In this paper, we sketch the development of two important themes of modern set theory, both of which can be regarded as growing out of work of Kurt Gödel. We begin with a review of some basic concepts and conventions of set theory.§0. The ordinal numbers were Georg Cantor's deepest contribution to mathematics. After the natural numbers 0, 1, …, n, … comes the first infinite ordinal number ω, followed by ω + 1, ω + 2, …, ω + (...) ω, … and so forth. ω is the first limit ordinal as it is neither 0 nor a successor ordinal. We follow the von Neumann convention, according to which each ordinal number α is identified with the set {ν ∣ ν α} of its predecessors. The ∈ relation on ordinals thus coincides with <. We have 0 = ∅ and α + 1 = α ∪ {α}. According to the usual set-theoretic conventions, ω is identified with the first infinite cardinal ℵ0, similarly for the first uncountable ordinal number ω1 and the first uncountable cardinal number ℵ1, etc. We thus arrive at the following picture:The von Neumann hierarchy divides the class V of all sets into a hierarchy of sets Vα indexed by the ordinal numbers. The recursive definition reads: ;Vλ = ∪v<λVv for limit ordinals λ. We can represent this hierarchy by the following picture. (shrink)

A Reply P. Flensted-Jensen/M. H. Hansen: Pseudo-Skylax' Use of the Term Polis M. H. Hansen: City-Ethnics as Evidence for Polis Identity .

Previously published: Princeton University Press, 1940.

Diverse lines of evidence point to a basic human aversion to physically harming others. First, we demonstrate that unwillingness to endorse harm in a moral dilemma is predicted by individual differences in aversive reactivity, as indexed by peripheral vasoconstriction. Next, we tested the specific factors that elicit the aversive response to harm. Participants performed actions such as discharging a fake gun into the face of the experimenter, fully informed that the actions were pretend and harmless. These simulated harmful actions increased (...) peripheral vasoconstriction significantly more than did witnessing pretend harmful actions or to performing metabolically-matched non-harmful actions. This suggests that the aversion to harmful actions extends beyond empathic concern for victim harm. Together, these studies demonstrate a link between the body and moral decision making processes. (shrink)

Excerpt from Die Entwicklung des Bewusstseinsbegriffes im XVII. Und XVIII. Jahrhundert Dunkelheit der Perzeptionen. Perceptions sans appet ception. Grunde für deren Annahme. Wesen der Apperzeption. Arten der Perzeptionen. About the Publisher Forgotten Books publishes hundreds of thousands of rare and classic books. Find more at www.forgottenbooks.com This book is a reproduction of an important historical work. Forgotten Books uses state-of-the-art technology to digitally reconstruct the work, preserving the original format whilst repairing imperfections present in the aged copy. In rare cases, (...) an imperfection in the original, such as a blemish or missing page, may be replicated in our edition. We do, however, repair the vast majority of imperfections successfully; any imperfections that remain are intentionally left to preserve the state of such historical works. (shrink)

Expressed emotion is a measure of the family environment that has been demonstrated to be a reliable, cross-culturally valid psychosocial predictor of relapse in patients with schizophrenia, mood disorders, and other — also somatic — illnesses. Assessed during the Camberwell Family Interview CFI, relatives are classified as being high in EE if they make more than a specified threshold number of critical comments or show any signs of hostility or marked emotional overinvolvement. In schizophrenia, the median relapse rate for patients (...) returning after hospital discharge to a high EE environment is 48%, compared with 21% in a low EE-environment. In this article, the history of EE research will be outlined, and the evidence for the association between family EE and the course of schizophrenia and mood disorders will be presented. Conclusions about the treatment of major mental disorders are discussed as well as the directions of future studies. (shrink)

Recent writers claim that responsibilist virtue epistemology courts skepticism, owing to the fact that most of us lack the virtues it deems necessary for justified belief and knowledge. A powerful version of this objection is the challenge from situationist social psychology pressed by Alfano (2012, 2013) and Olin and Doris (2014). This paper develops a new version of responsibilism that is immune from this objection, and shows that this view has many advantages over other forms of virtue epistemology. My responsibilism (...) dispenses with the ubiquitous but (I argue) mistaken idea that responsibilist virtue properties must be understood in terms of character traits. My view parallels an often overlooked form of virtue ethics suggested by Thomson (1997) that some situationists (e.g., Harman (2001)) have praised. That form shares with other forms the thought that virtue properties are normatively fundamental, but it adds that act-attaching ones are prior to person-attaching ones, and require no backing by character traits. Far from being an ad hoc retreat position, I argue that this view is independently attractive. (shrink)

