Logic and Existence: Timothy Williams

The paper defends the intelligibility of unrestricted quantification. For any natural number n , 'There are at least n individuals' is logically true, when the quantifier is unrestricted. In response to the objection that such sentences should not count as logically true because existence is contingent, it is argued by consideration of cross-world counting principles that in the relevant sense of 'exist' existence is not contingent. A tentative extension of the upward Löwenheim–Skolem theorem to proper classes is used to argue that a sound and complete axiomatization of the logic of unrestricted universal quantification results from adding all sentences of the form 'There are at least n individuals' as axioms to a standard axiomatization of the first-order predicate calculus.
Of the many questions on which logic is neutral, one is usually supposed to be this: 'How many individuals are there?' On the alternative view defended below, truths about the number of individuals are logically true. They are not contingent logical truths, for it is not contingent what individuals there are.     

What the Liar Taught Achilles

Zeno's paradoxes of motion and the semantic paradoxes of the Liar have long been thought to have metaphorical affinities. There are, in fact, isomorphisms between variations of Zeno's paradoxes and variations of the Liar paradox in infinite-valued logic. Representing these paradoxes in dynamical systems theory reveals fractal images and provides other geometric ways of visualizing and conceptualizing the paradoxes.     

The Role of Family Routines in the Intergenerational Transmission of Depressive Symptoms between Parents and their Adolescent Children

Whereas previous research on environmental factors implicated in the intergenerational transmission of depression has tended to focus on the role of parenting quality (e.g., harshness), the current study sought to assess whether structural aspects of families may contribute to depression-relevant affective and immune processes in youths. Specifically, the present study examined the role of family routines in linking parental depressive symptoms to youth emotion regulation, a depression-relevant marker of low-grade inflammation, and depressive symptoms in youths. 261 parent-adolescent dyads reported on their own depressive symptoms, family routines, and youths’ emotion regulation abilities. In addition, peripheral blood was drawn from youths to assess levels of the proinflammatory cytokine interleukin 6 (IL-6). Path analyses provided support for a model in which parental depressive symptoms related to fewer family routines, which in turn were associated with higher IL-6 and depressive symptoms in youths as well as marginally associated with worse youth emotion regulation. Moreover, family routines were found to statistically account for part of the association between parent- and youth- depressive symptoms. Together, these results suggest that family routines may represent an additional facet of the family environment that can potentially contribute to the intergenerational transmission of depressive symptoms.     

Chronicity, severity, and timing of maternal depressive symptoms: relationships with child outcomes at age 5

The relationships between severity, chronicity, and timing of maternal depressive symptoms and child outcomes were examined in a cohort of 4,953 children. Mothers provided self-reports of depressive symptoms during pregnancy, immediately postpartum, and when the child was 6 months old and 5 years old. At the age 5 follow-up, mothers reported on children's behavior and children completed a receptive vocabulary test. Results suggest that both the severity and the chronicity of maternal depressive symptoms are related to more behavior problems and lower vocabulary scores in children. The interaction of severity and chronicity of maternal depressive symptoms was significantly related to higher levels of child behavior problems. Timing of maternal symptoms was not significantly related to child vocabulary scores, but more recent reports of maternal depressive symptoms were associated with higher rates of child behavior problems.     

Biparental failure in the childhood experiences of borderline patients

The purpose of this study was to assess the role of biparental abuse and neglect in the development of borderline personality disorder (BPD). A semistructured research interview was used to blindly assess the childhood experiences of biparental abuse and neglect reported by 358 borderline inpatients and 109 axis II controls. Eighty-four percent of borderline patients reported having experienced some type of biparental abuse or neglect before the age of 18; 55% reported a childhood history of biparental abuse; 77% reported a childhood history of biparental neglect. These experiences were also reported by a substantial percentage of Axis II controls (biparental abuse or neglect [61%], biparental abuse [31%], and biparental neglect [55%]). However, borderline patients were significantly more likely than axis II controls to report having been verbally, emotionally, and physically but not sexually abused by caretakers of both sexes. They were also significantly more likely than controls to report having caretakers of both sexes deny the validity of their thoughts and feelings, fail to provide them with needed protection, neglect their physical care, withdraw from them emotionally, and treat them inconsistently. It was also found that female borderlines who reported a previous history of neglect by a female caretaker and abuse by a male caretaker were at significantly higher risk for having been sexually abused by a noncaretaker. Taken together, the results of this study suggest that biparental failure may be a significant factor in the etiology of BPD. They also suggest that biparental failure may significantly increase a preborderline girl's risk of being sexually abused by someone other than her parents.