The study of the sobriety of Scott spaces has got a relatively long history in domain theory. Lawson and Hoffmann independently proved that the Scott space of every continuous directed complete poset (usually called domain) is sober. Johnstone constructed the first directed complete poset whose Scott space is non-sober. Soon after, Isbell gave a complete lattice with a non-sober Scott space. Based on Isbell’s example, Xu, Xi, and Zhao showed that there is even a complete Heyting algebra whose Scott space is non-sober. Achim Jung then asked whether every countable complete lattice has a sober Scott space. The main aim of this paper is to answer Jung’s problem by constructing a countable complete lattice whose Scott space is non-sober. This lattice is then modified to obtain a countable distributive complete lattice with a non-sober Scott space. In addition, we prove that the topology of the product space $\Sigma P\times \Sigma Q$ coincides with the Scott topology of the product poset $P\times Q$ if the set Id(P) and Id(Q) of all incremental ideals of posets P and Q are both countable. Based on this, it is deduced that a directed complete poset P has a sober Scott space, if Id(P) is countable and $\Sigma P$ is coherent and well filtered. In particular, every complete lattice L with Id(L) countable has a sober Scott space.

For a $T_0$ space X, let $\mathsf{K}(X)$ be the poset of all nonempty compact saturated subsets of X endowed with the Smyth order $\sqsubseteq$. $(\mathsf{K}(X), \sqsubseteq)$ (shortly $\mathsf{K}(X)$) is called the Smyth power poset of X. In this paper, we mainly discuss some basic properties of the Scott topology on Smyth power posets. It is proved that for a well-filtered space X, its Smyth power poset $\mathsf{K}(X)$ with the Scott topology is still well-filtered, and a $T_0$ space Y is well-filtered iff the Smyth power poset $\mathsf{K}(Y)$ with the Scott topology is well-filtered and the upper Vietoris topology is coarser than the Scott topology on $\mathsf{K}(Y)$. A sober space Z is constructed for which the Smyth power poset $\mathsf{K}(Z)$ with the Scott topology is not sober. A few sufficient conditions are given for a $T_0$ space X under which its Smyth power poset $\mathsf{K}(X)$ with the Scott topology is sober. Some other properties, such as local compactness, first-countability, Rudin property and well-filtered determinedness, of Smyth power spaces, and the Scott topology on Smyth power posets, are also investigated.

Why do many societies moralize apparently harmless pleasures, such as lust, gluttony, alcohol, drugs, and even music and dance? Why do they erect temperance, asceticism, sobriety, modesty, and piety as cardinal moral virtues? According to existing theories, this puritanical morality cannot be reduced to concerns for harm and fairness: It must emerge from cognitive systems that did not evolve for cooperation (e.g., disgust-based “purity” concerns). Here, we argue that, despite appearances, puritanical morality is no exception to the cooperative function of moral cognition. It emerges in response to a key feature of cooperation, namely that cooperation is (ultimately) a long-term strategy, requiring (proximately) the self-control of appetites for immediate gratification. Puritanical moralizations condemn behaviors which, although inherently harmless, are perceived as indirectly facilitating uncooperative behaviors, by impairing the self-control required to refrain from cheating. Drinking, drugs, immodest clothing, and unruly music and dance are condemned as stimulating short-term impulses, thus facilitating uncooperative behaviors (e.g., violence, adultery, free-riding). Overindulgence in harmless bodily pleasures (e.g., masturbation, gluttony) is perceived as making people slave to their urges, thus altering abilities to resist future antisocial temptations. Daily self-discipline, ascetic temperance, and pious ritual observance are perceived as cultivating the self-control required to honor prosocial obligations. We review psychological, historical, and ethnographic evidence supporting this account. We use this theory to explain the fall of puritanism in western, educated, industrialized, rich, and democratic (WEIRD) societies, and discuss the cultural evolution of puritanical norms. Explaining puritanical norms does not require adding mechanisms unrelated to cooperation in our models of the moral mind.

Alcohol use disorder (AUD) has been a major cause of family, social, and personal strife for centuries, with current prevalence estimates of 14% for 12-month and 29% lifetime AUD. Neuropsychological testing of selective cognitive, sensory, and motor functions complemented with in vivo brain imaging has enabled tracking the consequences of AUD, which follows a dynamic course of development, maintenance, and recovery or relapse. Controlled studies of alcoholism reviewed herein provide evidence for disruption of selective functions involving executive, visuospatial, mnemonic, emotional, and attentional processes, response inhibition, prosody, and postural stability and brain systems supporting these functions. On a hopeful front, longitudinal study provides convincing evidence for improvement in brain structure and function following sustained sobriety. These discoveries have a strong legacy in the International Neuropsychological Society (INS), starting from its early days when assumptions regarding which brain regions were disrupted relied solely on patterns of functional sparing and impairment deduced from testing. This review is based on the symposium presentation delivered at the 2017 annual North American meeting of the INS in celebration of the 50th anniversary since its institution in 1967. In the spirit of the meeting’s theme, “Binding the Past and Present,” the lecture and this review recognized the past by focusing on early, rigorous neuropsychological studies of alcoholism and their influence on research currently conducted using imaging methods enabling hypothesis testing of brain substrates of observed functional deficits. (JINS, 2017, 23, 843–859)