Formal systems are standardly envisaged in terms of a grammar specifying well-formed formulae together with a set of axioms and rules. Derivations are ordered lists of formulae each of which is either an axiom or is generated from earlier items on the list by means of the rules of the system; the theorems of a formal system are simply those formulae for which there are derivations. Here we outline a set of alternative and explicitly visual ways of envisaging and analyzing (...) at least simple formal systems using fractal patterns of infinite depth. Progressively deeper dimensions of such a fractal can be used to map increasingly complex wffs or increasingly complex 'value spaces', with tautologies, contradictions, and various forms of contingency coded in terms of color. This and related approaches, it turns out, offer not only visually immediate and geometrically intriguing representations of formal systems as a whole but also promising formal links (1) between standard systems and classical patterns in fractal geometry, (2) between quite different kinds of value spaces in classical and infinite-valued logics, and (3) between cellular automata and logic. It is hoped that pattern analysis of this kind may open possibilities for a geometrical approach to further questions within logic and metalogic. (shrink)

Zeno's paradoxes of motion and the semantic paradoxes of the Liar have long been thought to have metaphorical affinities. There are, in fact, isomorphisms between variations of Zeno's paradoxes and variations of the Liar paradox in infinite-valued logic. Representing these paradoxes in dynamical systems theory reveals fractal images and provides other geometric ways of visualizing and conceptualizing the paradoxes.

The goal of philosophy of information is to understand what information is, how it operates, and how to put it to work. But unlike ‘information’ in the technical sense of information theory, what we are interested in is meaningful information. To understand the nature and dynamics of information in this sense we have to understand meaning. What we offer here are simple computational models that show emergence of meaning and information transfer in randomized arrays of neural nets. These we take (...) to be formal instantiations of a tradition of theories of meaning as use. What they offer, we propose, is a glimpse into the origin and dynamics of at least simple forms of meaning and information transfer as properties inherent in behavioral coordination across a community. (shrink)

Much innovation has taken place in the development of medical schools and licensure exam processes across the African continent. Still, little attention has been paid to education that enables the multidisciplinary, critical thinking needed to understand and help shape the larger social systems in which health care is delivered. Although more than half of medical schools in Canada, the United Kingdom, and the United States offer at least one medical humanities course, this is less common in Africa. We report on (...) the “liberal arts approach” to medical curricula undertaken by the University of Global Health Equity beginning in 2019. The first six-month semester of the curriculum, called Foundations in Social Medicine, includes courses in critical thinking and communication, African history and global political economy, medical anthropology and social medicine, psychology and health, gender and social justice, information technology and health, and community-based training. Additionally, an inquiry-based pedagogy with relatively small classes is featured within an overall institutional culture that emphasizes health equity. We identify key competencies for physicians interested in pursuing global health equity and how such competencies relate to liberal arts integration into the African medical school curriculum and pedagogical approach. We conclude with a call for a research agenda that can better evaluate the impact of such innovations on physicians’ education and subsequent practices. (shrink)

This book is an introduction, entirely by example, to the possibilities of using computer models as tools in phosophical research in general and in philosophical logic in particular. Topics include chaos, fractals, and the semantics of paradox; epistemic dynamics; fractal images of formal systems; the evolution of generosity; real-valued game theory; and computation and undecidability in the spatialized Prisoner's Dilemma.

Editorial Board: Karl P. Ameriks, Margaret Atherton, Frederick Beiser, Fabien Capeillères, Faustino Fabbianelli, Daniel Garber, Rudolf A. Makkreel, Steven Nadler, Alan Nelson, Christof Rapp, Ursula Renz, Wilhelm Schmidt-Biggemann, Denis Thouard, Paul Ziche, Günter Zöller The series publishes monographs and essay collections devoted to the history of philosophy as well as studies in the theory of writing the history of philosophy. A special emphasis is placed on the contextualization of philosophical historiography into the areas of the history of science, (...) culture, and the wider scope of intellectual history. (shrink)

