We extend the theory of “Fine structure and iteration trees” to models having more than one Woodin cardinal.

In this paper we shall answer some questions in the set theory of L, the universe of all sets constructible from the reals. In order to do so, we shall assume ADL, the hypothesis that all 2-person games of perfect information on ω whose payoff set is in L are determined. This is by now standard practice. ZFC itself decides few questions in the set theory of L, and for reasons we cannot discuss here, ZFC + ADL yields the most (...) interesting “completion” of the ZFC-theory of L.ADL implies that L satisfies “every wellordered set of reals is countable”, so that the axiom of choice fails in L. Nevertheless, there is a natural inner model of L, namely HODL, which satisfies ZFC.. The superscript “L” indicates, here and below, that the notion in question is to be interpreted in L.) HODL is reasonably close to the full L, in ways we shall make precise in § 1. The most important of the questions we shall answer concern HODL: what is its first order theory, and in particular, does it satisfy GCH?These questions first drew attention in the 70's and early 80's. (shrink)

Posner [6] has shown, by a nonuniform proof, that every ▵ 0 2 degree has a complement below 0'. We show that a 1-generic complement for each ▵ 0 2 set of degree between 0 and 0' can be found uniformly. Moreover, the methods just as easily can be used to produce a complement whose jump has the degree of any real recursively enumerable in and above $\varnothing'$ . In the second half of the paper, we show that the complementation (...) of the degrees below 0' does not extend to all recursively enumerable degrees. Namely, there is a pair of recursively enumerable degrees a above b such that no degree strictly below a joins b above a. (This result is independently due to S. B. Cooper.) We end with some open problems. (shrink)

As microeconomic calculus and macroeconomic estimation superseded earlier approaches to political economy, broad questions about how things are (ontology), how things might be known (epistemology), and how science should proceed (methodology) were neglected. As a corrective, Critical Realism (CR) has been proposed as an alternative to the orthodox deductive‐nomological (ODN) tradition; i.e., to mathematical deduction and statistical induction. In their place, retroduction—the use of analogy, metaphor, intuition and ordinary language—is supposed to illuminate root causes by identifying the deep mechanisms that (...) govern events. CR offers guidelines for social science that are of a most general kind: from initial “premises,” retroduction proceeds to hypotheses about deep structures and mechanisms. The initial premises are determined by a desire to understand events that surprise us. However, nothing is thereby excluded, including ODN. And since historical processes are revealed neither by assumption nor by the net effects of whatever initial conditions hold, it might be apposite to drop the search for (deep) socio‐economic laws and to use whatever evidence is at hand to see whether, and the extent to which, ideal types apply to any given historical sequence. (shrink)

In this paper we shall answer some questions in the set theory of L, the universe of all sets constructible from the reals. In order to do so, we shall assume ADL, the hypothesis that all 2-person games of perfect information on ω whose payoff set is in L are determined. This is by now standard practice. ZFC itself decides few questions in the set theory of L, and for reasons we cannot discuss here, ZFC + ADL yields the most (...) interesting “completion” of the ZFC-theory of L.ADL implies that L satisfies “every wellordered set of reals is countable”, so that the axiom of choice fails in L. Nevertheless, there is a natural inner model of L, namely HODL, which satisfies ZFC.. The superscript “L” indicates, here and below, that the notion in question is to be interpreted in L.) HODL is reasonably close to the full L, in ways we shall make precise in § 1. The most important of the questions we shall answer concern HODL: what is its first order theory, and in particular, does it satisfy GCH?These questions first drew attention in the 70's and early 80's. (shrink)

Background: Abortion policy varies significantly between Northern Ireland and Norway. This is the first study to compare medical students’ attitudes towards abortion in two different countries. Objective: To assess medical students’ attitudes to abortion at the University of Oslo (UiO) and Queen’s University Belfast (QUB). Design: An anonymous questionnaire completed by 59 medical students at UiO and 86 medical students at QUB. Participants: Students who had completed their obstetrics and gynaecology placements during 2006/2007. Results: The students’ responses (UiO versus QUB) (...) were as follows: response rate, 95.2% vs 92.5%; stated no religious affiliation, 48.0% vs 4.7%; pro-abortion, 78.2% vs 14.3% (χ2 = 58.160, p<0.001); had seen an abortion while studying medicine, 74.6% vs 9.4% (χ2 = 73.183, p<0.001); in favour of abortion when there was a threat to the mother’s life, 100% vs 93.3% (χ2 = 6.143, p = 0.150); in favour of providing abortion on the mother’s request, 86.4% vs 9.3% (χ2 = 42.067, p<0.001); in agreement that women should have access to free abortion services (mean value on a 5-point Likert scale 1.69 out of 5), versus in disagreement (mean 3.76, p<0.001). Conclusion: There were significant differences in students’ attitudes to abortion, reflecting differences in religious, legal and educational experiences. (shrink)

