In this article, we outline a simple and intuitively appealing procedure to derive default priors. The main idea is to regard the choice of such a prior as a formal Bayesian decision problem. We also discuss Jeffreys prior and more generally the reference prior of Bernardo (J R Stat Soc B 41:113–147, 1979) from this standpoint.

Infectious disease outbreaks in residential care are complex to manage and difficult to control. Research in this setting that includes individuals who lack capacity must conform to national legislation. We report here on our study that is investigating outbreaks of scabies, an itchy skin infection, in the residential care setting in the southeast of England. There appears to be a gap in legislative advice regarding the inclusion of people who lack capacity in research that takes place during time-limited acute scenarios (...) such as outbreaks. We received inconsistent advice from experts regarding, in particular, the role of nominated consultees. There is a potential inequality for vulnerable populations who cannot themselves provide informed consent in terms of their access to participation in a range of health-related research. (shrink)

For deliberations on the ethical and meta-ethical implications of Alfred North Whitehead's process philosophy, here are abstracts and papers from the Ethics Section of the 6th International Whitehead Conference held at the University of Salzburg in Salzburg, Austria in July 2006. In accordance with the conference schedule, there are three subsections. The subsection on "Metaphysics of Morals and Moral Theory" includes contributions from Franklin I. Gamwell (Does Morality Presuppose God?), John W. Lango (abstract only), Duane Voskuil ("Ethics' Dipolar Necessities and (...) Theistic Implications), and Theodore Walker Jr. ("Neoclassical Cosmology and Matthew 22:36-40). The subsection on "Evaluating Moral Practices" includes contributions from Frederick Ferrè (abstract only), Seung Gap Lee (Hope for the Earth: A Process Eschatological Eco-ethics for South Korea), Mary Elizabeth Mullino Moore (Compassion, Creativity, and Form: The Ethics of Institutions), and George W. Shields (Ruse, Altruism, and Process Philosophy). The subsection on "Ethics and Aesthetic Values" includes contributions from Stephen T. Franklin (abstract only), Brian G. Henning (Is There an Ethics of Creativity?), Mihàly Tòth (Art of Life and the Ethics of Life Forming), and Guorong Yang (Problems and Perspectives in the Emerging of Global Society). (shrink)

An examination of verbal hallucinations and thought insertion as examples of "alienated self-consciousness.".

We develop measure theory in the context of subsystems of second order arithmetic with restricted induction. We introduce a combinatorial principleWWKL (weak-weak König's lemma) and prove that it is strictly weaker thanWKL (weak König's lemma). We show thatWWKL is equivalent to a formal version of the statement that Lebesgue measure is countably additive on open sets. We also show thatWWKL is equivalent to a formal version of the statement that any Borel measure on a compact metric space is countably additive (...) on open sets. (shrink)

A mass problem is a set of Turing oracles. If P and Q are mass problems, we say that P is weakly reducible to Q if every member of Q Turing computes a member of P. We say that P is strongly reducible to Q if every member of Q Turing computes a member of P via a fixed Turing functional. The weak degrees and strong degrees are the equivalence classes of mass problems under weak and strong reducibility, respectively. We (...) focus on the countable distributive lattices P w and P s of weak and strong degrees of mass problems given by nonempty Π 1 0 subsets of 2 ω . Using an abstract Gödel/Rosser incompleteness property, we characterize the Π 1 0 subsets of 2 ω whose associated mass problems are of top degree in P w and P s , respectively. Let R be the set of Turing oracles which are random in the sense of Martin-Löf, and let r be the weak degree of R. We show that r is a natural intermediate degree within P w . Namely, we characterize r as the unique largest weak degree of a Π 1 0 subset of 2 ω of positive measure. Within P w we show that r is meet irreducible, does not join to 1, and is incomparable with all weak degrees of nonempty thin perfect Π 1 0 subsets of 2 ω . In addition, we present other natural examples of intermediate degrees in P w . We relate these examples to reverse mathematics, computational complexity, and Gentzen-style proof theory. (shrink)

Let ω be the set of natural numbers. For functions f, g: ω → ω, we say f is dominated by g if f < g for all but finitely many n ∈ ω. We consider the standard “fair coin” probability measure on the space 2ω of in-finite sequences of 0's and 1's. A Turing oracle B is said to be almost everywhere dominating if, for measure 1 many X ∈ 2ω, each function which is Turing computable from X is (...) dominated by some function which is Turing computable from B. Dobrinen and Simpson have shown that the almost everywhere domination property and some of its variant properties are closely related to the reverse mathematics of measure theory. In this paper we exposit some recent results of Kjos-Hanssen, Kjos-Hanssen/Miller/Solomon, and others concerning LR-reducibility and almost everywhere domination. We also prove the following new result: If B is almost everywhere dominating, then B is superhigh, i. e., 0″ is truth-table computable from B ′, the Turing jump of B. (shrink)

