This paper will introduce the notion of a naming convention and use this paradigm to both develop a new version of the Second Incompleteness Theorem and to describe when an axiom system can partially evade the Second Incompleteness Theorem.

Let us recall that Raphael Robinson's Arithmetic Q is an axiom system that differs from Peano Arithmetic essentially by containing no Induction axioms [13], [18]. We will generalize the semantic-tableaux version of the Second Incompleteness Theorem almost to the level of System Q. We will prove that there exists a single rather long Π 1 sentence, valid in the standard model of the Natural Numbers and denoted as V, such that if α is any finite consistent extension of Q + (...) V then α will be unable to prove its Semantic Tableaux consistency. The same result will also apply to axiom systems α with infinite cardinality when these infinite-sized axiom systems satisfy a minor additional constraint, called the Conventional Encoding Property. Our formalism will also imply that the semantic-tableaux version of the Second Incompleteness Theorem generalizes for the axiom system IΣ 0 , as well as for all its natural extensions. (This answers an open question raised twenty years ago by Paris and Wilkie [15].). (shrink)

In 1981, Paris and Wilkie raised the open question about whether and to what extent the axiom system did satisfy the Second Incompleteness Theorem under Semantic Tableaux deduction. Our prior work showed that the semantic tableaux version of the Second Incompleteness Theorem did generalize for the most common definition of appearing in the standard textbooks.However, there was an alternate interesting definition of this axiom system in the Wilkie–Paris article in the Annals of Pure and Applied Logic 35 , pp. 261–302 (...) which we did not examine in our year-2002 article in the Journal of Symbolic Logic. Our first goal is to show that the incompleteness results of our prior paper can generalize in this alternate context. We will also develop a formal analysis, using a new technique called Passive Induction, that is simpler than the formalism we had used before.A further reason our results are of interest is that we have shown in a companion paper published in Electronic Notes in Theoretical Computer Science 165 , pp. 213–226 that some very unorthodox axiomizations for are anti-thresholds for the Herbrandized version of the Second Incompleteness Theorem. Thus, different axiomizations for have nearly fully opposite incompleteness properties.This paper is self-contained. It will not require a knowledge of our earlier results. (shrink)

On the unorthodox ways in which people relate to each other.

The dominant language of politics in the United States has been political individualism, with minimal restrictions on property and personal, voluntary conduct. But there are second languages of community that stress cooperation and group action. These second languages include the constitutional tradition for public health. Public health offers a community justification for paternalistic measures that, for example, discourage smoking or require seatbelts.

This article will study a class of deduction systems that allow for a limited use of the modus ponens method of deduction. We will show that it is possible to devise axiom systems α that can recognize their consistency under a deduction system D provided that: (1) α treats multiplication as a 3-way relation (rather than as a total function), and that (2) D does not allow for the use of a modus ponens methodology above essentially the levels of Π1 (...) and Σ1 formulae. Part of what will make this boundary-case exception to the Second Incompleteness Theorem interesting is that we will also characterize generalizations of the Second Incompleteness Theorem that take force when we only slightly weaken the assumptions of our boundary-case exceptions in any of several further directions. (shrink)

Gödel’s Second Incompleteness Theorem states axiom systems of sufficient strength are unable to verify their own consistency. We will show that axiomatizations for a computer’s floating point arithmetic can recognize their cut-free consistency in a stronger respect than is feasible under integer arithmetics. This paper will include both new generalizations of the Second Incompleteness Theorem and techniques for evading it.

Perceptual judgments result from a dynamic process, but little is known about the dynamics of number‐line estimation. A recent study proposed a computational model that combined a model of trial‐to‐trial changes with a model for the internal scaling of discrete numbers. Here, we tested a surprising prediction of the model—a situation in which children's estimates of numerosity would be better than those of adults. Consistent with the model simulations, task contexts led to a clear developmental reversal: children made more adult‐like, (...) linear estimates when to‐be‐estimated numbers were descending over trials (i.e., backward condition), whereas adults became more like children with logarithmic estimates when numbers were ascending (i.e., forward condition). In addition, adults’ estimates were subject to inter‐trial differences regardless of stimulus order. In contrast, children were not able to use the trial‐to‐trial dynamics unless stimuli varied systematically, indicating the limited cognitive capacity for dynamic updates. Together, the model adequately predicts both developmental and trial‐to‐trial changes in number‐line tasks. (shrink)

With increasing momentum for health care reform, attention is shifting to finance reform that will provide for direct methods for controlling health care spending. This article outlines the two principal paths to direct cost control and outlines a national plan that retains our multiple sources of payment, yet also contains a powerful direct cost control technique: a single fund to finance all health care.