We work with a large spatialized array of individuals in an environment of drifting food sources and predators. The behavior of each individual is generated by its simple neural net; individuals are capable of making one of two sounds and are capable of responding to sounds from their immediate neighbors by opening their mouths or hiding. An individual whose mouth is open in the presence of food is “fed” and gains points; an individual who fails to hide when a predator (...) is present is “hurt” by losing points. Opening mouths, hiding, and making sounds each exact an energy cost. There is no direct evolutionary gain for acts of cooperation or “successful communication” per se. In such an environment we start with a spatialized array of neural nets with randomized weights. Using standard learning algorithms, our individuals “train up” on the behavior of successful neighbors at regular intervals. Given that simple setup, will a community of neural nets evolve a simple language for signaling the presence of food and predators? With important qualifications, the answer is “yes.” In a simple spatial environment, pursuing individualistic gains and using partial training on successful neighbors, randomized neural nets can learn to communicate. (shrink)

‘Pupil voice’ is a movement within state education in England that is associated with democracy, change, participation and the raising of educational standards. While receiving much attention from educators and policy makers, less attention has been paid to the theory behind the concept of pupil voice. An obvious point of theoretical departure is the work of Jürgen Habermas, who over a number of decades has endeavoured to develop a theory of democracy that places strong significance on language, communication and discourse. (...) This paper is an attempt to gauge the usefulness of Habermas’ approach to understanding the theory of pupil voice, in particular how his theory of universal pragmatics lends itself to a ‘philosophy of between’, a philosophy that finds echoes in the conflicted nature of schooling that ‘pupil voice’ is supposed to rectify to some extent. The paper also explores the drawbacks of a Habermasian approach, in particular his overreliance on rationality as a way of understanding communication. Lacan’s concept of the objet petit a is introduced as an alternative way of understanding pupil voice. (shrink)

In this paper we compare different models of vagueness viewed as a specific form of subjective uncertainty in situations of imperfect discrimination. Our focus is on the logic of the operator “clearly” and on the problem of higher-order vagueness. We first examine the consequences of the notion of intransitivity of indiscriminability for higher-order vagueness, and compare several accounts of vagueness as inexact or imprecise knowledge, namely Williamson’s margin for error semantics, Halpern’s two-dimensional semantics, and the system we call Centered semantics. (...) We then propose a semantics of degrees of clarity, inspired from the signal detection theory model, and outline a view of higher-order vagueness in which the notions of subjective clarity and unclarity are handled asymmetrically at higher orders, namely such that the clarity of clarity is compatible with the unclarity of unclarity. (shrink)

Three‐ to 4‐month‐old infants show asymmetric exclusivity in the acquisition of cat and dog perceptual categories. The cat perceptual category excludes dog exemplars, but the dog perceptual category does not exclude cat exemplars. We describe a connectionist autoencoder model of perceptual categorization that shows the same asymmetries as infants. The model predicts the presence of asymmetric retroactive interference when infants acquire cat and dog categories sequentially. A subsequent experiment conducted with 3‐ to 4‐month‐olds verifies the predicted pattern of looking time (...) behaviors. We argue that bottom‐up, associative learning systems with distributed representations are appropriate for modeling the operation of short‐term visual memory in early perceptual category learning. (shrink)

For [Formula: see text], the coarse similarity class of A, denoted by [Formula: see text], is the set of all [Formula: see text] such that the symmetric difference of A and B has asymptotic density 0. There is a natural metric [Formula: see text] on the space [Formula: see text] of coarse similarity classes defined by letting [Formula: see text] be the upper density of the symmetric difference of A and B. We study the metric space of coarse similarity classes (...) under this metric, and show in particular that between any two distinct points in this space there are continuum many geodesic paths. We also study subspaces of the form [Formula: see text] where [Formula: see text] is closed under Turing equivalence, and show that there is a tight connection between topological properties of such a space and computability-theoretic properties of [Formula: see text]. We then define a distance between Turing degrees based on Hausdorff distance in the metric space [Formula: see text]. We adapt a proof of Monin to show that the Hausdorff distances between Turing degrees that occur are exactly 0, [Formula: see text], and 1, and study which of these values occur most frequently in the senses of Lebesgue measure and Baire category. We define a degree a to be attractive if the class of all degrees at distance [Formula: see text] from a has measure 1, and dispersive otherwise. In particular, we study the distribution of attractive and dispersive degrees. We also study some properties of the metric space of Turing degrees under this Hausdorff distance, in particular the question of which countable metric spaces are isometrically embeddable in it, giving a graph-theoretic sufficient condition for embeddability. Motivated by a couple of issues arising in the above work, we also study the computability-theoretic and reverse-mathematical aspects of a Ramsey-theoretic theorem due to Mycielski, which in particular implies that there is a perfect set whose elements are mutually 1-random, as well as a perfect set whose elements are mutually 1-generic. Finally, we study the completeness of [Formula: see text] from the perspectives of computability theory and reverse mathematics. (shrink)

