Faces of irrationality in Euripides: on Medea's Irrationality

In Nascimento (2015) I criticized the thesis defended in Irwin (1983) according to which two of the most famous characters in Euripides’ plays, Phaedra and Medea, could be said to exemplify akratic behavior and, in the case of Phaedra, even to explain it. In that article, I’ve pointed out several weakness in these thesis in order to justify my disagreement. I also suggested that, although there was no reason why we should stop looking for examples and explanations of akratic behavior in Euripides’ plays, that should not be the only kind of irrational behavior we ought to be interested in finding there. In this paper, I argue that Medea actually instantiates a form of irrational behavior that is different from akratic behavior. The argument that follows is divided in four parts. After a brief introduction (section I), I clarify what sort of irrationality I believe to be instantiated by Medea’s behavior using Michael Bratman’s theory of plan stability (section II). Then, I analyze Euripides’ text in order to show why I think we should say that Medea does display that kind of irrationality (section III). The paper concludes with a brief summary of the argument (section IV)

Aristotle on the Normative Value of Friendship Duties

In this article, I present an interpretation of Aristotle’s thought regarding the normative value of friendship duties.The argument is divided in VII sections. In Section I, I provide brief summaries of the main arguments defended by me in a previous article about the normative consequences of virtue and utility friendships in Aristotle, the objectives that are to be defended in this article and of the conclusions that I take them to support. In section II, I offer an interpretation of Aristotle’s thought regarding the normative value of friendship duties in cases where there is no practical conflict between friendship duties. In section III, I outline Aristotle’s theory about how we should deal with cases where there is such practical conflict. In the next sections, I analyze three other passages of the Aristotelian corpus where we have good reason to think that this kind of conflict appears, namely, NE, III 1, 1110a20-29 (IV), Pol., III 10, 1286b23-28 (V) and Pol., VII 9, 1330a9-25 (VI), in order to flesh out the outline presented in section III. In section VII I conclude with a summary of the argument

Spatial and spin symmetry breaking in semidefinite-programming-based Hartree-Fock theory

The Hartree-Fock problem was recently recast as a semidefinite optimization over the space of rank-constrained two-body reduced-density matrices (RDMs) [Phys. Rev. A 89, 010502(R) (2014)]. This formulation of the problem transfers the non-convexity of the Hartree-Fock energy functional to the rank constraint on the two-body RDM. We consider an equivalent optimization over the space of positive semidefinite one-electron RDMs (1-RDMs) that retains the non-convexity of the Hartree-Fock energy expression. The optimized 1-RDM satisfies ensemble $N$-representability conditions, and ensemble spin-state conditions may be imposed as well. The spin-state conditions place additional linear and nonlinear constraints on the 1-RDM. We apply this RDM-based approach to several molecular systems and explore its spatial (point group) and spin ($S^2$ and $S_3$) symmetry breaking properties. When imposing $S^2$ and $S_3$ symmetry but relaxing point group symmetry, the procedure often locates spatial-symmetry-broken solutions that are difficult to identify using standard algorithms. For example, the RDM-based approach yields a smooth, spatial-symmetry-broken potential energy curve for the well-known Be--H$_2$ insertion pathway. We also demonstrate numerically that, upon relaxation of $S^2$ and $S_3$ symmetry constraints, the RDM-based approach is equivalent to real-valued generalized Hartree-Fock theory.Comment: 9 pages, 6 figure

Entre a família e a comunidade política: amizade, justiça e conflito prático em Aristóteles

O artigo tem por objetivo mostrar que, ao contrário do que muitos parecem ainda acreditar, a filosofia aristotélica reconhece a possibilidade de um conflito prático genuíno entre a busca do bem individual e a busca do bem da comunidade política por parte de um mesmo indivíduo. As conclusões alcançadas são puramente negativas. Este artigo terá cumprido o seu objetivo se contribuir para despertar no leitor o reconhecimento do problema e da necessidade de investigações ulteriores

Akrasia e irracionalidade em Eurípides

O principal objetivo deste artigo é criticar a leitura de duas peças de Eurípides, Hipólito e Medéia, que nos é oferecida por Terence Irwin, no artigo intitulado “Euripides and Socrates”, de 1983. No final, aponto para a necessidade de um estudo cuidadoso das diferentes formas de irracionalidade encenadas na obra de Eurípides

Constrangimento e ignorância da teoria aristotélica do ato voluntário

Neste artigo é apresentada uma interpretação dos critérios propostos por Aristóteles para separar as ações voluntárias das demais ações, assim como do tratamento aristotélico das ações mistas, das não-voluntárias e das reações morais que lhes são devidas. A interpretação defendida se concentra na Ética Nicomaquéia (EN) e faz uso da Ética Eudêmia (EE) apenas ocasionalmente. Só podemos afirmar que agimos de forma involuntária ou não-voluntária quando somos constrangidos a sofrer uma determinada ação ou quando realizamos algo por acidente

Socrates, Vlastos, Scanlon and the Principle of the Sovereignty of Virtue

Abstract: This article offers a new formulation of the Socratic principle known as the Principle of the Sovereignty of Virtue (PSV). It is divided in three sections. In the first section I criticize Vlastos’ formulation of the PSV. In the second section I present the weighing model of practical deliberation, introduce the concepts of reason for action, simple reason, sufficient reason and conclusive reason that were offered by Thomas Scanlon in Being realistic about reasons (2014), and then I adapt these concepts so as to render them apt to be used in the formulation I intend to offer. In the third section I present my formulation of the PSV using the concepts introduced in the second section and explain why I believe this formulation is better than the one offered by Vlastos