We investigate the reverse-mathematical status of several theorems to the effect that the natural number system is second-order categorical. One of our results is as follows. Define a system to be a triple A,i,f such that A is a set and i∈A and f:A→A. A subset X⊆A is said to be inductive if i∈X and ∀a ∈X). The system A,i,f is said to be inductive if the only inductive subset of A is A itself. Define a Peano system to be (...) an inductive system such that f is one-to-one and i∉the range of f. The standard example of a Peano system is N,0,S where N={0,1,2,…,n,…}=the set of natural numbers and S:N→N is given by S=n+1 for all n∈N. Consider the statement that all Peano systems are isomorphic to N,0,S. We prove that this statement is logically equivalent to WKL0 over RCA0⁎ source. From this and similar equivalences we draw some foundational/philosophical consequences. (shrink)

We investigate the provability or nonprovability of certain ordinary mathematical theorems within certain weak subsystems of second order arithmetic. Specifically, we consider the Cauchy/Peano existence theorem for solutions of ordinary differential equations, in the context of the formal system RCA 0 whose principal axioms are ▵ 0 1 comprehension and Σ 0 1 induction. Our main result is that, over RCA 0 , the Cauchy/Peano Theorem is provably equivalent to weak Konig's lemma, i.e. the statement that every infinite {0, 1}-tree (...) has a path. We also show that, over RCA 0 , the Ascoli lemma is provably equivalent to arithmetical comprehension, as is Osgood's theorem on the existence of maximum solutions. At the end of the paper we digress to relate our results to degrees of unsolvability and to computable analysis. (shrink)

Let CKDT be the assertion that for every countably infinite bipartite graph G, there exist a vertex covering C of G and a matching M in G such that C consists of exactly one vertex from each edge in M. (This is a theorem of Podewski and Steffens [12].) Let ATR0 be the subsystem of second-order arithmetic with arithmetical transfinite recursion and restricted induction. Let RCA0 be the subsystem of second-order arithmetic with recursive comprehension and restricted induction. We show that (...) CKDT is provable in ART0. Combining this with a result of Aharoni, Magidor, and Shore [2], we see that CKDT is logically equivalent to the axioms of ATR0, the equivalence being provable in RCA0. (shrink)

By , we denote the system of second-order arithmetic based on recursive comprehension axioms and Σ10 induction. is defined to be plus weak König's lemma: every infinite tree of sequences of 0's and 1's has an infinite path. In this paper, we first show that for any countable model M of , there exists a countable model M′ of whose first-order part is the same as that of M, and whose second-order part consists of the M-recursive sets and sets not (...) in the second-order part of M. By combining this fact with a certain forcing argument over universal trees, we obtain the following result : if proves X!Y with arithmetical, so does . We also discuss several improvements of this results. (shrink)

We examine the concept of almost everywhere domination from the viewpoint of mass problems. Let AED and MLR be the sets of reals which are almost everywhere dominating and Martin-Löf random, respectively. Let b1, b2, and b3 be the degrees of unsolvability of the mass problems associated with AED, MLR × AED, and MLR ∩ AED, respectively. Let [MATHEMATICAL SCRIPT CAPITAL P]w be the lattice of degrees of unsolvability of mass problems associated with nonempty Π01 subsets of 2ω. Let 1 (...) and 0 be the top and bottom elements of [MATHEMATICAL SCRIPT CAPITAL P]w. We show that inf, inf, and inf belong to [MATHEMATICAL SCRIPT CAPITAL P]w and 0 < inf < inf < inf < 1. Under the natural embedding of the recursively enumerable Turing degrees into [MATHEMATICAL SCRIPT CAPITAL P]w, we show that inf and inf but not inf are comparable with some recursively enumerable Turing degrees other than 0 and 0′. In order to make this paper more self-contained, we exposit the proofs of some recent theorems due to Hirschfeldt, Miller, Nies, and Stephan. (shrink)

Stephen Salkever shows that reading Aristotle is a starting point for discussing contemporary political problems in new ways that avoid the opposition between liberal individualism and republican communitarianism, between the politics of rights and the politics of virtues. Originally published in 1990. The Princeton Legacy Library uses the latest print-on-demand technology to again make available previously out-of-print books from the distinguished backlist of Princeton University Press. These editions preserve the original texts of these important books while presenting them in (...) durable paperback and hardcover editions. The goal of the Princeton Legacy Library is to vastly increase access to the rich scholarly heritage found in the thousands of books published by Princeton University Press since its founding in 1905. (shrink)

