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.

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.

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 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.

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)

Significant associations have been found between specific human leukocyte antigen (HLA) alleles and organ transplant rejection, autoimmune disease development, and the response to infection. Traditional searches for disease associations have conventionally measured risk associated with the presence of individual HLA alleles. However, given the high level of HLA polymorphism, the pattern of amino acid variability, and the fact that most of the HLA variation occurs at functionally important sites, it may be that a combination of variable amino acid sites shared (...) by several alleles (shared epitopes) are better descriptors of the actual causative genetic variants. Here we describe a novel approach to genetic association analysis in which genes/proteins are broken down into smaller sequence features and then variant types defined for each feature, allowing for independent analysis of disease association with each sequence feature variant type. We have used this approach to analyze a cohort of systemic sclerosis patients and show that a sequence feature composed of specific amino acid residues in peptide binding pockets 4 and 7 of HLA-DRB1 explains much of the molecular determinant of risk for systemic sclerosis. (shrink)

"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_.

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)

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)

Critical Discourse Analysis, or more popularly known as CDA, reflects the trend on the investigation of ideology and power struggle that is implied in the text and sound of discourse and language. With Norman Fairclough and the group in Lancaster University as the leading theorists of this discipline, this paper deals on extracting the very foundation of its theoretical claims in hope of unearthing the rich philosophical ideations and nuances that may have contributed towards its creation and formation through the (...) years. In this way, this would not only expose its philosophical framework but also would provide its readers and its practitioners a theoretical base and scope of related disciplines for the furthering of their interests and practices. This diachronic sketch legitimizes the claims of CDA as it rests on the more popular and stable conceptual skeleton of the major prominent thinkers of critical theory, poststructuralism, and postmodernism. (shrink)

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)

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

This anthology of readings in the survey of Western philosophy--from the Ancient Greeks to the 20th Century--is designed to be accessible to today's readers. Striking a balance between major and minor figures, it features the best available translations of texts--complete works or complete selections of works-- which are both central to each philosopher's thought and are widely accepted as part of the canon. The selections are readable and accessible, while still being faithful to the original. Includes Introductions to each historical (...) period and to each philosopher, and an abundance of drawings, diagrams, photographs, and a timeline. This Combined Volume contains the most important works from Baird's Philosophic Classics, Volumes I-V. ANCIENT GREEK PHILOSOPHY. Plato. Aristotle. HELLENISTIC PHILOSOPHY. Epicurus. Epictetus. Plotinus. MEDIEVAL PHILOSOPHY. Augustine. Boethius. Anselm (and Guanilo). Moses Maimonides. Thomas Aquinas. William of Ockham. Pico Della Mirandola. MODERN PHILOSOPHY. Ren Descartes. Thomas Hobbes. Blaise Pascal. Baruch Spinoza. John Locke. Gottfried Leibniz. George Berkeley. David Hume. Immanuel Kant. NINETEENTH-CENTURY PHILOSOPHY. G.W.F. Hegel. John Stuart Mill. Soren Kierkegaard. Karl Marx. Friedrich Nietzsche. TWENTIETH-CENTURY PHILOSOPHY. Edmund Husserl. Bertrand Russell. Martin Heidegger. Ludwig Wittgenstein. A.J. Ayer. Jean-Paul Sartre. Willard Van Orman Quine. Jacques Derrida. For anyone interested in Philosophy, History of Philosophy, or History of Intellectual Thought. (shrink)