of any underlying material realisation for perceiving. The positive aim of II 5 is to introduce the distinction between first and second potentiality, each with their own type of actuality. In both cases the actuality is an alteration different from ordinary alteration. Perception exemplifies one of these new types of alteration, another is found in the acquisition of knowledge and in an embryo's first acquisition of the power of perception. The introduction of suitably refined meanings of 'alteration' allows Aristotle to explain perception and learning within the framework of his physics, which by definition is the study of things that change. He adapts his standard notion of alteration, familiar from "Physics" III 1-3 and "De Generatione et Corruptione" I, to the task of accounting for the cognitive accuracy of (proper object) perception and second potentiality knowledge: both are achievements of a natural, inborn receptivity to objective truth. Throughout the paper I pay special attention to issues of text and translation, and to Aristotle's cross-referencing, and I emphasise what the chapter does not say as well as what it does. In particular, the last section argues that the textual absence of any underlying material realisation for perceiving supports a view I have defended elsewhere, that Aristotelian perception involves no material processes, only standing material conditions. This absence is as telling as others noted earlier. Our reading must respect the spirit of the text as Aristotle wrote it. (shrink)

Context: The dominant approach to the study of perception is representational/computational, with an emphasis on the achievements of the brain and the nervous system, which are taken to construct internal models of the world. Alternatives include ecological, embedded, embodied, and enactivist approaches, all of which emphasize the centrality of action in understanding perception. Problem: Despite sharing many theoretical commitments that lead to a rejection of the classical approach, the alternatives are characterized by important contrasts and points of divergence. Here we (...) focus on the enactive and ecological approaches, in particular, on how they construe the status of the environment and the content of perception. Method: We begin with a review of James Gibson’s ecological psychology, highlighting it as a psychology for all organisms not just humans. Against this backdrop, we consider enactivist arguments against direct perception - a central assertion of the ecological approach - and in favor of interpreting the activity of perceptual agents as a kind of construction of a perceptually meaningful world. Results: We assess the merits of this interpretation and we conclude that it cannot be grounded on fundamental principles such as thermodynamics and organism-environment mutuality. Implications: As a consequence, enactivism remains close to representationalism and entails a form of dualism. Constructivist content: We advance a criticism of the constructivist foundations of the enactive approach to perception. Perception-action mutuality at the heart of enactivism does not require mental construction; indeed, perception-action mutuality obviates construction. (shrink)

A continuoxis t- norm is a continuous map * from [0, 1]² into [0,1] such that is a commutative totally ordered monoid. Since the natural ordering on [0,1] is a complete lattice ordering, each continuous t-norm induces naturally a residuation → and becomes a commutative naturally ordered residuated monoid, also called a hoop. The variety of basic hoops is precisely the variety generated by all algebras, where * is a continuous t-norm. In this paper we investigate the structure of the (...) variety of basic hoops and some of its subvarieties. In particular we provide a complete description of the finite subdirectly irreducible basic hoops, and we show that the variety of basic hoops is generated as a quasivariety by its finite algebras. We extend these results to Hájek's BL-algebras, and we give an alternative proof of the fact that the variety of BL-algebras is generated by all algebras arising from continuous t-norms on [ 0,1] and their residua. The last part of the paper is devoted to the investigation of the subreducts of BL- algebras, of Gödel algebras and of product algebras. (shrink)

It is a standing temptation for philosophers to find anticipations of their own views in the great thinkers of the past, but few have been so bold in the search for precursors, and so utterly mistaken, as Berkeley when he claimed Plato and Aristotle as allies to his immaterialist idealism. InSiris: A Chain of Philosophical Reflexions and Inquiries Concerning the Virtues of Tar-Water, which Berkeley published in his old age in 1744, he reviews the leading philosophies of antiquity and finds (...) them on the whole a good deal more sympathetic to his own ideas than the ‘modern atheism’, as he calls it, of Hobbes and Spinoza or the objectionable principles of ‘the mechanic and geometrical philosophers’ such as Newton. But his strongest and, I think, his most interesting claim is that neither Plato nor Aristotle admitted ‘an absolute actual existence of sensible or corporeal things’. (shrink)