Stephen Salkever shows that reading Aristotle is a starting point for discussing contemporary political problems in new ways that avoid the opposition between liberal individualism and republican communitarianism, between the politics of rights and the politics of virtues. Originally published in 1990. The Princeton Legacy Library uses the latest print-on-demand technology to again make available previously out-of-print books from the distinguished backlist of Princeton University Press. These editions preserve the original texts of these important books while presenting them in (...) durable paperback and hardcover editions. The goal of the Princeton Legacy Library is to vastly increase access to the rich scholarly heritage found in the thousands of books published by Princeton University Press since its founding in 1905. (shrink)

Science and the End of Ethics examines some of the most important positive and negative implications that science has for ethics. Addressing the negative implications first, author Stephen Morris discusses how contemporary science provides significant challenges to moral realism. One threat against moral realism comes from evolutionary theory, which suggests that our moral beliefs are unconnected to any facts that would make them true. Ironically, many of the same areas of science (e.g. evolutionary biology, neuroscience, psychology) that present difficulties (...) for moral realism point to a new ethical approach that focuses on achieving some of the key practical goals shared by ethicists. Chief among these is how to increase amicable behavior among people. (shrink)

In this paper, we introduce a system of nonstandard second-order arithmetic $\mathsf{ns}$-$\mathsf{WWKL_0}$ which consists of $\mathsf{ns}$-$\mathsf{BASIC}$ plus Loeb measure property. Then we show that $\mathsf{ns}$-$\mathsf{WWKL_0}$ is a conservative extension of $\mathsf{WWKL_0}$ and we do Reverse Mathematics for this system.

ABSTRACTIn Democratic Reason, Hélène Landemore makes an epistemic argument for democracy. She contends that, due to their greater cognitive diversity, democratic groups will engage in superior deliberation and information aggregation than will groups of experts; consequently, the quality of their policies will be better. But the introduction of value diversity into Landemore's model—which is necessary if the argument is to apply to the real world—undermines her argument for the epistemic superiority of democratic deliberation. First, the existence of value diversity threatens (...) to stop deliberation prematurely. This has the effect of making the outcome of group deliberation more dependent on individual ability, which gives groups of experts a distinct advantage. Second, the introduction of value diversity raises the question of how to understand the standard of correctness of an epistemic argument, which Landemore does not adequately answer. (shrink)

Two recent publications highlight the role of bone‐forming cells, the osteoblasts, in controlling the development of neighboring haematopoietic stem cells (HSCs).1,2 Using two distinct transgenic mouse models, one using the conditional deletion of the Bone Morphogenetic Protein Receptor 1A (BMPR1A) gene, the other using over‐expression of an active PTH/PTHrP receptor (PPR) mutant within osteoblasts, the authors show parallel, concordant increases in the generation of trabecular osteoblasts and the number of HSCs. In situ staining showed that rarely cycling HSCs sporadically attach (...) to endosteal osteoblasts, while in vitro assays indicated that ligation of Jag1 on osteoblasts by Notch1 on HSCs promotes HSC proliferation. These two independent works have revived and revitalized the notion that osteoblasts are a major, defining component of the HSC niche within the bone marrow (BM). This minireview discusses these results in the context of other recent studies of mesenchymal cells within the BM microenvironment, presents one potential unified model of the functional anatomy of the BM HSC niche, and highlights new questions raised by these and other studies of osteoblasts and HSCs. BioEssays 26:595–599, 2004. © 2004 Wiley Periodicals, Inc. (shrink)

The evidence-based medicine movement advocates basing all medical decisions on certain types of quantitative research data and has stimulated protracted controversy and debate since its inception. Evidence-based medicine presupposes an inaccurate and deficient view of medical knowledge. Michael Polanyi’s theory of tacit knowledge both explains this deficiency and suggests remedies for it. Polanyi shows how all explicit human knowledge depends on a wealth of tacit knowledge which accrues from experience and is essential for problem solving. Edmund Pellegrino’s classic treatment of (...) clinical judgment is examined, and a Polanyian critique of this position demonstrates that tacit knowledge is necessary for understanding how clinical judgment and medical decisions involve persons. An adequate medical epistemology requires much more qualitative research relevant to the clinical encounter and medical decision making than is currently being done. This research is necessary for preventing an uncritical application of evidence-based medicine by health care managers that erodes good clinical practice. Polanyi’s epistemology shows the need for this work and provides the structural core for building an adequate and robust medical epistemology that moves beyond evidence-based medicine. (shrink)

