In The Republic, Plato presents the analogy of the divided line in order to unify his ontological, epistemological and cosmological doctrine. It is rarely noted, however, that the divided line has mathematical applications. In this paper, we explore the relationship ofthe divided line to the problem ofderiving Pythagorean triples, that is, sets of three integers that serve as the sides of Pythagorean triangles. We also note the significance of this application within a broader context.

Neste artigo revisa-se a literatura sobre paradoxos matemático-físicos gregos antigos. Trata-se de paradoxo de números irracionais, o dilema de Democritus, a antinomia de mudança, bem como os seguintes paradoxos de Zenon: a dicotomia, o Aquiles, os blocos móveis, o argumento contra a pluralidade, o dilema e a semente de painço.

Dictionary of Paradox is a fascinating reference work for scholars, students, and the general public. It describes those paradoxes that are either especially interesting today or that have a continuing interest from the historical point of view.

Os mais importantes paradoxos de decisáo social, ou seja, de votaçáo sáo apresentados. A apresentaçáo indica tanto a origem dos paradoxos discutidos quanto uma breve discussáo das mais importantes tentativas de os resolver. Sáo considerados paradoxos em que a regra de votaçáo preve ruma igualdade de peso entre os eleitores, bem como paradoxos com regras altemativas de votaçáo. A democracia tem se firmado entre a grande maioria dos povos como a maneira mais justa de organizaçáo social e , especialmente em (...) se tratando da esco lha das autoridades de uma democracia representativa, em quase axiomático 0 uso da regra da igualdade de peso de cada eleitor, embora outras regras tambem sejam usadas em clubes, instituições finançeiras e outros bastante conhecido, porem que tanto o proprio conceito de democracia quanto a referida a regra de escolh sáo isentas de problemas e, em especial, geram certos paradoxos. Assim passa-se em revista aqui alguns dos mais importantesparadoxos eleitorais, sem a pretensáo de resoIve-los", mas com o intuito de ampliar a discussao critica e portanto, fortalecer praticas politicas desejaveis. (shrink)

Resenha do livro de Glenn W. Erickson e John A. Fossa. Panacum de Paradoxos . Natal: EDUFRN, 2006. 191 páginas  .

Investigamos a lógica de Leonhard Euler com ênfase no papel dos “diagramas de Euler”. Concluímos que os referidos diagramas constituem um instrumento intuitivo, embora não sistemático, para determinar validade na silogística tradicional, isto é, a silogística munida de implicações conversacionais. Nisto, contrastam-se com os diagramas de Venn que constituem um instrumento sistemático, porém menos intuitivo, para determinar validade numa silogística mais voltada para os fundamentos da matemática moderna.: We investigate the logic of Leonhard Euler, giving emphasis to the role of (...) “Euler diagrams”. We conclude that these diagrams are an intuitive, non-systematic instrument for determining validity in the traditional syllogistic, that is, the syllogistic furnished with conversational implications. In this regard, they contrast with Venn diagrams which are a systematic, less intuitive instrument for determining validity in a syllogistic more appropriate for the foundation of modern mathematics. Keywords: History of Logic. Leonhard Euler. Euler Diagrams. Venn Diagrams. (shrink)

Resenha do livro de E rickson, Glenn W. e Fossa, John A.. Número e razáo : os fundamentos matemáticos da metafísica platônica. Natal: EDUFRN, 2005. 252 páginas.

Resenha do livro de Erickson, Glenn W.; e Fossa, John A.. A linha dividida : uma abordagem matemática à filosofia platônica . Rio de Janeiro: Relume Dumará, 2006. 186 páginas. [Coleçáo Metafísica, n. 4].

