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)

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)

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)

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.

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)

This paper supersedes an ealier version, entitled "A Non-Standard Semantics for Inexact Knowledge with Introspection", which appeared in the Proceedings of "Rationality and Knowledge". The definition of token semantics, in particular, has been modified, both for the single- and the multi-agent case.

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)

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".

This work has been selected by scholars as being culturally important, and is part of the knowledge base of civilization as we know it. This work was reproduced from the original artifact, and remains as true to the original work as possible. Therefore, you will see the original copyright references, library stamps (as most of these works have been housed in our most important libraries around the world), and other notations in the work. This work is in the public domain (...) in the United States of America, and possibly other nations. Within the United States, you may freely copy and distribute this work, as no entity (individual or corporate) has a copyright on the body of the work. As a reproduction of a historical artifact, this work may contain missing or blurred pages, poor pictures, errant marks, etc. Scholars believe, and we concur, that this work is important enough to be preserved, reproduced, and made generally available to the public. We appreciate your support of the preservation process, and thank you for being an important part of keeping this knowledge alive and relevant. (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)

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)

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.

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)

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)

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)

Les travaux du Comité public de suivi Le comité a été créé le 12 avril 2016. À cette occasion, il a annoncé le dépôt d’un rapport de suivi à l’occasion du premier anniversaire du dépôt du rapport de la Commission Charbonneau. Dans les derniers mois, le comité s’est penché sur les initiatives répondant aux recommandations de la Commission, en étudiant les informations rendues publiques sur ce sujet. Aidé d’une équipe...

Michael A. PetersBeijing Normal UniversityMy deepest condolences to Pepe, Dom and Marcus and to Jim’s grandchildren. Tina and I spent a lot of time at the Marshall family home, often attending dinn...

Bundle theory takes objects to be bundles of properties. Some bundle theorists take objects to be bundles of instantiated universals, and some take objects to be bundles of tropes. Tropes are instances of properties: some take instantiated universals to be tropes, while others deny the existence of universals and take tropes to be ontologically fundamental. Historically, the bundling relation has been taken to be a primitive relation, not analyzable in terms of or ontologically reducible to some other relation, and has (...) been variously characterized as, e.g., “compresence,” “concurrence,” or “consubstantiation.” Bertrand Russell (1940) defends compresence of universals, and Hector-Neri Castañeda (1974) defends consubstantiation of universals. John Bacon (1995) defends concurrent tropes and Keith Campbell (1990) defends compresent tropes. Jonathan Schaffer (2001) bucks this trend, endorsing compresence understood as co-location in spacetime, but this brings with it undesireable consequences such as the impossibility of distinguishing between objects (such as electrons or other microentities) with the same location. Mereological bundle theory improves upon traditional bundle theory by taking the primitive relation of bundling to be the more familiar relation of fusing or composing, such that objects are fusions of properties or fusions of property instances. Hence, mereological bundle theorists endorse a property mereology: a mereology where properties or property instances can be parts of objects. An advantage of the approach derives from the fact that standard mereologies take composition to be primitive or define it using a different primitive mereological notion (such as primitive parthood). Thus, taking the basic primitive of bundle theory to be composition can reduce the need for.. (shrink)

In an effort to deny the ongoing effect of colonialism and imperialism on contemporary political life, the death knell for a multicultural society has been sounded from all sides. That's the provocative argument Paul Gilroy makes in this unorthodox defense of the multiculture. Gilroy's searing analyses of race, politics, and culture have always remained attentive to the material conditions of black people and the ways in which blacks have defaced the "clean edifice of white supremacy." In _Postcolonial Melancholia_, he (...) continues the conversation he began in the landmark study of race and nation _'There Ain't No Black in the Union Jack'_ by once again departing from conventional wisdom to examine--and defend--multiculturalism within the context of the post-9/11 "politics of security." This book adapts the concept of melancholia from its Freudian origins and applies it not to individual grief but to the social pathology of neoimperialist politics. The melancholic reactions that have obstructed the process of working through the legacy of colonialism are implicated not only in hostility and violence directed at blacks, immigrants, and aliens but in an inability to value the ordinary, unruly multiculture that has evolved organically and unnoticed in urban centers. Drawing on the seminal discussions of race begun by Frantz Fanon, W. E. B. DuBois, and George Orwell, Gilroy crafts a nuanced argument with far-reaching implications. Ultimately, _Postcolonial Melancholia_ goes beyond the idea of mere tolerance to propose that it is possible to celebrate the multiculture and live with otherness without becoming anxious, fearful, or violent. (shrink)

In an effort to deny the ongoing effect of colonialism and imperialism on contemporary political life, the death knell for a multicultural society has been sounded from all sides. That's the provocative argument Paul Gilroy makes in this unorthodox defense of the multiculture. Gilroy's searing analyses of race, politics, and culture have always remained attentive to the material conditions of black people and the ways in which blacks have defaced the "clean edifice of white supremacy." In _Postcolonial Melancholia_, he (...) continues the conversation he began in the landmark study of race and nation _'There Ain't No Black in the Union Jack'_ by once again departing from conventional wisdom to examine -- and defend -- multiculturalism within the context of the post-9/11 "politics of security." This book adapts the concept of melancholia from its Freudian origins and applies it not to individual grief but to the social pathology of neoimperialist politics. The melancholic reactions that have obstructed the process of working through the legacy of colonialism are implicated not only in hostility and violence directed at blacks, immigrants, and aliens but in an inability to value the ordinary, unruly multiculture that has evolved organically and unnoticed in urban centers. Drawing on the seminal discussions of race begun by Frantz Fanon, W. E. B. DuBois, and George Orwell, Gilroy crafts a nuanced argument with far-reaching implications. Ultimately, _Postcolonial Melancholia_ goes beyond the idea of mere tolerance to propose that it is possible to celebrate the multiculture and live with otherness without becoming anxious, fearful, or violent. (shrink)

