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)

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.

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.

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)

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.

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)

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

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.

We will study several weak axiom systems that use the Subtraction and Division primitives (rather than Addition and Multiplication) to formally encode the theorems of Arithmetic. Provided such axiom systems do not recognize Multiplication as a total function, we will show that it is feasible for them to verify their Semantic Tableaux, Herbrand, and Cut-Free consistencies. If our axiom systems additionally do not recognize Addition as a total function, they will be capable of recognizing the consistency of their Hilbert-style deductive (...) proofs. Our axiom systems will not be strong enough to recognize their Canonical Reflection principle, but they will be capable of recognizing an approximation of it, called the "Tangibility Reflection Principle". We will also prove some new versions of the Second Incompleteness Theorem stating essentially that it is not possible to extend our exceptions to the Incompleteness Theorem much further. (shrink)

--The energy of the new world, By E. E. Slosson.--The new energies and the new man, by W. D. Scott.--The future of our economic system, by F S. Deibler.--Business in the new era, by W. B. Hotchkiss.--Consumers in the modern world, by Stuart Chase.

In a range of contexts, individuals arrive at collective decisions by sharing confidence in their judgements. This tendency to evaluate the reliability of information by the confidence with which it is expressed has been termed the ‘confidence heuristic’. We tested two ways of implementing the confidence heuristic in the context of a collective perceptual decision-making task: either directly, by opting for the judgement made with higher confidence, or indirectly, by opting for the faster judgement, exploiting an inverse correlation between confidence (...) and reaction time. We found that the success of these heuristics depends on how similar individuals are in terms of the reliability of their judgements and, more importantly, that for dissimilar individuals such heuristics are dramatically inferior to interaction. Interaction allows individuals to alleviate, but not fully resolve, differences in the reliability of their judgements. We discuss the implications of these findings for models of confidence and collective decision-making. (shrink)

Background Noninvasive prenatal testing (NIPT) designed to screen for fetal genetic conditions, is increasingly being implemented as a part of routine prenatal care screening in the United States (US). However, these advances in reproductive genetic technology necessitate empirical research on the ethical and social implications of NIPT among populations underrepresented in genetic research, particularly Black women with sickle cell disease (SCD).Methods Forty (N = 40) semi-structured interviews were conducted virtually with Black women in the US (19 participants with SCD; 21 (...) participants without SCD) from June 2021 to January 2022. We employed a qualitative approach to examine the study participants’ perceptions of the potential advancement of NIPT for screening SCD in the fetus. Data were analyzed using NVivo 12 qualitative software.Results The themes revealed the complexities involving the intersectional lived experiences of SCD, prenatal care, lack of synergy among health providers, and NIPT decision-making. The results further revealed that even when Black women have shared commonalities in their lived experiences while navigating SCD and motherhood, their perceptions of NIPT screening technologies are divergent.Conclusion Expanding the ethical discourse on the social implications of NIPT is critical to fully elucidate how Black women perceive NIPT’s utility, particularly as NIPT advances to screen for SCD in the fetus. Neglecting to include Black women with genetic conditions in empirical studies on NIPT may contribute to ongoing health inequities and limit and constrain reproductive choices among Black women with and without SCD. (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)

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)

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)