Analysing film. Distinguishing the filmic contribution to meaning -- Examples of filmic "textual organisation" -- Redrawing boundaries -- Organisation of the book -- Semiotics and documents. Semiotics and its relations to film -- The nature of discourse semantics -- The film as cinematographic document -- A combined view: filmic documents for filmic discourse -- Constructing the semiotic mode of film. Semiotic multimodality -- The internal organisation of semiotic strata -- Composing and combining semiotic modes -- Materiality and "epistemological commitment" -- (...) Christian Metz and the grande syntagmatique of the image track. The original model -- Two examples of analysis with the grande syntagmatique -- Revisions and rebuttals -- Foundations for analysis: filmic units. The basic units of film: preliminaries -- Audiovisual iconic representations -- Perception, perceptual realism and reliable measurement -- Multiplicity: from perception to discourse -- Filmic units revisited: discourse-motivated definitions -- The paradigmatic organisation of film. Beyond Metz: towards a grande paradigmatique -- Capturing discourse dependency structures in film -- The paradigmatic dimensions of projection, taxis and plane -- Two examples of paradigmatic analysis -- Summary and conclusions. (shrink)

Closure is the epistemological thesis that if S knows that P and knows that P implies Q, then if S infers that Q, S knows that Q. Fred Dretske acknowledges that closure is plausible but contends that it should be rejected because it conflicts with the plausible thesis: Conclusive reasons (CR): S knows that P only if S believes P on the basis of conclusive reasons, i.e., reasons S wouldn‘t have if it weren‘t the case that P. Dretske develops an (...) analysis of knowing that centers on CR, and argues that the requirement undermines skepticism by implying the falsity of closure. We develop a Dretske-style analysis of knowing that incorporates CR, and we argue that this analysis not only accords with closure, but also implies it. In addition, we argue that the analysis accounts for the prima facie plausibility of closure-invoking skeptical arguments, and nonetheless implies that they are fallacious. If our arguments turn out to be sound, the acceptability of Dretske‘s analysis of knowing will be significantly enhanced by the fact that, despite implying closure, it undermines closure-based skepticism. (shrink)

It is argued that one answer to the question of the rationality of emotion hinges on the different roles in action selection played by emotions when one is aware of them versus when one is not aware of them . When unaware of one’s emotions, they are: not able to enter into one’s deliberations about what to do, and more likely to be automatically acted out. This is a problem for rationality because emotional action urges are often “false positives”. In (...) contrast, awareness of emotions crucially allows emotional responses to be inhibited: such inhibition is necessary for truly rational action selection. Furthermore, awareness enables Reflective Revision—the modification of one’s theories and action plans as a result of awareness of inconsistencies between theories and data, and action plans and goals. (shrink)

This overview of 10 years of stem cell controversy reviews the moral conflict that has made ESCs so controversial and how this conflict plays itself out in the legal realm, focusing on the constitutional status of efforts to ban ESC research or ESC-derived therapies. It provides a history of the federal funding debate from the Carter to the Obama administrations, and the importance of the Raab memo in authorizing federal funding for research with privately derived ESCs despite the Dickey-Wicker ban (...) on federal funding of embryo research. It also reviews the role that scientists themselves have played in developing regulations for ESC research, the emergence of ESCROs as special review bodies for ESC research, and the thorough consent requirements for donation of IVF embryos to ESC research. With research now transitioning from the lab to the clinic, the article reviews the challenges of ensuring safety and consent in translational research. It concludes with a call for respecting those persons who have to using or working with ESC products and an account of how obtaining stem cells from a person's own cells will alleviate some but not all of the controversy surrounding ESC research. (shrink)

Recent research suggests an “Internet paradox”—that a communications technology might reduce social involvement and psychological well–being. In this article I examine some of the limitations of current Internet communication, including those of access, medium, presentation, and choice, that bear on the formation and maintenance of social relationships. I also explore issues central to human meaning in a technological culture—those of the history of the self, of individuality, and of human relationships—and suggest that social forces, technological and otherwise, have increasingly eroded (...) our social interconnectedness and even produced psychological fragmentation. Finally, by considering the psychology of privacy, subjectivity, and intimacy, I look at the historical and developmental processes of internalization by which we construct the “virtual interior” of mind. Understanding this link between human meaning and technological culture, in the form and pattern of our virtual interiors, may help us to see opportunities as well as dangers for the growth of our humanity, our ethics, and our spirituality. (shrink)

An "overview article" that (a) clarifies the nature of theological anti-realism and how that thesis should be formulated, and (b) negatively assesses some of the most common arguments for being a theological anti-realist.