Book reviewed in this article: Seeking Fair Treatment: From the AIDS Epidemic to National Health Care Reform. By Norman Daniels.

This book is the most comprehensive treatment available of one of the most urgent - and yet in some respects most neglected - problems in bioethics: decision-making for incompetents. Part I develops a general theory for making treatment and care decisions for patients who are not competent to decide for themselves. It provides an in-depth analysis of competence, articulates and defends a coherent set of principles to specify suitable surrogate decisionmakers and to guide their choices, examines the value of advance (...) directives, and investigates the role that considerations of cost ought to play in decisions concerning incompetents. Part II applies this theoretical framework to the distinctive problems of three important classes of individuals, many of whom are incompetent: minors, the elderly and psychiatric patients. The authors' approach combines a probing analysis of fundamental issues in ethical theory with a sensitive awareness of the concrete realities of health care institutions and the highly personal and individual character of difficult practical problems. Its broad scope will appeal to health professionals, moral philosophers and lawyers alike. (shrink)

Belongingness is a central biopsychosocial system. Challenges to belongingness (i.e. exclusion/ostracism) engender robust negative effects on affect and cognitions. Whether overinclusion – getting more than one’s fair share of social attention – favourably impacts affect and cognitions remains an open question. This pre-registered meta-analysis includes twenty-two studies (N = 2757) examining overinclusion in the context of the Cyberball task. We found that the estimated overall effect size of overinclusion on positive affect was small but robust, and the effect on fundamental (...) needs cognitions (belongingness, self-esteem, meaningful existence and control) was moderate in size and positive in direction. Notably, the effect sizes of overinclusion were smaller than the corresponding effects of exclusion. Finally, the effects of overinclusion on positive affect were greater for high, as compared to low, socially anxious individuals. Exploring the sequelae of the full range of inclusion experiences – from exclusion to overinclusion – may enrich our understanding of the functioning of the belongingness system as well as its interaction with another central biosocial system – the social status system. (shrink)

Overestimation of one’s ability to argue their position on socio-political issues may partially underlie the current climate of political extremism in the U.S. Yet very little is known about what factors influence overestimation in argumentation of socio-political issues. Across three experiments, emotional investment substantially increased participants’ overestimation. Potential confounding factors like topic complexity and familiarity were ruled out as alternative explanations. Belief-based cues were established as a mechanism underlying the relationship between emotional investment and overestimation in a measurement-of-mediation and manipulation-of-mediator (...) design. Representing a new bias blind spot, participants believed emotional investment helps them argue better than it helps others ; where in reality emotional investment harmed or had no effect on argument quality. These studies highlight misguided beliefs about emotional investment as a factor underlying metacognitive miscalibration in the context of socio-political issues. (shrink)

What kind of futures does agro-food imaginaries enable and who can get involved in the making of agro-food futures? In this respect, what can the increasingly influential idea of circular economy potentially offer in terms of enabling more sustainable agrofood futures? We approach this task by first outlining the interconnected challenges that the agro-food system is facing related to environmental degradation, economic crises and social problems. Then we consider the way these challenges are being addressed in agro-food studies. We argue (...) that agro-food research in recent years has seen important contributions in relation to studies of alternative food networks and the “quality” turn. These research agendas have challenged the current logic of the food system in terms of offering alternative visions of future development. We highlight two examples from the literature—the eco-economy and the integrated territorial agri-food paradigm—that develop broader frameworks for rethinking the future of the agro-food system and which have distinguished themselves in contrast to the industrialized and globalized conventional food system. We find that with respect to reorienting and reconfiguring economic structures and relations all three approaches share a common goal, but circular economy stands out in relation to the actors that are included by, for example, emphasizing collaborations and partnerships with extant agro-food businesses. Also with regards to scalar politics, it would be prudent to consider the potentials offered by the increasingly influential ideas around circular economy. (shrink)