I agree with Paul Lewis that mathematics has a valuable but not all-encompassing role in economics, that event regularities must be supplemented with a persuasive narrative, and that inferences can inform our understanding of economic behavior. However, Lewis's full-throated defense of critical realism does little to allay my original concerns. It is absurd to maintain, as critical realists do, that mainstream economics has nothing valuable to offer heterodox economists, as their critique of the quantity theory of money tries to demonstrate. (...) More crucially, critical realists—unlike Austrian economists—neglect to provide an epistemological explanation of economic actors’ perceptions, which is necessary if we are to bridge critical realism's own division of the social world into the “actual,” “empirical,” and “non-actual real.”. (shrink)

I agree with Paul Lewis that mathematics has a valuable but not all-encompassing role in economics, that event regularities must be supplemented with a persuasive narrative, and that inferences can inform our understanding of economic behavior. However, Lewis's full-throated defense of critical realism does little to allay my original concerns. It is absurd to maintain, as critical realists do, that mainstream economics has nothing valuable to offer heterodox economists, as their critique of the quantity theory of money tries to demonstrate. (...) More crucially, critical realists—unlike Austrian economists—neglect to provide an epistemological explanation of economic actors’ perceptions, which is necessary if we are to bridge critical realism's own division of the social world into the “actual,” “empirical,” and “non-actual real.”. (shrink)

Neural activity and social activity share close parallels, particularly the fact that spontaneous adaptations are paramount in both realms. Environmental pressures require organisms and societies to adapt to new and uncertain situations. Adaptations create, respectively, stronger neural and social networks that may, in turn, make the system more resilient to future uncertainties—but only if the adaptations are beneficial to the system.

Neural activity and social activity share close parallels, particularly the fact that spontaneous adaptations are paramount in both realms. Environmental pressures require organisms and societies to adapt to new and uncertain situations. Adaptations create, respectively, stronger neural and social networks that may, in turn, make the system more resilient to future uncertainties—but only if the adaptations are beneficial to the system.

Ethics courses are most commonly evaluated using reaction measures. However, little is known about the specific types of reaction data being collected and how these reaction data relate to improvements in trainee performance. Using a sample of 381 ethics training sessions, major reaction data categories were identified. Content and course satisfaction were the most frequently collected types of reaction criteria. Furthermore, content relevance and course satisfaction showed strong, positive relationships with performance criteria, whereas content satisfaction demonstrated a moderate, negative relationship. (...) These results and future directions for ethics training evaluation are discussed. (shrink)

Let M\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${\mathcal{M}}$$\end{document} be a fine structural mouse. Let D\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${\mathbb{D}}$$\end{document} be a fully backgrounded L[E]\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${L[\mathbb{E}]}$$\end{document}-construction computed inside an iterable coarse premouse S. We describe a process comparing M\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${\mathcal{M}}$$\end{document} with D\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${\mathbb{D}}$$\end{document}, through forming iteration trees on M\documentclass[12pt]{minimal} \usepackage{amsmath} (...) \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${\mathcal{M}}$$\end{document} and on S. We then prove that this process succeeds. (shrink)

Part of the ambiguity lies in the various points of view from which this question might be considered. The crudest di erence lies between the point of view of the working mathematician and that of the logician concerned with the foundations of mathematics. Now some of my fellow mathematical logicians might protest this distinction, since they consider themselves to be just more of those \working mathematicians". Certainly, modern logic has established itself as a very respectable branch of mathematics, and there (...) are quite a few highly technical journals in logic, such as The Journal of Sym-. (shrink)

