Consider an axiomatic set theory in which there is a distinction between “sets” and “classes,” only sets being allowable as elements. How can one define a finite sequence of classes? This problem was proposed to me by A. Tarski, and a solution is given in this note. We shall assume the axiom system Σ used by Godei in his study of the continuum hypothesis, and shall use the same notation.1.

1. The theory of classes presented in this paper is a simplification of that presented by J. von Neumann in his paper Die Axiomatisierung der Mengenlehre. However, this paper is written so that it can be read independently of von Neumann's. The principal modifications of his system are the following.(1) The idea of ordered pair is defined in terms of the other primitive concepts of the system. (See Axiom 4.3 below.)(2) A much simpler proof of the well-ordering theorem, based on (...) von Neumann's equivalence axiom (Axiom 2.2 below) is given. (More exactly, the theory of ordinal numbers, on which the proof of the well-ordering theorem is based, is simplified—see §8.)(3) Functions are not assumed to be defined for all arguments. In place of “ = A” we have “is undefined.” This makes possible a constructive interpretation of the system. (See §2.)2. We wish first to give a rough picture of the system which we are trying to construct. Suppose that we have the idea “class,” but no material from which to construct classes. Nevertheless, we can construct the class 0 having no elements. And then the class 1 having 0 as its only element. And then the classes {1}, and {0, 1}, etc., using always the previously constructed classes as elements. To extend this method to infinite classes, we must give rules telling what elements are to be included. Since the nature of the rules which we can use is not altogether clear, we try to formalize the whole system; that is, to set up a system of axioms which seems to characterize this system of classes. Now in this set of axioms we find it necessary to use the idea of function (in the “Axiom of Replacement”). (shrink)

This book covers a remarkable amount of ground and has become something of a classic. Besides the Discourse and the Meditations, it contains Private Thoughts, the third set of Objections and Replies, most of the Regulae, parts of the Principia and the Dioptrics, together with crrespondence with Elizabeth, Princess Palatine, Mersenne and others.

Este libro es un homenaje a la trayectoria intelectual y académica de la profesora María Teresa López de la Vieja, Catedrática emérita de la Universidad de Salamanca. En él se trazan algunos de los caminos que, con su obra, nos invita a transitar. El volumen recoge contribuciones de colegas de varias nacionalidades y procedentes de diversos ámbitos de reflexión que le son afines: la filosofía moral y política, la literatura, la teoría de la argumentación, los estudios feministas, las éticas aplicadas, (...) la bioética. Los capítulos que componen este libro dan voz a varias generaciones de investigadoras e investigadores que han acompañado y acompañan su andadura académica y que aquí dialogan con ella haciendo propias sus preocupaciones intelectuales. Con su participación contribuyen al justo reconocimiento de su dedicación a la labor docente e investigadora. (shrink)

P. M. Asaro: What should We Want from a Robot Ethic? G. Tamburrini: Robot Ethics: A View from the Philosophy of Science B. Becker: Social Robots - Emotional Agents: Some Remarks on Naturalizing Man-machine Interaction E. Datteri, G. Tamburrini: Ethical Reflections on Health Care Robotics P. Lin, G. Bekey, K. Abney: Robots in War: Issues of Risk and Ethics J. Altmann: Preventive Arms Control for Uninhabited Military Vehicles J. Weber: Robotic warfare, Human Rights & The Rhetorics of Ethical Machines T. (...) Nishida: Towards Robots with Good Will R. Capurro: Ethics and Robotics. (shrink)

Over the last few years, automatic facial micro-expression analysis has garnered increasing attention from experts across different disciplines because of its potential applications in various fields such as clinical diagnosis, forensic investigation and security systems. Advances in computer algorithms and video acquisition technology have rendered machine analysis of facial micro-expressions possible today. Although the study of facial micro-expressions is a well-established field in psychology, it is still relatively new from the computational perspective with many interesting problems. In this survey, we (...) present a comprehensive review of state-of-the-art databases and methods for micro-expressions spotting and recognition. Individual stages involved in the automation of these tasks are also described and reviewed at length. In addition, we also deliberate on the challenges and future directions in this growing field of automatic facial micro-expression analysis. (shrink)

A historically-informed account of the lasting importance of embodied thought in the intellectual trajectory of René Descartes, still remembered today as the founding father of dualism.

Progressive supranuclear palsy is a movement disorder with prominent tau neuropathology. Brain diseases with abnormal tau deposits are called tauopathies, the most common of which is Alzheimer's disease. Environmental causes of tauopathies include repetitive head trauma associated with some sports. To identify common genetic variation contributing to risk for tauopathies, we carried out a genome-wide association study of 1,114 individuals with PSP and 3,247 controls followed by a second stage in which we genotyped 1,051 cases and 3,560 controls for the (...) stage 1 SNPs that yielded P ≤ 10-3. We found significant previously unidentified signals associated with PSP risk at STX6, EIF2AK3 and MOBP. We confirmed two independent variants in MAPT affecting risk for PSP, one of which influences MAPT brain expression. The genes implicated encode proteins for vesicle-membrane fusion at the Golgi-endosomal interface, for the endoplasmic reticulum unfolded protein response and for a myelin structural component. © 2011 Nature America, Inc. All rights reserved. (shrink)

The aim of this study was to analyze the association between physical activity and eating habits during the COVID-19 pandemic among Brazilian adults. A sample of 1,929 participants answered an online survey, however 1,874 were included in the analysis. The impact of the COVID-19 pandemic on eating habits was assessed inquiring about participants' intake of fruits, vegetables, fried foods, and sweets during the pandemic. Physical activity was assessed by asking participants about their weekly frequency, intensity and number of minutes/hours engaging (...) in structured physical activities per week. Participants were then stratified into categories based on moderate-to-vigorous intensity and into active or inactive. Increased sweets consumption was the most commonly reported change to eating habits, followed by an increase in the consumption of vegetables, fruits, and fried foods. Physical activity practice was related to lower consumption of fried foods and sweets. A cluster analysis revealed subjects with higher the level of physical activity was more likely to follow a healthy diet. Thus, physical activity was positively associated with healthier eating habits. Health authorities must recommend regular physical as a strategy to improve overall health during the COVID-19 pandemic. Future studies should address the physical activity interventions to improve health status during a pandemic. (shrink)

BackgroundThe outbreak of novel coronavirus disease 2019 has caused a global panic and public concern due to its mortality ratio and lack of treatments/vaccines. Reduced levels of physical activity have been reported during the outbreak, affecting the normal daily pattern.ObjectiveTo investigate the relationship of physical activity level with sleep quality and the effects of reduction physical activity levels on sleep quality.MethodsA Google form was used to address personal information, COVID-19 personal care, physical activity, and mental health of 1,907 adult volunteers. (...) Binary logistic regression was used to verify the association of physical activity parameters and sleep quality.ResultsInsufficient physical activity levels were a risk factor to have disturbed sleep pattern [OR: 1.28, 95% CI ]; however, when the BMI was added to the analysis, there was no more statistical difference [OR: 1.23, 95% CI ]. On the other hand, we found that the reduction of physical activity levels was associated with negative changes in sleep quality [OR: 1.73, 95% CI ], regardless all the confounders [OR: 1.30, 95% CI ], unless when feeling of depression was added in Model 6 [OR: 1.28, 95% CI ].ConclusionDisruption in daily physical activity routine, rather than physical activity level, negatively influences sleep quality during the COVID-19 quarantine. (shrink)