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 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)

Aristotle's Politics is widely recognized as one of the classics of the history of political philosophy, and like every other such masterpiece, it is a work about which there is deep division.

What is the temporal course of gratitude and indebtedness and how do these feelings influence helping in the context of reciprocity? In an online-game tapping real-life behaviour, Study 1 (N = 106) finds that while gratitude towards a benefactor remains elevated after an opportunity to reciprocate, indebtedness declines along with helping. Yet, indebtedness rather than gratitude better predicts real-life helping of a benefactor. Using a vignette-based experiment, Study 2 (N = 217) finds that after reciprocation indebtedness and likelihood of helping (...) a benefactor reset to a baseline level while gratitude endures. Furthermore, the decrease in helping after reciprocation is better explained by indebtedness than by gratitude. Study 3 (N = 217) assessed the unique influences of gratitude and indebtedness on helping by comparing contexts in which gratitude is at a baseline level but indebtedness is elevated (e.g. before a monetary payment for a service received) to contexts in which indebtedness is at a baseline level but gratitude is elevated (e.g. after reciprocation of benefits freely given by a friend). People are more likely to help in the former compared to latter context, and this difference is better explained by indebtedness rather than by gratitude. We discuss the interrelated and understudied relationships between gratitude, indebtedness, and reciprocity. (shrink)

In lieu of an abstract, here is a brief excerpt of the content:BOOK REVIEWS 387 and contributed an important and helpful study. This dissertation is a model of its kind. One hopes the author will continue his scholarly efforts. The Catholic University of America Washington, D.C. WILLIAM E. MAY John Henry Newman: A Biography. By IAN KER. New York: Oxford University Press, 1990. Pp. xii + 764. $24.95 (paper). The Achievement of John Henry Newman. By IAN KER. Notre Dame: University (...) of Notre Dame Press, 1990. Pp. x + 209. $24.95 (cloth). Ian Ker has inherited the mantle of the late Charles Stephen Dessain as the finest textual expositor of the Newman corpus, and Ker's biography should become a standard reference tool in the field. Ker ap· prenticed under Dessain in the production of the monumental (31volume ) Letters and Diaries, and his biography shows his command of the materials of that as yet unfinished project. Ker's hook joins the biographies of W. Ward (1912) and M. Trevor (1962) as significant "lives of Newman" to consider, and it addresses their earlier shortcomings : Ward's inadequate appraisal of the Anglican Newman and Trevor's unconcern for Newman's theological writings. Of Newman's intellectual contribution, Ker's treatment is similar to Dessain's John Henry Newman, an exposition of the major themes and intellectual moves, and theologically-minded inquirers need read both. Ker offers the hook as a personal life, a literary appraisal, and an intellectual study. The personal life and literary analysis are ably carried off; Ker's background in English literature and his editorial work on the letters have served him well. The intellectual study takes the form of synopses of Newman's hooks and articles, which are woven into the chronological narrative of the life. This aspect of Ker's hook is by no means "the theological achievement of JHN" (cf. Tracy's work on Lonergan); such a project still awaits Newman studies and someone of the conceptual breadth of the late Jan Walgrave to achieve it. Ker provides accurate and readable summaries of Newman's writings, and if a biography is meant to introduce the sundry aspects of a person, especially a complex thinker like Newman, then Ker's treatment of the intellectual aspect offers a fine introduction. I shall consider these three dimensions of the biography, and first the personal life. Newman considered that a person's life is best told 888 BOOK REVIEWS through that person's correspondence. Ker's biography is approached chronologically, and Newman's published letters guide the tale. Newman 's advice is particularly apropos for his own biographer, since Newman 's hooks and articles often displayed a "reserve" in which his true feelings were couched and nuanced. His letters, especially to confidants, were candid and often hard-hitting, as when he described the Curia in these words: " And who is Propaganda? one sharp man of business, who works day and night, and dispatches his work quick off, to the East and West, a high dignitary, [perhaps an Archbishop], hut after all little more than a clerk... with two or.three clerks under him " (p. 519). (Ker displays some reserve himself, omitting Newman's episcopal aside.) Ker's use of the letters is most revealing during Newman's Roman Catholic period when he encountered opposition from Archbishop Manning and W. G. Ward in England, from Archbishop Cullen in Dublin, and from Cardinal Barnaho in Rome. One senses how the laity rallied round him. Some of Newman's most pungent thoughts on ·theological freedom, on the suspicious nature of the clergy toward educated laity, on the wherewithal to make an institution a genuine university, on the role of patience and.trust in God when authorities are hearing down, are to he found in Ker's choice of letters. With so much material to mine-Newman wrote 20,000 letters-it is understandable that Ker does not include, save rarely, what Newman's opponents were thinking. Ker's account of Newman's Anglican period is equally illuminating, and indeed it is a highlight of the biography. While the Apologia has provided the main lines of the story, Ker puts flesh and hones to Newman 's struggle with his conscience. In coming to Oxford, Newman... (shrink)