The double membrane of the nuclear envelope is a formidable barrier separating the nucleus and cytoplasm of eukaryotic cells. However, movement of specific macromolecules across the nuclear envelope is critical for embryonic development, cell growth and differentiation. Transfer of molecules between the nucleus and cytoplasm occurs through the aqueous channel formed by the nuclear pore complex (NPC)Abbreviations: NPC, nuclear pore complex; GlcNac, N‐acetylglucosamine; WGA, wheat germ agglutinin. Although small molecules may simply diffuse across the NPC, transport of large proteins and (...) RNA requires specific transport signals and is energy dependent. A family of pore glycoproteins modified by O‐linked N‐acetylglucosamine moieties are essential for transport through the NPC. Recent evidence suggests that the regulation of nuclear transport may also involve the inteaction of RNA and nuclear proteins with specific binding proteins that recognize these transport signals. Are these nuclear pore glycoproteins and signal binding proteins the ‘gatekeepers’ that control access to the genetic material? Recent evidence obtained from a combination of biochemical and genetic approaches suggests – perhaps. (shrink)

The notion of Simulative Reasoning in the study of propositional attitudes within Artificial Intelligence (AI) is strongly related to the Simulation Theory of mental ascription in Philosophy. Roughly speaking, when an AI system engages in Simulative Reasoning about a target agent, it reasons with that agent’s beliefs as temporary hypotheses of its own, thereby coming to conclusions about what the agent might conclude or might have concluded. The contrast is with non-simulative meta-reasoning, where the AI system reasons within a detailed (...) theory about the agent’s (conjectured) reasoning acts. The motive within AI for preferring Simulative Reasoning is that it is more convenient and efficient, because of a simplification of the representations and reasoning processes. The chapter discusses this advantage in detail. It also sketches the use of Simulative Reasoning in an AI natural language processing system, ATT-Meta, that is currently being implemented. This system is directed at the understanding of propositional attitude reports. In ATT-Meta, Simulative Reasoning is yoked to a somewhat independent set of ideas about how attitude reports should be treated. Central here are the claims that (a) speakers often employ commonsense (and largely metaphorical) models of mind in describing agents’ attitudes, (b) the listener accordingly needs often to reason within the terms of such models, rather than on the basis of any objectively justifiable characterization of the mind, and (c) the commonsense models filter the suggestions that Simulative Reasoning comes up with concerning target agents’ reasoning conclusions. There is a yet tighter connection between the commonsense models and the Simulative Reasoning. It turns out that Simulative Reasoning can be rationally reconstructed in terms of a more general type of reasoning about the possibly-counterfactual “world” that the target agent believes in, together with an assumption that that agent has a faithful representation of the world. In the ATT-Meta approach, the reasoner adopts that assumption when it views the target agent through a particular commonsense model (called IDEAS-AS-MODELS). (shrink)

There is growing interest in developing co-operation between adult literacy researchers and practitioners to further research skills and approaches. Canada’s National Literacy Secretariat has recently initiated a series of policy debates that suggested several possibilities: targeted research grants, research internships for practitioners, practical sabbaticals for researchers, support for networking between literacy researchers and practitioners, and joint seminars and workshops between researchers and practitioners. A common theme throughout these discussions is the need to develop critical thinking about both collaborative research and (...) adult literacy. In this paper we discuss two collaborative initiatives between university-based researchers and adult literacy groups in the provinces of British Columbia and Ontario. Each project was based on the notion of “research circles” and specifically designed to enhance research capacity and critical thinking about literacy research. (shrink)