In this essay I ask the reader to consider the “end of life” as a life stage, rather than as a health state. At one end of the life course is childhood and at the other end is elderhood. The basic inter-generational social compact in most societies is that working adults take care of their children and their parents, and count on their children to do the same for them. In developed countries, these obligations are met in part through government (...) programs, with taxpayers funding significant portions of education, health care, and income support. (shrink)

We are drowning in information, while starving for wisdom.Are the smartest people also the wisest? Not necessarily. While traditional intellectual reasoning and procedural knowledge have helped build the communities we live in, there is a growing scientific understanding that we need emotionally balanced and better-fitting prosocial frameworks for coping with the uncertainties and complexities of life and addressing new challenges of the modern world. We are now poised on the edge of a new science of wisdom.The concept of wisdom, long (...) considered the “pinnacle of insight into the human condition”, has been that of an intangible, subjective, culturally specific entity—an unscientific... (shrink)

We report on the deliberations of an interdisciplinary group of experts in science, law, and philosophy who convened to discuss novel ethical and policy challenges in stem cell research. In this report we discuss the ethical and policy implications of safety concerns in the transition from basic laboratory research to clinical applications of cell-based therapies derived from stem cells. Although many features of this transition from lab to clinic are common to other therapies, three aspects of stem cell biology pose (...) unique challenges. First, tension regarding the use of human embryos may complicate the scientific development of safe and effective cell lines. Second, because human stem cells were not developed in the laboratory until 1998, few safety questions relating to human applications have been addressed in animal research. Third, preclinical and clinical testing of biologic agents, particularly those as inherently complex as mammalian cells, present formidable challenges, such as the need to develop suitable standardized assays and the difficulty of selecting appropriate patient populations for early phase trials. We recommend that scientists, policy makers, and the public discuss these issues responsibly, and further, that a national advisory committee to oversee human trials of cell therapies be established. **NB we did not reccommend a NAC, we think it might be appropriate**. (shrink)

Whereas 20 or 30 years ago one might have been inclined to characterize the development of 20th century philosophy in terms of a linguistic turn, a turn from a philosophy of subjectivity to a philosophy of language, it might today be more apt to describe the development in terms of a turn from anti-naturalism to naturalism. But insofar as naturalists consider the scientific account of reality authoritative, a commitment to naturalism is bound to put pressure on the idea that philosophy (...) can make a distinct and autonomous contribution to the study of reality. In the following, I will discuss the question of how phenomenology ought to respond to this challenge. What sense can we make of recent proposals to naturalize phenomenology? (shrink)

In The Second Sex, Simone de Beauvoir revealed that it is just this freedom of withdrawal from self that woman cannot gain because of the constant effort of establishing and guarding her identity against an enforced background of passivity, ornamentality and self-enclosure. Even as a small child, woman is taught how to.

Quel type de releve pour la metaphysique l'ethique envisagee comme - philosophie premiere - propose-t-elle? La phenomenologie peut-elle ressaisir le fondement de tout phenomene, obeir a une demarche encore transcendantale tout en destituant l'ego de sa principialite sans cesse reconduite depuis Descartes? La requalification des categories theologiques imposee par la distance de l'autrement qu'etre peut-elle laisser inchange le nom meme de Dieu auquel elle nous ordonne comme a notre definitive tache? Ces questions, Levinas aura contribue a les formaliser et a (...) en imposer l'urgence avec une radicalite a nulle autre pareille. Cet ouvrage se propose d'en eclairer quelques unes a partir d'analyses genetiques de sa pensee, de confrontations avec quelques hautes figures de la tradition philosophique (Husserl et Heidegger, mais aussi Descartes, Spinoza, Derrida, etc.) et de la reactivation de quaestiones disputatae lourdes d'enjeux. Car l'ethique dispense une lumiere propre, sans laquelle nombre de questions nous resteraient durablement insoupconnees; cette lumiere elle-meme doit etre decomposee et se preter a analyse. Lumiere jetee par l'ethique, lumiere jetee sur l'ethique: telle est, en son double genitif, la lucidite de l'ethique.". (shrink)