Most clinicians take for granted a simple, reductionist understanding of medical knowledge that is at odds with how they actually practice medicine; routine medical decisions incorporate more complicated kinds of information than most standard accounts of medical reasoning suggest. A better understanding of the structure and function of knowledge in medicine can lead to practical improvements in clinical medicine. This understanding requires some familiarity with epistemology, the study of knowledge and its structure, in medicine. Michael Polanyi's theory of tacit knowing (...) is advanced as the basis for developing a more accurate understanding of medical knowledge. Tacit knowing, which explores the taken-for-granted background knowledge that underlies all human knowing, is explained in detail with a focus on its relevance for clinical medicine. The implications of recognizing tacit knowing in medicine and medical decisions are discussed. These include the ability to explain the importance of the clinical encounter in medical practice, mechanisms for analysing patient and doctor as persons, and the need for humility given the uncertainty that the tacit dimension injects into all medical decisions. This more robust medical epistemology allows clinicians to better articulate the nature and importance of patient-centred care, to avoid pitfalls inherent in reductionist approaches to medical knowledge, and to think more clearly about the relationships between medicine and health care at the individual and population levels. (shrink)

The thesis that scientists give greater weight to novel predictions than to explanations of known facts is tested against historical cases in physical science. Several theories were accepted after successful novel predictions but there is little evidence that extra credit was given for novelty. Other theories were rejected despite, or accepted without, making successful novel predictions. No examples were found of theories that were accepted primarily because of successful novel predictions and would not have been accepted if those facts had (...) been previously known. (shrink)

If effective anti-aging interventions were achieved, they would likely bring about profound alterations in the experiences of individual and collective life. What if modern scientists could find the modern equivalent to the Fountain of Youth that Ponce de Leon sought? This book addresses this question by exploring the ramifications of possible anti-aging interventions on both individual and collective life. Through a series of essays, it examines the biomedical goal of prolongevity from cultural, scientific, religious, and ethical perspectives, offering a sweeping (...) view into the future of aging. (shrink)

A well known fact is that every Lebesgue measurable set is regular, i.e., it includes an F$_{\sigma}$ set of the same measure. We analyze this fact from a metamathematical or foundational standpoint. We study a family of Muchnik degrees corresponding to measure-theoretic regularity at all levels of the effective Borel hierarchy. We prove some new results concerning Nies's notion of LR-reducibility. We build some $\omega$-models of RCA$_0$which are relevant for the reverse mathematics of measure-theoretic regularity.

The authors explore how urban versus rural community location shapes the extent to which various individual, relational, and structural factors affect the gender gap in small business success. Building on previous research on gender and small business success, gender queuing theories, and gendered organization/institution theories, they develop a place-specific theory of the gender gap in small business success. The findings, based on small business data collected in urban and rural Iowa, support queuing arguments and raise questions about the effectiveness of (...) crowded-sector explanations. They indicate that the gender gap in small business success operates such that men-owned businesses are more successful in both urban and rural settings but that men-owned businesses are even more successful than women-owned businesses in urban than rural communities. The authors discuss the causes and consequences of the gender gap in small business success in rural and urban places and identify key issues for further research. (shrink)

This essay traces the interlinked origins of two concepts found in Charles Darwin's writings: "unconscious selection," and sexual selection as applied to humanity's anatomical race distinctions. Unconscious selection constituted a significant elaboration of Darwin's artificial selection analogy. As originally conceived in his theoretical notebooks, that analogy had focused exclusively on what Darwin later would call "methodical selection," the calculated production of desired changes in domestic breeds. By contrast, unconscious selection produced its results unintentionally and at a much slower pace. Inspiration (...) for this concept likely came from Darwin's early reading of works on both animal breeding and physical ethnology. Texts in these fields described the slow and unplanned divergence of anatomical types, whether animal or human, under the guidance of contrasting ideals of physical perfection. These readings, it is argued, also led Darwin to his theory of sexual selection as applied to race, a theme he discussed mainly in his book The Descent of Man. There Darwin described how the racial version of sexual selection operated on the same principle as unconscious selection. He thereby effectively reunited these kindred concepts. (shrink)

We consider implicit definability over the natural number system $\mathbb{N},+,\times,=$. We present a new proof of two theorems of Leo Harrington. The first theorem says that there exist implicitly definable subsets of $\mathbb{N}$ which are not explicitly definable from each other. The second theorem says that there exists a subset of $\mathbb{N}$ which is not implicitly definable but belongs to a countable, explicitly definable set of subsets of $\mathbb{N}$. Previous proofs of these theorems have used finite- or infinite-injury priority constructions. (...) Our new proof is easier in that it uses only a nonpriority oracle construction, adapted from the standard proof of the Friedberg jump theorem. (shrink)