Hegel, Derrida, and Restricted Economy: The Case of Mechanical Memory STEPHEN HOULGA'FE A GLANCE AT THE TEXTS OF Jacques Derrida and at the texts and lectures of G. W. F. Hegel indicates that Hegel and Derrida are extraordi- narily different thinkers. Hegel is clearly what Derrida would regard as a philosopher of presence, working toward the point "where knowledge no longer needs to go beyond itself, where knowledge finds itself," where con- sciousness is present to itself as it is (...) in itself. 1 Derrida, on the other hand, suggests that everything that is present, here, now, at this moment, bears within it, as constitutive features of itself, the marks or traces of what is irredeemably past, and that, consequently, we can never talk of entities such as ourselves being simply or wholly present to themselves. ~ Derrida claims in Positions that he tries hard to distinguish "diff6rance" from tlegelian "differ- ence," indeed that "diff~rance" might well be defined precisely as "the inter- ruption, the destruction of Hegelian sublation [relive] wherever it operates"; and, to judge at least from the look of his texts, he would seem to have G. W. F. Hegel, Werke in zwamag B~inden, edited by E. Moldenhauer and K. M. Michel, 20 vols. and Index , Ill [Phi~nomenologie des Geistes], 74. For the English translation, see Hegel, Phenomenolog) of Spirit, translated by A. V. Miller, with analysis of the.. (shrink)

This essay responds to the characterization Ted Miller offers (in his December 2008 essay in Political Theory) of the kind of nonfoundationalism I have referred to as "weak ontology," and that Gianni Vattimo frequently calls "weak thought." Miller argues that such a position embodies, first, a philosophy of history in which strong ontologies (e.g., religion) are assessed categorically as passé, and, second, are associated essentially with violence. I show that while these characterizations may be appropriate for Vattimo's thought, (...) they are not for weak ontology as I understand it. Finally, I suggest that the former might more usefully be categorized as "antifoundationalism" and the latter as "nonfoundationalism.". (shrink)

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

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)

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)

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)

Historically, the scientific method has been said to require proposing a theory, making a prediction of something not already known, testing the prediction, and giving up the theory (or substantially changing it) if it fails the test. A theory that leads to several successful predictions is more likely to be accepted than one that only explains what is already known but not understood. This process is widely treated as the conventional method of achieving scientific progress, and was used throughout the (...) twentieth century as the standard route to discovery and experimentation. But does science really work this way? In Making 20th Century Science, Stephen G. Brush discusses this question, as it relates to the development of science throughout the last century. Answering this question requires both a philosophically and historically scientific approach, and Brush blends the two in order to take a close look at how scientific methodology has developed. Several cases from the history of modern physical and biological science are examined, including Mendeleev's Periodic Law, Kekule's structure for benzene, the light-quantum hypothesis, quantum mechanics, chromosome theory, and natural selection. In general it is found that theories are accepted for a combination of successful predictions and better explanations of old facts. Making 20th Century Science is a large-scale historical look at the implementation of the scientific method, and how scientific theories come to be accepted. (shrink)