Standard Kripke models are inadequate to model situations of inexact knowledge with introspection, since positive and negative introspection force the relation of epistemic indiscernibility to be transitive and euclidean. Correlatively, Williamson’s margin for error semantics for inexact knowledge invalidates axioms 4 and 5. We present a new semantics for modal logic which is shown to be complete for K45, without constraining the accessibility relation to be transitive or euclidean. The semantics corresponds to a system of modular knowledge, in which iterated (...) modalities and simple modalities are not on a par. We show how the semantics helps to solve Williamson’s luminosity paradox, and argue that it corresponds to an integrated model of perceptual and introspective knowledge that is psychologically more plausible than the one defended by Williamson. We formulate a generalized version of the semantics, called token semantics, in which modalities are iteration-sensitive up to degree n and insensitive beyond n. The multi-agent version of the semantics yields a resource-sensitive logic with implications for the representation of common knowledge in situations of bounded rationality. (shrink)

Axiomatic and problematic approaches to ontology are discussed, at first in relation to the work of Badiou and Deleuze in mathematics. This discussion is then broadened focussing on problematics in Deleuze and Guattari’s critiques of capitalism and psychoanalysis which results in an analysis of the implications of this discussion for education. From this, education as being already there, which is an assumption in some strands of philosophy of education, following Deleuze’s critique of axiomatic presentations of ontological identities, is described as (...) a repressive, stabilizing operation, which produces objectives which are characterized as peculiar things. By contrast, those aspects of practice, knowledge, behaviours and populations which cannot be accommodated and resolved by axiomatic formulae and fall from axiomatic systems are characterized as queer things that constitute counter cultures. (shrink)

Forthcoming in S. Artemov and R. Parikh, Proceedings of the ESSLLI 2006 Workshop on Rationality and Knowledge.

Version of March 05, 2007. An extended abstract of the paper appeared in the Proceedings of the 2006 Prague Colloquium on "Reasoning about Vagueness and Uncertainty".

Human adults appear different from other animals in their ability to form abstract mental representations that go beyond perceptual similarity. In short, they can conceptualize the world. This book brings together leading psychologists and neuroscientists to tackle the age-old puzzle of what might be unique about human concepts.

Physics tells us that the world that we live in is “really” composed of vast numbers of tiny particles, defined and individuated by their mass, charge, velocity and position. That is all there is, the rest being empty space. In contrast the world that we interact with in our every day lives is composed of rooms with windows, people and cats, and plates filled with milk and cornflakes. It is a world of individual objects and stuffs, most of which can (...) be effortlessly identified and labelled as being of a particular kind. Like an illustration in a child’s reader, we could look around our environment and attach labels to all of the objects and kinds of things around us. (shrink)

For many years, biology was largely descriptive (natural history), but with its emergence as a scientific discipline in its own right, a reductionist approach began, which has failed to be matched by adequate understanding of function of cells, organisms and species as whole entities. Every effort was made to explain biological phenomena in physico-chemical terms.It is argued that there is and always has been a clear distinction between life sciences and physical sciences, explicit in the use of the word biology. (...) If this distinction is real, it implies that biological phenomena can never be entirely satisfactorily explained in terms of extant physicochemical laws. One notable manifestation of this is that living organisms appear to -- actually do -- behave in purposeful ways, and the inanimate universe does not. While this fundamental difference continues to be suppressed, the purposiveness (or teleology) which pervades biology remains anathema to almost all scientists (including most biologists) even to the present day. We argue here that it can, however, become a perfectly tenable position when the Theory of Natural Selection is accepted as the main foundation, the essential tenet, of biology that distinguishes it from the realm of physical sciences. In accepting this position, it remains quite legitimate to expect that in many but not all circumstances, extant physical laws (and presumably others still to be discovered) are in no way breached by biological systems, which cannot be otherwise since all organisms are composed of physical material. (shrink)

