In this paper we prove three theorems about the theory of Borel sets in models of ZF without any form of the axiom of choice. We prove that if \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${B\subseteq 2^\omega}$$\end{document} is a Gδσ-set then either B is countable or B contains a perfect subset. Second, we prove that if 2ω is the countable union of countable sets, then there exists an Fσδ set \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} (...) \setlength{\oddsidemargin}{-69pt} \begin{document}$${C\subseteq 2^\omega}$$\end{document} such that C is uncountable but contains no perfect subset. Finally, we construct a model of ZF in which we have an infinite Dedekind finite \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${D\subseteq 2^\omega}$$\end{document} which is Fσδ. (shrink)

In lieu of an abstract, here is a brief excerpt of the content: Hume's Skepticism about Inductive Inference N. SCOTT ARNOLD IT HAS BEEN A COMMONPLACE among commentators on Hume's philosophy that he was a radical skeptic about inductive inference. In addition, he is alleged to have been the first philosopher to pose the so-called problem of induction. Until recently, however, Hume's argument in this connection has not been subject to very close scrutiny. As attention has become focused on (...) this argument, a debate has been shaping up concerning just what Hume intended to establish here. The principal purpose of this article is to settle this interpretive issue as decisively as the texts permit. I should also like to locate Hume's main argument about induction in the larger context of his discussion of skepti- cism in book 1 of the Treatise. I shall suggest that arguments for the radical skepticism commonly attributed to Hume can be found only very late in book 1 of the Treatise and that the most famous argument about inductive inference establishes and is intended to establish only a relatively modest form of skepticism. The argument under consideration can found in book l, part 3, section 6 of the Treatise. It can also be found in essays 4 and 5 of the Enquiries and in the abstract of the Treatise published anonymously by Hume. I shall concen- trate on the Treatise version since it is the first and perhaps most explicit formulation of the argument and because part of my purpose is to place this argument in the larger context of book 1 of the Treatise. The received opinion concerning Hume's argument has it that Hume was highly skeptical about the mind's claims to knowledge about the future (or, more generally, about the unobserved). All beliefs arrived at via inductive I should like to thank M. G. Anderson, John Bahde, Jon Nordy, and Robert Paul Wolff, as well as David Fate Norton and a referee for the Journal of the History of Philosophy, for helpful comments on earlier drafts on this article. 32 HISTORY OF PHILOSOPHY inferences are unreasonable or unjustified. The alternative interpretation, to be defended below, is that Hume held that no such belief is or can be rendered certain relative to past experience and that such beliefs are not, upon that account, unreasonable or unjustified. Something like this inter- pretation has been defended by Tom L. Beauchamp, Thomas Mappes, and Alexander Rosenberg. ~ My view differs from theirs in that I shall argue that Hume did offer arguments for the more radical skepticism commonly attri- buted to him (though it is unclear whether he regarded them as decisive). These arguments, however, come at the end of book ~ of the Treatise and are independent of the more famous argument to be discussed below. Defenders of the received view are both numerous and distinguished. Versions of this interpretation of the main argument can be found in the writings of Karl Popper, Wesley Salmon, F. L. Will, and Norman Kemp Smith; most recently a variation on the standard interpretation has been defended by Barry Stroud. The fullest and most elaborate defense of the standard interpretation can be found in a monograph by D. C. Stove. '~ Stove's discussion is perhaps the most impressive because of his painstaking efforts to lay bare the structure of Hume's reasoning and to give a line-by- line analysis of the argument. This has the effect of bringing more clearly into focus the main grounds for the standard view. If this standard interpre- tation is correct, then Hume's position is that scientific method is epistemically no better than "superstition" and "enthusiasm." And, Hume would be among those for whom this claim, if true, would be very bad news, because one of his primary purposes in the Treatise is to construct a science of man. Thus, this argument is of considerable internal significance because, if my opponents are correct, Hume appears to have cut the ground out from under what he took to be one of his most important projects -- the construc- tion of a science of man. The other feature of this argument that makes it worthy of serious con- sideration is that it is philosophically... (shrink)