Over the last decades, the Commissio Leonina has built up a very strong reputation. Editions such as theSentencia libri De anima and the Sentencia libri de sensu et sensato by R.-A. Gauthier or the commentaries on Boethius by P.-M. Gils, L.-J. Bataillon and C.A. Grassi have set new philological standards, not only because of their fine critical introductions and excellent reconstructions of Thomas Aquinas’ texts, but also because of their rich and accurate apparatus fontium. It may be doubted, however, whether (...) the present edition of De spiritualibus creaturis by Father J. Cos lives up to the same high standards. (shrink)

THE PRINCIPLES OF SOCIAL EVOLUTION by C. R. Hallpike New York: Oxford University Press, 1987. 426pp., $59.00 CULTURE AND THE EVOLUTIONARY PROCESS by Robert Boyd and Peter J. Richerson Chicago: University of Chicago Press, 1985. 339pp., $29.95.

The emergence of an autocatalytic network from an available set of elements is a fundamental step in early evolutionary processes, such as the origin of metabolism. Given the set of elements, the reactions between them (chemical or otherwise), and with various elements catalysing certain reactions, a Reflexively Autocatalytic F-generated (RAF) set is a subset R′\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$'$$\end{document} of reactions that is self-generating from a given food set, and with each reaction in R′\documentclass[12pt]{minimal} \usepackage{amsmath} (...) \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$'$$\end{document} being catalysed from within R′\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$'$$\end{document}. RAF theory has been applied to various phenomena in theoretical biology, and a key feature of the approach is that it is possible to efficiently identify and classify RAFs within large systems. This is possible because RAFs can be described as the (nonempty) subsets of the reactions that are the fixed points of an (efficiently computable) interior map that operates on subsets of reactions. Although the main generic results concerning RAFs can be derived using just this property, we show that for systems with at least 12 reactions there are generic results concerning RAFs that cannot be proven using the interior operator property alone. (shrink)

La logique spécifique des jugements de valeur est à chercher dans le discours rhétorique. Cette thèse développée par Ch. Perelman dans L'Empire rhétorique (1977) nous rappelle l'introduction à l'éthique de Jean Buridan (XIVe s.). Selon Buridan la philosophie morale ne peut se contenter d'appliquer la logique générale: elle a besoin d'une logique spéciale, une „logique morale” qui n'est rien autre que la technique persuasive qu'on étudie dans la Rhétorique. Roger Bacon (XlIIe s.) a même essayé d'intégrer cette rhétorique dans l'éthique (...) : elle est la partie pratique de la science morale. Bien que leur textes rappellent parfois les considérations de la ‘nouvelle rhétorique’, la relation entre l'éthique et la rhétorique y est envisagée d'une manière toute différente. Pour les auteurs médiévaux la rhétorique est une science auxiliaire de l'éthique : elle sert de liaison entre la théorie et la pratique. Dans la partie théorétique de l'éthique la logique ‘générale’ reste en vigeur. Ce n'est que pour mettre en pratique les règles et valeurs qui ont été ‘démontrées’ par la théorie qu'on a recours à la technique persuasive et sa logique ‘spéciale’. La rhétorique n'a donc qu'une fonction subsidaire. On retrouve la même conception au début des temps modernes chez Francis Bacon qui attribue à la rhétorique la fonction d'appliquer le dictamen rationis à l'imagination pour exciter ainsi la volonté. Une tout autre conception est défendue par l'humaniste Lorenzo Valla qui essaie de réintégrer l'argumentation morale dans le discours rhétorique où elle trouve sa place originaire. Notre propre point de vue est développé en confrontation avec Aristote, de qui nous avons hérité le projet d'une ‘science pratique’ et l'ambiguité qui en est inhérente 1° La rhétorique présuppose l'éthique. 2° L'éthique qui se veut epistème, ne relève pas de la rhétorique qui n'est qu'une technè. Elle se présente comme une science à caractère dialectique. 3° Les difficultés arrivent dès qu'on exalte la fonction pratique de cette science (cf. récemment R. Hare). Dès que l'éthique veut être efficace dans la vie concrète, elle devient une argumentation qui relève plutôt du discours épidectique (Weltanschauung). Notre société, en pleine crise morale, a certainement besoin d'un tel discours qui essaie d'intensifier l'adhésion à des valeurs morales. Mais il nous semble qu'il reste à côté d'un tel discours - en pleine expansion des nos jours - une place bien discrète pour une reflection critique qui en analyse les raisons : qui n'est pas inutile, bien que peu efficace. (shrink)