In _ Plato's Camera_, eminent philosopher Paul Churchland offers a novel account of how the brain constructs a representation -- or "takes a picture" -- of the universe's timeless categorical and dynamical structure. This construction process, which begins at birth, yields the enduring background conceptual framework with which we will interpret our sensory experience for the rest of our lives. But, as even Plato knew, to make singular perceptual judgments requires that we possess an antecedent framework of abstract categories (...) to which any perceived particular can be relevantly assimilated. How that background framework is assembled in the first place is the motivating mystery, and the primary target, of Churchland's book. Unexpectedly, this neurobiologically grounded account of human cognition also provides a systematic story of how such low-level epistemological activities are integrated within an enveloping framework of linguistic structures and regulatory mechanisms at the social level. As Churchland illustrates, this integration of cognitive mechanisms at several levels has launched the human race on an epistemological adventure denied to all other terrestrial creatures. (shrink)

Paul Boghossian defends a meaning‐based approach to the apriority of the propositions of logic. His model is based on the idea that the logical constants are implicitly defined by some of the axioms and inference rules in which they are involved, thereby offering an alternative to those theories that deny that grasp of meaning can contribute to the explanation of a thinker's entitlement to a particular type of transition or belief.

In _ Plato's Camera_, eminent philosopher Paul Churchland offers a novel account of how the brain constructs a representation -- or "takes a picture" -- of the universe's timeless categorical and dynamical structure. This construction process, which begins at birth, yields the enduring background conceptual framework with which we will interpret our sensory experience for the rest of our lives. But, as even Plato knew, to make singular perceptual judgments requires that we possess an antecedent framework of abstract categories (...) to which any perceived particular can be relevantly assimilated. How that background framework is assembled in the first place is the motivating mystery, and the primary target, of Churchland's book. Unexpectedly, this neurobiologically grounded account of human cognition also provides a systematic story of how such low-level epistemological activities are integrated within an enveloping framework of linguistic structures and regulatory mechanisms at the social level. As Churchland illustrates, this integration of cognitive mechanisms at several levels has launched the human race on an epistemological adventure denied to all other terrestrial creatures. (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.

In this doctoral dissertation I consider, and reject, the claim that recent varieties of non-reductive physicalism, particularly Donald Davidson's anomalous monism, are committed to a new kind of epiphenomenalism. Non-reductive physicalists identify each mental event with a physical event, and are thus entitled to the belief that mental events are causes, since the physical events with which they are held to be identical are causes. However, Jaegwon Kim, Ernest Sosa and others have argued that if we follow the non-reductive physicalist (...) in denying that mental features can be reduced to physical properties, then we must regard mental properties as being causally irrelevant to their bearers' effects, In short, the non-reductive physicalist is said to be committed to the belief that while there are mental causes, they do not cause their effects in virtue of being the types of mental state that they are. It is in this sense that non-reductive physicalists are thought to represent a new form of epiphenomenalism. After a brief survey of the history of epiphenomenalism, and its mutation into the contemporary strain that is believed to afflict non-reductive physicalism, 1 argue against the counterfactual criterion of the sort of causal relevance that we take mental features to enjoy. I then criticize the 'trope' response to the epiphenomenalist threat, and conclude that much of the current debate on this topic is premised on the mistaken belief that there is some variety of causal relevance that is not simply a brand of explanatory relevance. Once this is seen, it will seem much less plausible that mental properties are excluded from relevance to the phenomena of which we typically take them to be explanatory. (shrink)

L’auteur revisite certains textes de Paul Ricœur publiés entre 1960 et 1992, afin d’exposer le rapport de cette philosophie avec la théologie chrétienne. Il interroge le statut de la théologie spéculative, dévolu par cette pensée, qui accorde un certain privilège à la théologie herméneutique et à la théologie politique.

Paul Boghossian has pointed out a ’circularity problem’ for dispositionalist theories of meaning: as a result of the holistic character of belief fixation, one cannot identify someone’s meaning such and such with facts of the form S is disposed to utter P under conditions C, without C involving the semantic and intentional notions that such a theory was to explain. Alex Miller has recently suggested an ’ultra‐sophisticated dispositionalism’ (modelled on David Lewis’s well known version of functionlism) and has argued (...) that this version of dispositionalism escapes Boghossian’s ’circularity problem’. Miller argues, nonetheless, that another of Boghossian’s criticisms of dispositionalism, ’the infinity problem’ still applies to this ’ultra‐sophisticated dispositionalism’: C will still draw upon a potential infinity of mediating background clusters of belief. The present paper argues that the feature that ’the infinity problem’ presents as problematic is a feature of a host of familiar explanations. Our fundamental difficulty in this area is not our inability to understand how a more general model can be applied to a particular domain (the intentional understood as dispositional) but our failure to understand that general model itself (dispositional explanation). (shrink)