This article is detective work, not philosophy. J. S. Mill's Autobiography records that at the age of seven he read, in Greek, ‘the first six dialogues of Plato, from the Euthyphron to the Theaetetus inclusive’. Which were the other dialogues? On the arrangement common today, it would be Crito, Apology, Phaedo, Cratylus. On the arrangement common then, Theages and Erastai replace Cratylus, which makes seven dialogues. I show that this must be the answer by the evidence of James Mill's commonplace (...) books and his writings on Plato. These reveal which collected edition of Plato he owned and which he would want to own. Conditions for studying Plato in the original were much harder than we are used to. The inquiry highlights both the ideological purity of the education James Mill designed for his son, and the difficulties he faced in realizing his plan. (shrink)

The question contrasts two ways of expressing the role of the sense organ in perception. In one the expression referring to the sense organ is put into the dative case ; the other is a construction with the preposition δiá governing the genitive case of the word for the sense organ.

Recent research on the cognitive abilities and emotional capacities of animals has fueled the animal rights movement and renewed debate over the differences between human and non-human animals. This debate has not been central to sociology, although George Herbert Mead drew a very hard line between humans and animals by asserting that the latter were not capable of symbolic interaction. Sociologists are now beginning to question this assumption, and this article falls within this new line of research. We begin by (...) presenting alternative interpretations of symbolic interaction that allow for the possibility of such activity in non-human animals. We review recent research on symbolic interaction between humans and dogs, and we present our own research findings on human-feline interaction. We conclude that there is growing evidence that symbolic interaction is widely distributed throughout the animal kingdom, and that it enables animals to survive more effectively in a wide variety of environments. (shrink)

M. F. Burnyeat taught for 14 years in the Philosophy Department of University College London, then for 18 years in the Classics Faculty at Cambridge, 12 of them as the Laurence Professor of Ancient Philosophy, before migrating to Oxford in 1996 to become a Senior Research Fellow in Philosophy at All Souls College. The studies, articles and reviews collected in these two volumes of Explorations in Ancient and Modern Philosophy were all written, and all but two published, before that decisive (...) change. Whether designed for a scholarly audience or for a wider public, they range from the Presocratics to Augustine, from Descartes and Bishop Berkeley to Wittgenstein and G. E. Moore. Their subject-matter falls under four main headings: 'Logic and Dialectic' and 'Scepticism Ancient and Modern', which are contained in this first volume; 'Knowledge' and 'Philosophy and the Good Life' make up the second volume. The title 'Explorations' well expresses Burnyeat's ability to discover new aspects of familiar texts, new ways of solving old problems. In his hands the history of philosophy becomes itself a philosophical activity. (shrink)

Theoretical and empirical research in bioethics frequently focuses on ethical dilemmas or problems. This paper draws on anthropological and phenomenological sources to develop an alternative framework for bioethical enquiry that allows examination of a broader range of how the moral is experienced in the everyday lives of individuals and groups. Our account of moral experience is subjective and hermeneutic. We define moral experience as “Encompassing a person's sense that values that he or she deem important are being realised or thwarted (...) in everyday life. This includes a person's interpretations of a lived encounter, or a set of lived encounters, that fall on spectrums of right-wrong, good-bad or just-unjust”. In our conceptualisation, moral experience is not limited to situations that are heavily freighted with ethically-troubling ramifications or are sources of debate and disagreement. Important aspects of moral experience are played out in mundane and everyday settings. Moral experience provides a research framework, the scope of which extends beyond the evaluation of ethical dilemmas, processes of moral justification and decision-making, and moral distress. This broad research focus is consistent with views expressed by commentators within and beyond bioethics who have called for deeper and more sustained attention in bioethics scholarship to a wider set of concerns, experiences and issues that better captures what is ethically at stake for individuals and communities. In this paper we present our conceptualisation of moral experience, articulate its epistemological and ontological foundations and discuss opportunities for empirical bioethics research using this framework. (shrink)