ZusammenfassunuIn dem vorliegenden Bericht über einige Arbeiten des Verfassers und eine daran anschliessende Arbeit von G. Emde, Marburg, wird eine Reihe von Ergebnissen behandelt, die die Kombinationen der Grundmodalitäten « Möglichkeit » und « Notwendigkeit » betreffen. Ausgehend von sehr allgemeinen Rahmenkodifikaten wird die durch Basisreduktion zu gewinnende Liste der endlich vielen implikativen Modalitätenlogiken mit idempotenter Möglichkeit erörtert; bei wichtigen Unterklassen der nicht notwendig idempotenten implikativen Modalitätenlogiken treten neben der Basisreduktion vor allem spezielle Entscheidungsprobleme in den Vordergrund.RésuméDans le rapport ci‐dessus (...) concernant quelques travaux de l'auteur et le travail de M. G. Emde qui s'y rapporte, il s'agit d'un ensemble de résultats sur la combinaison des modalités fondamentales de « possibilité» et de « nécessité». Partant de quelques codifications cadres très générales, I'auteur discute la liste en nombre fini des logiques modales implicatives à« possibilité» idempotente, une liste qui est obtenue par une réduction des bases. Quant à certaines sous‐classes importantes des logiques implicatives qui ne sont pas nécessairement idempotentes, outre la réduction des bases, les problèmes de décision qui leur sont spéciaux, se trouvent placés au premier plan.In the present report on some papers of the author and on a sequel to them by G. Emde, Marburg, a series of results concerning the combination of the basic modalities « possibility » and « necessity » are treated. Starting from some very general framing‐codifications, the list of the finitely many implicative modal logics with idempotent « possibility » which is obtainable through basis reduction is discussed. Besides basis reduction, in the case of some important subclasses of the not‐necessarily‐idempotent implicative modal logics, attention is given to the special decision problems. (shrink)

Originally published in 1972, this book is a systematic analysis of the objectives and methods of history teaching. The book considers the criticisms of the 1960s and 70s of history as a subject and the pressures for its replacement in the school curriculum. It examines the complex psychological background of learning history and suggests that historical understanding makes an important contribution to cognitive growth. It also stresses the important part played by historical material in the emotional and imaginative life of (...) the child. Concluding with a discussion of practical classroom methods, the author proposes objectives and characteristic concepts of the subject which may be embodied in all levels of teaching. (shrink)

In this book James D. G. Dunn explores the nature of the religious experiences that were at the forefront of emerging Christianity.

Human dignity has long been used as a foundational principle in policy documents and ethical guidelines intended to govern various forms of biomedical research. Despite the vast amount of literature concerning human dignity and embryonic tissues, the majority of biomedical research uses non-embryonic human tissue. Therefore, this contribution addresses a notable lacuna in the literature: the relationship, if any, between human dignity and human tissue. This paper first elaborates a multidimensional understanding of human dignity that overcomes many of the shortcomings (...) associated with the use of human dignity in other ethical debates. Second, it discusses the relationship between such an understanding of human dignity and ‘non-embryonic’ human tissue. Finally, it considers the implications of this relationship for biomedical research and practice involving human tissue. The contribution demonstrates that while human tissue cannot be said to have human dignity, human dignity is nevertheless implicated by human tissue, making what is done with human tissue and how it is done worthy of moral consideration. (shrink)

This study investigates the performance of psychopathic individuals on tasks believed to be sensitive to dorsolateral prefrontal and orbitofrontal cortex (OFC) functioning. Psychopathic and non-psychopathic individuals, as defined by the Hare psychopathy checklist revised (PCL-R) [Hare, The Hare psychopathy checklist revised, Toronto, Ontario: Multi-Health Systems, 1991] completed a gambling task [Cognition 50 (1994) 7] and the intradimensional/extradimensional (ID/ED) shift task [Nature 380 (1996) 69]. On the gambling task, psychopathic participants showed a global tendency to choose disadvantageously. Specifically, they showed an (...) impaired ability to show learning over the course of the task. On the ID/ED task, the performance of psychopathic individuals was not significantly different from incarcerated controls on attentional set-shifting, but significant impairments were found on response reversal. These results are interpreted with reference to an OFC and amygdala dysfunction explanation of psychopathy. (shrink)

One of Hume's most well-known works and a masterpiece of philosophy, A Treatise of Human Nature is indubitably worth taking the time to read.

Physicalists motivate their position by posing a problem for the opposition: given the causal completeness of physics and the impact of the mental (or, more broadly, the seemingly nonphysical) on the physical, antiphysicalism implies that causal overdetermination is rampant. This argument is, however, equivocal in its use of 'physical'. As Scott Sturgeon has recently argued, if 'physical' means that which is the object of physical theory, completeness is plausible, but the further claim that the mental has a causal impact on (...) the physical is no longer so evident. In this paper I assess the damage due to the ambiguity of 'physical' and provide a repair to the overdetermination strategy. (shrink)

The concept of brain birth has assumed a position of some significance in discussions on the status of the human embryo and on the point in embryonic development prior to which experimental procedures may be undertaken on human embryos. This paper reviews previous discussions of this concept, which have placed brain birth at various points between 12 days' and 20 weeks' gestation and which have emphasised the symmetry of brain birth and brain death. Major developmental features of brain development are (...) outlined, including the gradualness with which new features generally appear, and also the electroencephalogram (EEG) characteristics of premature infants. From this it is concluded that, if the concept of brain birth is a valid one, it should be placed at 24-28 weeks' gestation. More importantly, it is concluded that the differences between brain development and brain death throw doubt on the concept itself. (shrink)