James Griffin has considered a form of superiority in value that is weaker than lexical priority as a possible remedy to the Repugnant Conclusion. In this article, I demonstrate that, in a context where value is additive, this weaker form collapses into the stronger form of superiority. And in a context where value is non-additive, weak superiority does not amount to a radical value difference at all. These results are applied on one of Larry Temkin's cases against transitivity. I demonstrate (...) that Temkin appeals to two conflicting notions of aggregation. I then spell out the consequences of these results for different interpretations of Griffin's suggestion regarding population ethics. None of them comes out very successful, but perhaps they nevertheless retain some interest. (shrink)

One potentially morally justified use of torture is found in philanthropic torture of a perpetrator (PTP): scenarios in which a perpetrator has instigated significant pending suffering against innocents and in which the suffering can be prevented by means of the perpetrator’s cooperation. These situations involve a clash of two intuitions: that torture is in some strong and obvious sense absolutely morally wrong, and that torture or harm of an immoral perpetrator may be permissible to prevent equally abhorrent, if not greater, (...) moral wrongs. My view is that a dually grounded view—permissible on theoretical grounds but wrong on practical grounds—can do justice to the conflicting intuitions we have about torture in cases of PTP. Further, I hold that practical “absolutism” will only be “mostly” or “likely” absolute, but that we should accept as adequate this “near absolutism”—it will give us the practical result we seek while also satisfying the intuition that we may act in otherwise untoward ways to prevent horrific moral harms. (shrink)

[ES] El principio de contexto que Frege establece en Fundamentos de la Aritmética no reaparece en sus escritos posteriores, hecho que podría sugerir que a consecuencia de la sustitución de la noción de contenido juzgable por las de sentido y significado Frege lo rechazara después de 1890. Dummett arguye en 1995 que el principio de contexto continúa formando una parte central de la filosofía de lenguaje de Frege, pero que las teorías establecidas a partir del tomo I de Leyes fundamentales (...) de la aritmética ya no son compatibles con la noción de la perspectiva internalista atribuida a Frege por van Heijenoort e Hintikka. El presente trabajo arguye que Frege no sólo jamás abandonó el principio de contexto, sino que también mantuvo toda su vida la fe en el lenguaje como medio universal con la consiguiente imposibilidad de establecer, vía una teoría semántica, externamente las referencias de nuestros términos. [EN] Frege´s context principle, as put forward in Foundations of Arithmetic, is not mentioned in his later writings which might suggest that as a consequence of substituting the notion of judgeable content by sense and meaning, Frege would have abandoned the context principle after 1890. Dummett argues in 1993 that the context principle continues to form a central part of Frege’s language philosophy; theories put forth from volume I of Fundamental Laws of Arithmetic, however, are no longer compatible with the notion of an internalist perspective attributed to Frege by van Heijenoort and Hintikka. I argue currently that Frege not only never abandoned the context principle but all his life maintained his faith en language as universal medium making and therefore held it impossible to establish reference for our terms externally by means of a theory of meaning. (shrink)

*Tackles the Thomistic debate surrounding the inherent good and evil of human actions*.

Plausibility models are Kripke models that agents use to reason about knowledge and belief, both of themselves and of each other. Such models are used to interpret the notions of conditional belief, degrees of belief, and safe belief. The logic of conditional belief contains that modality and also the knowledge modality, and similarly for the logic of degrees of belief and the logic of safe belief. With respect to these logics, plausibility models may contain too much information. A proper notion (...) of bisimulation is required that characterises them. We define that notion of bisimulation and prove the required characterisations: on the class of image-finite and preimage-finite models, two pointed Kripke models are modally equivalent in either of the three logics, if and only if they are bisimilar. As a result, the information content of such a model can be similarly expressed in the logic of conditional belief, or the logic of degrees of belief, or that of safe belief. This, we found a surprising result. Still, that does not mean that the logics are equally expressive: the logics of conditional and degrees of belief are incomparable, the logics of degrees of belief and safe belief are incomparable, while the logic of safe belief is more expressive than the logic of conditional belief. In view of the result on bisimulation characterisation, this is an equally surprising result. We hope our insights may contribute to the growing community of formal epistemology and on the relation between qualitative and quantitative modelling. (shrink)

Arts and Humanities in Higher Education, Volume 21, Issue 2, Page 198-219, April 2022. This article presents playfulness as an emerging approach to learning in higher education that emphasises the arts and humanities across disciplines. The article is based on a qualitative, hermeneutical literature review in light of educational culture in higher education. The literature review indicates that playful approaches to learning stand in opposition to educational cultures that focus on rapidness and student performance. However, an educational culture of play (...) is about to establish itself, and this culture of play emphasises creativity in learning and human flourishing in education, perspectives that are connected to arts and humanities. The main findings cultures of time, performance and play lead to several questions about societal, institutional, and organisational educational culture, and regarding approaches to teaching, learning, humanity and society. The main contribution of this article is that a focus on playfulness offer the field of arts and humanities new possibilities in future education. (shrink)