This study explores the value of traditional ethnographic methods in sociology for the study of human-animal and animal-animal interactions and culture. Itargues that some measure of human-animal intersubjectivity is possible and that the method of participant observation is best suited to achieve this. Applying ethnographic methods to human-cat and cat-cat relationships in a no-kill cat shelter, the study presents initial findings; it concludes that the social structure of the shelter is the product of interaction both between humans and cats and (...) cats and cats and that the observed structure represents, to a large degree, choices made by the cats. The study also concludes that, within the cat community of the shelter, a distinctive cat culture has emerged, which represents the cats' adaptation to the particular conditions of shelter life. Specifically, the shelter allows for the emergence of higher order needs and goals that stress affection, friendship, and social cohesion among the cats rather than territoriality and conflict. The study further argues that traditional animal researchers have mistaken the relative equality of cat colonies for a lack of social structure, as opposed to a different structure from that found in sharply ranked nonhuman animal communities. (shrink)

"M. F. Simone Roberts's A Poetics of Being-Two is animated by a lively and engaging voice, drawing readers in with a sense of serious purpose working (delightfully) in tandem with a sense of humor. Roberts's aesthetics and her close readings of Yves Bonnefoy, St-John Perse, and Jorie Graham clearly demonstrate the literary effectiveness of Irigarayan sexual difference as an analytic trope, even as they emphasize the philosophical and political possibilities sexual difference opens up for feminism, environmentalism, and all levels of (...) contemporary cultural critique and activism."—Gail M. Schwab, Hofstra University -/- In An Ethics of Sexual Difference, Irigaray calls for a new poetics in the sense of both art and life. Rather than a critique from within philosophy, A Poetics of Being-Two tests Irigaray's ethics by extending it to other sites of cultural production. Where Irigaray's method finds stirrings and repressions of sexual difference in philosophy, this project explores that tension in poetics. Building from Irigaray's ethics, the book describes a poetics of being-two as concerns gendered subjectivity in literary poetics and then traces the on-going emergence of a poetics of being-two in the post-symbolist poetic tradition. Irigaray scholars will be interested in the sustained interpolation of Irigaray's ethical concepts as principles for a critical aesthetics and in their hermeneutic application in reading a literary tradition. Readers in comparative literature will find the first sustained feminist engagements with the major French poets Bonnefoy and Perse and an elucidation of their influence on the Pulitzer Prize winning poet Jorie Graham. (shrink)

This essay argues that the Putnam-Nussbaum thesis that modern functionalism is Aristotelian is false. It fails as an interpretation of Aristotle since it fails to notice that Aristotle’s conception of the material or physical side of the soul-body relation is one which no modern functionalist could share. The Putnam-Nussbaum thesis is examined within the context of the theory of perception. This involves the need to understand one of the most mysterious Aristotelian doctrines – the doctrine that in perception, the sense-organ (...) assumes the sensible form of the object perceived without its matter. (shrink)

There is general acknowledgement that both the anterior cingulate and orbitofrontal cortex are implicated in reinforcement-guided decision making, and emotion and social behaviour. Despite the interest that these areas generate in both the cognitive neuroscience laboratory and the psychiatric clinic, ideas about the distinctive contributions made by each have only recently begun to emerge. This reflects an increasing understanding of the component processes that underlie reinforcement- guided decision making, such as the representation of reinforcement expectations, the exploration, updating and representation (...) of action values, and the appreciation that choices are guided not just by the prospect of reward but also by the costs that action entails. Evidence is emerging to suggest that the anterior cingulate and orbitofrontal cortex make distinct contributions to each of these aspects of decision making. (shrink)