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)

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.

Deep brain stimulation of the subthalamic nucleus is a clinically effective tool for treating medically refractory Parkinson’s disease, but its neural mechanisms remain debated. Previous work has demonstrated that STN DBS results in evoked potentials in the primary motor cortex, suggesting that modulation of cortical physiology may be involved in its therapeutic effects. Due to technical challenges presented by high-amplitude DBS artifacts, these EPs are often measured in response to low-frequency stimulation, which is generally ineffective at PD symptom management. This (...) study aims to characterize STN-to-cortex EPs seen during clinically relevant high-frequency STN DBS for PD. Intraoperatively, we applied STN DBS to 6 PD patients while recording electrocorticography from an electrode strip over the ipsilateral central sulcus. Using recently published techniques, we removed large stimulation artifacts to enable quantification of STN-to-cortex EPs. Two cortical EPs were observed – one synchronized with DBS onset and persisting during ongoing stimulation, and one immediately following DBS offset, here termed the “start” and the “end” EPs respectively. The start EP is, to our knowledge, the first long-latency cortical EP reported during ongoing high-frequency DBS. The start and end EPs differ in magnitude and latency, and the end, but not the start, EP magnitude has a significant relationship to ongoing high gamma power during the EP. These contrasts may suggest mechanistic or circuit differences in EP production during the two time periods. This represents a potential framework for relating DBS clinical efficacy to the effects of a variety of stimulation parameters on EPs. (shrink)

We provide an overview of a transdisciplinary project about sustainable forest management under climate change. Our project is a partnership with members of the Menominee Nation, a Tribal Nation located in northern Wisconsin, United States. We use immersive virtual experiences, translated from ecosystem model outcomes, to elicit human values about future forest conditions under alternative scenarios. Our project combines expertise across the sciences and humanities as well as across cultures and knowledge systems. Our management structure, governance, and leadership behaviors have (...) both fostered and constrained our work and must be continuously responsive to changing group dynamics. Our project presents opportunities for substantial contributions to society, including insights and knowledge about complementary ways of knowing, skills training, and professional development, and opportunities for reflexive learning about effective transdisciplinary, translational, and transformative scientific processes. (shrink)

Although trust has been widely recognized as a vital component ofrelationships and a critical element to the success of organizations,the literature describing trust and trustworthiness is known for itsvarying perspectives and its inconsistencies. Trustworthiness has beenidentified as a condition precedent to the development of trust.Building upon the established constructs of interpersonaltrustworthiness, we propose a related model containing the sevenconstructs of Competence, Legal Compliance, Responsibility to Inform,Quality Assurance, Procedural Fairness, Interactional Cour-tesy, andFinancial Balance. Citing evidence from trust-related literature, weidentify the utility (...) of these seven constructs in encompassingorganizational trustworthiness as a subjectively perceived aspect oforganizational effectiveness. We analyzed questionnaire data andconducted comparative world-region analyses. (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 world increasingly described as turbulent and chaotic, management scholars have acknowledged the importance of a virtue-based set of criteria to serve as a moral rubric for the stakeholders that an organization serves. Business schools play a unique role in helping their students to understand the ethical issues facing business. Business schools can also model the way for creating a clear statement of values and principles, by creating a bill of rights for business schools that recognizes the importance of (...) rights and responsibilities and articulates the important ethical issues that apply not only to business but to the business school context. Four models for creating a bill of rights in schools of business are presented and a framework of a bill of rights is provided. The advantages of a virtue ethics model for a bill of rights are explained as the most practical approach for business faculty to consider. (shrink)

Knowledge is good, ignorance is bad. So it seems, anyway. But in this dissertation, I argue that some ignorance is epistemically valuable. Sometimes, we should suspend judgment even though by believing we would achieve knowledge. In this apology for ignorance (ignorance, that is, of a certain kind), I defend the following four theses: 1) Sometimes, we should continue inquiry in ignorance, even though we are in a position to know the answer, in order to achieve more than mere knowledge (e.g. (...) understanding) while minimizing the effects of confirmation bias. 2) It’s false that we should believe every proposition such that we are guaranteed to be right about it (and even such that we are guaranteed to know it) if we believe it. 3) Being in a position to know is the norm of assertion: importantly, this does not require belief or (thereby) knowledge, and so proper assertion can survive speaker-ignorance. 4) It can be permissible and conversationally useful to tell audiences things that it is logically impossible for them to come to know: Proper assertion can survive (necessary) audience-side ignorance. Cumulatively, this project suggests that, properly understood, ignorance has an important role to play in the good epistemic life. (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)

Do our lives have meaning? Should we create more people? Is death bad? Should we commit suicide? Would it be better to be immortal? Should we be optimistic or pessimistic? Since Life, Death, and Meaning: Key Philosophical Readings on the Big Questions first appeared, David Benatar's distinctive anthology designed to introduce students to the key existential questions of philosophy has won a devoted following among users in a variety of upper-level and even introductory courses.

"No one has done so much as Mr. Eliade to inform literature students in the West about 'primitive' and Oriental religions.... Everyone who cares about the human adventure will find new information and new angles of vision."—Martin E. Marty, _New York Times Book Review_.

Based on an unfinished manuscript by the late philosopher Dallas Willard, this book makes the case that the 20th century saw a massive shift in Western beliefs and attitudes concerning the possibility of moral knowledge, such that knowledge of the moral life and of its conduct is no longer routinely available from the social institutions long thought to be responsible for it. In this sense, moral knowledge--as a publicly available resource for living--has disappeared. Via a detailed survey of main (...) developments in ethical theory from the late 19th through the late 20th centuries, Willard explains philosophy's role in this shift. In pointing out the shortcomings of these developments, he shows that the shift was not the result of rational argument or discovery, but largely of arational social forces--in other words, there was no good reason for moral knowledge to have disappeared. The Disappearance of Moral Knowledge is a unique contribution to the literature on the history of ethics and social morality. Its review of historical work on moral knowledge covers a wide range of thinkers including T.H Green, G.E Moore, Charles L. Stevenson, John Rawls, and Alasdair MacIntyre. But, most importantly, it concludes with a novel proposal for how we might reclaim moral knowledge that is inspired by the phenomenological approach of Knud Logstrup and Emmanuel Levinas. Edited and eventually completed by three of Willard's former graduate students, this book marks the culmination of Willard's project to find a secure basis in knowledge for the moral life. (shrink)

Review of All Things Wise and Wonderful by E. Janet Warren.

This paper argues for extreme rational permissivism—the view that agents with identical evidence can rationally believe contradictory hypotheses—and a mild version of steadfastness. Agents can rationally come to different conclusions on the basis of the same evidence because their way of weighing the theoretic virtues may differ substantially. Nevertheless, in the face of disagreement, agents face considerable pressure to reduce their confidence. Indeed, I argue that agents often ought to reduce their confidence in the higher-order propositions that they know or (...) rationally believe disputed content. I argue, however, that when the subject matter is difficult, there is more flexibility for agents to simultaneously believe that p while withholding belief about whether such belief is rational or known. This allows for modest steadfastness on hard questions in, e.g., philosophy and religion. (shrink)