Soeurs ennemies ou soeurs jumelles, servante et maîtresse ou compagnes de labeur, s'ignorant l'une l'autre ou unies au point de presque s'identifier, la foi et la raison entretiennent à l'évidence une relation intense et tumultueuse. N'est-ce pas justement au coeur du mouvement qui tantôt les rapproche tantôt les oppose que s'ajuste leur rapport? Plus que d'un état stable acquis une fois pour toutes il s'agit bien d'une dynamique, d'un processus. C'est cc que visent à montrer les essais réunis dans cc (...) livre, qui rassemble les fruits d'un colloque de théologie et de philosophie tenu à l'initiative du Studium de Philosophie de Chartres et de l'Institut de Théologie des Dombes, centres de formation de la Communauté du Chemin Neuf. (shrink)

It is always risky to make sweeping statements about the development of philosophy, but if one were nevertheless asked to describe 20th century philosophy in broad strokes, one noteworthy feature might be the following: Whereas important figures at the beginning of the century, figures such as Frege and Husserl, were very explicit in their rejection of naturalism (both are known for their rejection of the attempt to naturalize the laws of logic, i.e., for their criticism of psychologism), the situation has (...) changed considerably. Today many philosophers – not the least within analytical philosophy – would subscribe to some form of naturalism. In fact, naturalism is seen by many as the default metaphysical position. If you don’t subscribe to naturalism you must be subscribing to some form of Cartesian substance dualism. Thus, whereas 20 or 30 years ago one might have been inclined to characterize the development of 20th century philosophy in terms of a linguistic turn, a turn from a philosophy of subjectivity to a philosophy of language, it might today be more apt to describe the development in terms of a turn from anti-naturalism to naturalism. (shrink)

Durkheim écrit ce livre avec un but double : d'abord il voulait expliquer ce qui crée une société, ce qui la tient ensemble ; ensuite il voulait éclaircir l'influence qu'a la société sur la pensée logique. Pour Durkheim, la religion est la clé utilisée pour déverrouiller ces deux problématiques.Dans ce livre, Durkheim argumente que les représentations religieuses sont en fait des représentations collectives : l'essence du religieux ne peut être que le sacré. Il est une caractéristique qui se trouve universellement (...) dans toutes les religions. Le sacré, être collectif et impersonnel, représente ainsi la société elle-même. Ensuite il argumente que la société a un impact majeur dans la genèse de la pensée logique. C'est la société qui fournit à l'individu les catégories (le temps, l'espace, le nombre etc.) et les concepts nécessaires pour la pensée logique. (shrink)

There is good evidence that the cerebral cortex is the seat of the human mind, so an understanding of representation in the cortex could help us understand the nature of mental representation. I argue that the cortex represents in the way that models do; it is an evolutionarily designed model-building machine. The cortex belongs to a general class of model-building machines that produce isomorphisms to structures in the environment by interacting with them. The representational content of a particular model produced (...) by such a machine is determined by the operational principles according to which the machine was designed, and the history of machine-environment interaction that resulted in the production of that model. ;I explore the possibility that the operational principles according to which the cerebral cortex was designed, i.e. aspects of its causal profile that were selected for, are those described by the SINBAD theory. The SINBAD theory implies that it is the biological function of the cortex to make its constituent neurons come to interact in a way that is isomorphic to regularities structured around "sources of correlation". In the context of this isomorphism, it is the function of a particular SINBAD cell to correspond to a particular source of correlation, the one that is responsible for that cell's tuning. In other words, the cortex builds models of environmental regularities structured around sources of correlation. ;Understanding mental representation as cortical representation of this kind allows us to explain a number of important and/or puzzling features of mental intentionality as we know it: the possibility of equivocation, misrepresentation, empty representation, and twin cases, the relation between concepts and inferential roles, how it is possible for us to acquire objective concepts and beliefs via our subjective and idiosyncratic senses, and the distinction between usefulness and truth. I conclude by outlining an account of the occurrent propositional attitudes as non-representational uses of a SINBAD model that has been built up through experience. Non-representational use is cashed out in terms of causal role. Together with an account of the non-occurrent attitudes, this yields an understanding of the nature of psychological explanation. (shrink)