Diffusion theory explains in physical terms how materials move through a medium, e.g. water or a biological fluid. There are strong and widely acknowledged grounds for doubting the applicability of this theory in biology, although it continues to be accepted almost uncritically and taught as a basis of both biology and medicine. Our principal aim is to explore how this situation arose and has been allowed to continue seemingly unchallenged for more than 150 years. The main shortcomings of diffusion theory (...) will be briefly reviewed to show that the entrenchment of this theory in the corpus of biological knowledge needs to be explained, especially as there are equally valid historical grounds for presuming that bulk fluid movement powered by the energy of cell metabolism plays a prominent note in the transport of molecules in the living body. First, the theory's evolution, notably from its origins in connection with the mechanistic materialist philosophy of mid nineteenth century physiology, is discussed. Following this, the entrenchment of the theory in twentieth century biology is analyzed in relation to three situations: the mechanism of oxygen transport between air and mammalian tissues; the structure and function of cell membranes; and the nature of the intermediary metabolism, with its implicit presumptions about the intracellular organization and the movement of molecules within it. In our final section, we consider several historically based alternatives to diffusion theory, all of which have their precursors in nineteenth and twentieth century philosophy of science. (shrink)

Whilst previous observational studies have linked negative thought processes such as an external locus of control and holding negative cognitive styles with depression, the directionality of these associations and the potential role that these factors play in the transition to adulthood and parenthood has not yet been investigated. This study examined the association between locus of control and negative cognitive styles in adolescence and probable depression in young adulthood and whether parenthood moderated these associations. Using a UK prospective population-based birth (...) cohort study: the Avon Longitudinal Study of Parents and Children, we examined the association between external locus of control and negative cognitive styles in adolescence with odds of depression in 4,301 young adults using logistic regression models unadjusted and adjusted for potential confounding factors. Interaction terms were employed to examine whether parenthood moderated these associations. Over 20% of young adults in our sample were at or above the clinical threshold indicating probable depression. For each standard deviation increase in external locus of control in adolescence, there was a 19% higher odds of having probable depression in young adulthood, after adjusting for various confounding factors including baseline mood and different demographic and life events variables. Similarly, for each SD increase in negative cognitive styles in adolescence, there was a 29% higher odds of having probable depression in the adjusted model. We found little evidence that parenthood status moderated the relationship between external locus of control or negative cognitive styles in adolescence and probable depression following adjustment for confounding factors. Effect estimates were comparable when performed in the complete case dataset. These findings suggest that having an external locus of control and holding negative cognitive styles in mid- to late adolescence is associated with an increased likelihood of probable depression in young adulthood. (shrink)

Disjunctivists maintain that perceptual experiences and hallucinatory experiences are distinct kinds of event with different metaphysical natures. Moreover, given their view about the nature of perceptual cases, disjunctivists must deny that the perceptual kind of experience can occur during hallucination. However, it is widely held that disjunctivists must grant the converse claim, to the effect that the hallucinatory kind of experience occurs even during perception. This paper challenges that thought. As we will see, the argument for thinking that the hallucinatory (...) kind of experience is present even in cases of perception depends on prior acceptance of a ‘non-demanding’ conception of hallucination, on which all it takes to produce an hallucinatory experience is to induce in the subject the right kind of neurological condition. On the view developed here, by contrast, there are substantive causal conditions, going beyond the mere occurrence of the right kind of neurological state, that must be met if an experience of the hallucinatory kind is to occur. By drawing on this view, I argue, disjunctivists can deny that the kind of experience involved in hallucination ever occurs during perception. This then allows disjunctivists to avoid certain important problems they would otherwise face. It also leaves them with considerably more freedom when it comes to theorising about the nature of hallucinatory experience. (shrink)

Denis, Lara. Moral Self-Regard: Duties to Oneself in Kant's Moral Theory. New York: Garland Publishing. 2001. Engstrom, Stephen. “The Concept ofthe Highest Good in Kant's Moral The- ory.” Philosophy and Phenomenological Research 52, ...