Evolutionary theorists have encountered difficulty in explaining how altruistic behavior can evolve. I argue that these theorists have made this task more difficult than it needs to be by focusing their efforts on explaining how nature could select for a strong type of altruism that has powerful selection forces working against it. I argue that switching the focus to a weaker type of altruism renders the project of explaining how altruism can evolve significantly less difficult. I offer a model of (...) weak altruism that can avoid many of the difficulties that evolutionary accounts of altruism have traditionally faced. (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)

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)

Higher order unification is a way of combining information (or equivalently, solving equations) expressed as terms of a typed higher order logic. A suitably restricted form of the notion has been used as a simple and perspicuous basis for the resolution of the meaning of elliptical expressions and for the interpretation of some non-compositional types of comparative construction also involving ellipsis. This paper explores another area of application for this concept in the interpretation of sentences containing intonationally marked focus, or (...) various semantic constructs which are sensitive to focus.Similarities and differences between this approach, and theories using alternative semantics, structured meanings, or flexible categorial grammars, are described. The paper argues that the higher order unification approach offers descriptive advantages over these alternatives, as well as the practical advantage of being capable of fairly direct computational implementation. (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)

SummaryIn the first part of the 19th century, geologists explained volcanoes, earthquakes and mountain-formation on the assumption that the earth has a large molten core underneath a very thin (25–50 mile) solid crust. This assumption was attacked on astronomical grounds by William Hopkins, who argued that the crust must be at least 800 miles thick, and on physical grounds by William Thomson, who showed that the earth as a whole behaves like a solid with high rigidity. Other participants in the (...) debate insisted that there is evidence for a fluid or plastic layer not far below the crust. It was also suggested that the interior of the earth is a supercritical fluid. By the end of the century many geologists had incorporated the doctrine of a completely solid earth into their theories. Acceptance of a relatively small liquid core, indicated by seismological research, was delayed for another two decades. (shrink)

The history of science has often been presented as a story of the achievements of geniuses: Galileo, Newton, Maxwell, Darwin, Einstein. Recently it has become popular to enrich this story by discussing the social contexts and motivations that may have influenced the work of the genius and its acceptance; or to replace it by accounts of the doings of scientists who have no claim to genius or to discoveries of universal importance but may be typical members of the scientific community (...) at a particular time and place. In this article I consider a different type of story, which further research might reveal to be more common than we now suspect: progress stimulated by gadflies – outspoken critics who challenge the ideas of geniuses, forcing them to revise and improve those ideas, resulting in new knowledge for which the genius gets the credit while the gadfly is forgotten. (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.

While many philosophers agree that evolutionary theory has important implications for the study of ethics, there has been no consensus on what these implications are. I argue that we can better understand these implications by examining two related yet distinct issues in evolutionary theory: the evolution of our moral beliefs and the evolution of cooperative behavior. While the prevailing evolutionary account of morality poses a threat to moral realism, a plausible model of how altruism evolved in human beings provides the (...) grounding for a research program that focuses on achieving some of the more practical goals shared by ethicists. †To contact the author, please write to: Department of Political Science, Economics, and Philosophy, College of Staten Island/City University of New York, 2800 Victory Blvd., Staten Island, NY 10314; e‐mail: stephen[email protected]. (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.

Are theories judged on the basis of empirical tests of their predictions, as proposed by Karl Popper and others, or are new theories adopted by younger scientists while old theories fade away when their advocates die, as Max Planck suggested? A famous historical episode, the rejection of steady state cosmology and the revival of the big bang cosmology following the 1965 discovery of the cosmic microwave background radiation, is examined to determine whether the scientific community followed Popper’s or Planck’s principle. (...) It is found that by 1975 almost all supporters of the steady state had either switched to the big bang or stopped publishing on cosmology. This case therefore seems to exemplify Popper’s principle, although it should be noted that two of the founders of steady state cosmology had strongly proclaimed their adherence to that principle. The case does not support the Popperian claim that successful novel predictions provide better evidence for a theory than deductions of known facts. (shrink)