The science of the mind, and of consciousness in particular, needs carefully to consider people's common-sense views of the mind, not just what the mind really is. Such views are themselves an aspect of the nature of (conscious) mind, and therefore part of the object of study for a science of mind. Also, since the common-sense views allow broadly successful social interaction, it is reasonable to look to the common-sense views for some rough guidance as to the real nature of (...) the mind. On the other hand, to the extent that common-sense views are inaccurate, and perhaps even in gross conflict with the true nature of the mind, one interesting scientific question is: why do we hold such views, given our access to our own minds? Why should introspection be limited in a way that allows inaccurate views to hold sway? Now, common-sense views of the mind are revealed in natural language discourse that describes mental states, and such descriptions are largely metaphorical. The metaphors are used within thinking about the mind as well as in language. Therefore the study of metaphor is central to the study of mind. The present article is a preliminary study of the importance of metaphor in the scientific study of consciousness. It concentrates on analysing the nature of a range of important metaphors of mind, briefly discussing the extent to which they can be used to describe or qualify states of consciousness, and pointing to important questions about the nature of consciousness that the study of the metaphors raises. The article further conjectures that the reason people use metaphors in describing themselves is often not (just) that they have intellectually worked out some structural analogy --- e.g., between interactions of physical objects in physical space and interactions of ideas in the mind --- but rather that they {\it feel} their own minds to be as described by the metaphor --- e.g., they feel that the ideas in their minds are interacting physical entities. This matter of how a mind feels to itself is an aspect of the central issue of consciousness, namely its phenomenal quality. -/- (NB: The archived file is a preprint. However, it is substantially the same as the published version.). (shrink)

How neuropsychology is necessary but insufficient for understanding spirituality is explored. Multileveled spiritual requisites are systematically examined in terms of their neuropsychological constituents and limitations. The central “problem of integrity” is articulated via the “modularity” of our neuropsychology, and evidence is presented for disunities of self and consciousness. It is argued that the integrity of self or spirit is a contingent achievement rather than a necessary given. Integrating possibilities include belief, emotion, and relationships. Understanding integrity, and the transformations of self-surrender (...) and sacrifice, may require explicitly stepping beyond neuropsychology and including the self in a larger system. (shrink)

This paper is a commentary on the target article by Lokendra Shastri & Venkat Ajjanagadde [S&A]: “From simple associations to systematic reasoning: A connectionist representation of rules, variables and dynamic bindings using temporal synchrony” in same issue of the journal, pp.417–451. -/- It puts S&A's temporal-synchrony binding method in a broader context, comments on notions of pointing and other ways of associating information - in both computers and connectionist systems - and mentions types of reasoning that are a challenge to (...) S&A's system (amongst many other connectionist systems, recognizing that S&A's is much more capable as regards reasoning than most other contemporary systems). (shrink)

This paper is a commentary on the target article by Dana H. Ballard, “Cortical connections and parallel processing: Structure and function”, in the same issue of the journal, pp. 67–120. -/- I raise some issues about the connectionist or neural-network implementation of information and information processing. Issues include the sharing of information by different parts of a connectionist/neural network, the copying of complex information from one place to another in a network, the possibility of connection weights not being synaptic weights, (...) and the possibility of fast communication within single neurons as complex systems in their own right. (shrink)

The paper is a commentary on the target article by Christine A. Skarda & Walter J. Freeman, “How brains make chaos in order to make sense of the world”, in the same issue of the journal, pp.161–195. -/- I confine my comments largely to some philosophical claims that Skarda & Freeman make and to the relationship of their model to connectionism. Some of the comments hinge on what symbols are and how they might sit in neural systems.

This paper is a commentary on the target article by Michael Arbib, “Levels of modeling of mechanisms of visually guided behavior”, in the same issue of the journal, pp. 407–465. -/- I focus on the importance of the inclusion of an ability of a system to entertain, at a given time, multiple instantiations of a given schema (situation template, frame, script, action plan, etc.), and complications introduced into neural/connectionist network systems by such inclusion.

Jackendoff comes to some appealing overall conclusions, but several of his assumptions and arguments are questionable. The present commentary points out the following problems: oversimplifications in the translation-based argument for the independence of language and thought; a lack of consideration of the possibility of unconscious use of internalized natural languages; insufficient consideration of possible characteristics of languages of thought ; neglect of the possibility of thinking in example-oriented and metaphorical ways; unfair bias in contrasting visual to linguistic imagery; neglect of (...) other types of imagery; and neglect of the possibility of unconscious attentional processes. (shrink)