Standard responses to the knowledge argument grant that Mary could know all of the physical facts even while trapped inside her black‐and‐white room. What they deny is that upon leaving her black‐and‐white room and experiencing red for the first time, Mary learns a genuinely new fact. This paper develops an alternate response in a grounding physicalist framework, on which Mary does not know all of the physical facts while trapped inside the room. The main thesis is that Mary does not (...) know certain phenomenal facts while trapped inside the room, whereby these facts classify as physical due to being wholly and fully metaphysically grounded in the underlying fundamental facts which are themselves entirely physical. (shrink)

Evolution - both the fact that it occurred and the theory describing the mechanisms by which it occurred - is an intrinsic and central component in modern biology. Theodosius Dobzhansky captures this well in the much-quoted title of his 1973 paper 'Nothing in biology makes sense except in the light of evolution'. The correctness of this assertion is even more obvious today: philosophers of biology and biologists agree that the fact of evolution is undeniable and that the theory of evolution (...) explains that fact. Such a theory has far-reaching implications. In this volume, eleven distinguished scholars address the conceptual, metaphysical and epistemological richness of the theory and its ethical and religious impact, exploring topics including DNA barcoding, three grand challenges of human evolution, functionalism, historicity, design, evolution and development, and religion and secular humanism. The volume will be of great interest to those studying philosophy of biology and evolutionary biology. (shrink)

Throughout his career, Husserl identifies naturalism as the greatest threat to both the sciences and philosophy. In this paper, I explicate Husserl’s overall diagnosis and critique of naturalism and then examine the specific transcendental aspect of his critique. Husserl agreed with the Neo-Kantians in rejecting naturalism. He has three major critiques of naturalism: First, it (like psychologism and for the same reasons) is ‘countersensical’ in that it denies the very ideal laws that it needs for its own justification. Second, naturalism (...) essentially misconstrues consciousness by treating it as a part of the world. Third, naturalism is the inevitable consequence of a certain rigidification of the ‘natural attitude’ into what Husserl calls the ‘naturalistic attitude’. This naturalistic attitude ‘reifies’ and it ‘absolutizes’ the world such that it is treated as taken-for-granted and ‘obvious’. Husserl’s transcendental phenomenological analysis, however, discloses that the natural attitude is, despite its omnipresence in everyday life, not primary, but in fact is relative to the ‘absolute’ transcendental attitude. The mature Husserl’s critique of naturalism is therefore based on his acceptance of the absolute priority of the transcendental attitude . The paradox remains that we must start from and, in a sense, return to the natural attitude, while, at the same time, restricting this attitude through the on-going transcendental vigilance of the universal epoché. (shrink)

The phenomenology of Edmund Husserl had a permanent and profound impact on the philosophical formation of Paul Ricoeur. One could truly say, paraphrasing Maurice Merleau-Ponty’s brilliant 1959 essay ‘The Philosopher and his Shadow’,that Husserl is the philosopher in whose shadow Ricoeur, like Merleau-Ponty, also stands, the thinker to whom he constantly returns. Husserl is Ricoeur’s philosopher of reflection, par excellence. Indeed, Ricoeur always invokes Husserl when he is discussing a paradigmatic instance of contemporary philosophy of ‘reflection’ and also of (...) descriptive, ‘eidetic’ phenomenology. Indeed, I shall argue in this chapter that Husserl’s influence on Ricoeur was decisive and provided an eidetic, descriptive methodology which is permanently in play, even when it has to be concretized and mediated by hermeneutics, as Ricoeur proposes after 1960. (shrink)

(2013). Heidegger, Wittgenstein and St Paul on the Last Judgement: On the Roots and Significance of ‘The Theoretical Attitude’. British Journal for the History of Philosophy: Vol. 21, No. 1, pp. 143-164. doi: 10.1080/09608788.2012.686980.

Early in the course of undertaking empirical research on the sexual diversity of the judiciary I had to address a particular challenge. Sexuality, I was repeatedly told, is not and ought not to be a difference that is taken into account. At best it ought to be disregarded or taken out of consideration. This generated a number of challenges for my research. How do you research and make sense of sexuality as a difference that key informants assert is absent or (...) seek to make invisible and irrelevant? How do you research the operation and effects of that which is not to be spoken about? How do you research the sexual norm when its existence and operation is denied? This article explores one response. It is a project that may for some be surprising and unexpected. It is a study of judicial portraits. Drawing on the insights of queer theory and art historical scholarship on portraits I undertake a textual analysis of these images, focusing upon the aesthetic and artistic traditions used to make them. A small case study of portraits of the Chief Justices of the Supreme Court of New South Wales is used to explore how, if at all, sexuality figured in these portraits. (shrink)