The seminal ideas of the most influential modern art educator are presented here as he developed them, in edited transcripts of Viktor Lowenfeld's 1958 class lectures and discussions on art education and art therapy. The transcripts serves as explication of Lowenfeld's_ Creative and Mental Growth_, now going into a seventh edition—with posthumous collaborators since the author's death in 1960—translated into all the world's major languages. The experiential basis of Lowenfeld's ideas is revealed through the autobiographical and reflective quality of his (...) lectures and his Socratic dialogs with students. Both his vicarious experience, arising from his erudition, and his immediate experience, stemming from his sensitivity to everyday stimuli, are focused on the problem at hand. The result is a freshness and immediacy as though the author were speaking directly to the reader about mutual concerns. The book presents transcripts of 31 class sessions conducted by Lowenfeld on Art and the Child, Art and the Adolescent, and Art Education Therapy in the year after his election as "Art Educator of the Year" by national Art Education Association. The editor's introduction gives the highlights of Lowenfeld's life and work and the circumstances surrounding the recorded class meetings. The book concludes with a selected bibliography of the works of Viktor Lowenfeld. (shrink)

In lieu of an abstract, here is a brief excerpt of the content:Comment on Hospice of Washington's PolicyJohn A. Robertson (bio)The recent history of medical ethics may accurately be described as a history of coming to terms with personal autonomy and informed consent across the range of medical practice. Nowhere has this recognition been more important than in decisions to withhold or withdraw life-sustaining medical procedures from terminal and chronically ill patients.Despite the widespread acceptance of autonomy in these decisions, many (...) people—physicians, families, and policymakers—have balked at extending it to the withdrawal of artificially supplied fluids and nutrition. The symbolic connotations of food and water have led some persons to perceive cessation of medically-supplied fluids and nutrition to be a cruel, barbarous act, rather than the merciful respect for the dying patient that such withdrawal usually represents.Two recent events might help resolve the controversy, and ensure that decisions about artificial fluid and nutrition are handled like any other medical intervention—according to patient and family choice and patient welfare. One event is the Supreme Court decision in Cruzan (Cruzan v. Director of Missouri Department of Health, 110 S.Ct. 2841, 1990). Although the Supreme Court upheld Missouri's constitutional power to require artificial nutrition for a patient in a persistent vegetative state, its decision was not based on the symbolic importance of artificial fluids and nutrition. No Supreme Court justice saw a significant difference between medically-supplied nutrition and hydration and other medical interventions, thus allowing them to be discontinued either directly or by advance directive on the same basis as other medical interventions.The second event is the publication of the statement of "Philosophy Regarding Medical Intervention to Supply Fluids and Nutrition" by Hospice of Washington (or similar statements by other organizations). This statement is useful and important because it removes the issue of food and water from its symbolic overlay [End Page 139] and places it in the real context of dying hospice patients. It makes clear that the overriding consideration should be benefit to the patient "in accord with the patient's wishes or those of the appropriate surrogate(s) for the patient." Depending on those wishes and their impact on the patient, this position may or may not involve medically-supplied fluids and nutrition.This statement is also helpful in showing the medical complexity of such decisions in terms of their actual effect on dying patients. Rather than an either/or position, it recognizes that fluids may harm a dying patient by increasing discomfort, and that "persons near death do not ordinarily tolerate substantial volumes of enteral feedings." Thus rather than adhere to a symbolically-based position about the meaning of food and water to a dying patient, the important thing is to look to that patient's needs and give fluids or not, as the patient's wishes and situation demand.Fortunately, the law in most jurisdictions will recognize such a position. In those few jurisdictions that have made a fetish of artificial fluids and nutrition, the law should be changed, for the HOW statement makes clear that such a position may actually end up harming dying patients. Patient welfare should be privileged above all else, and patient welfare may often entail that fluids and nutrition not be medically supplied. Even then, however, caregivers will look to patient comfort and remedy dry mouths and lips with lubricants and ice chips.The HOW statement is, in my view, a very useful guideline not only for hospices but for hospitals, too—for any situation in which a patient is terminally ill and soon to die. A somewhat different set of issues arises, however, when the patient is chronically ill and incompetent, and will survive for long periods with medically-supplied fluids and nutrition. Recognition of patient rights in those situation should also permit cessation of fluids and nutrition on the same basis that respirators, antibiotics, and other life-sustaining measures may be withheld. But the withholding of medically-supplied fluids and nutrition from a patient who no longer has interests in surviving in an extremely debilitated condition raises different issues from withholding fluids that could cause such discomfort and nutrition when the patient is imminently dying. In either case, patient... (shrink)