On the status of proofs by contradiction in the seventeenth century

In this paper I show that proofs by contradiction were a serious problem in seventeenth century mathematics and philosophy. Their status was put into question and positive mathematical developments emerged from such reflections. I analyse how mathematics, logic, and epistemology are intertwined in the issue at hand. The mathematical part describes Cavalieri's and Guldin's mathematical programmes of providing a development of parts of geometry free of proofs by contradiction. The logical part shows how the traditional Aristotelean doctrine that perfect demonstrations are causal demonstrations influenced the reflection on proofs by contradiction. The main protagonist of this part is Wallis. Finally, I analyse some epistemological developments arising from the Cartesian tradition. In particular, I look at Arnauld's programme of providing an epistemologically motivated reformulation of Geometry free of proofs by contradiction. The conclusion explains in which sense these epistemological reflections can be compared with those informing contemporary intuitionism.     

I know a dog when I see one: dogs (Canis familiaris) recognize dogs from videos

Animal Cognition - Several aspects of dogs’ visual and social cognition have been explored using bi-dimensional representations of other dogs. It remains unclear, however, if dogs do...     

Bayesian inference for graphical factor analysis models

We generalize factor analysis models by allowing the concentration matrix of the residuals to have nonzero off-diagonal elements. The resulting model is named graphical factor analysis model. Allowing a structure of associations gives information about the correlation left unexplained by the unobserved variables, which can be used both in the confirmatory and exploratory context. We first present a sufficient condition for global identifiability of this class of models with a generic number of factors, thereby extending the results in Stanghellini (1997) and Vicard (2000). We then consider the issue of model comparison and show that fast local computations are possible for this purpose, if the conditional independence graphs on the residuals are restricted to be decomposable and a Bayesian approach is adopted. To achieve this aim, we propose a new reversible jump MCMC method to approximate the posterior probabilities of the considered models. We then study the evolution of political democracy in 75 developing countries based on eight measures of democracy in two different years. We acknowledge support from M.U.R.S.T. of Italy and from the European Science Foundation H.S.S.S. Network. We are grateful to the referees and the Editor for many useful suggestions and comments which led to a substantial improvement of the paper. We also thank Nanny Wermuth for stimulating discussions and Kenneth A. Bollen for kindly providing us with the data-set.     

Response demands and the recruitment of heuristic strategies in syllogistic reasoning

Two experiments investigated whether dealing with a homogeneous subset of syllogisms with time-constrained responses encouraged participants to develop and use heuristics for abstract (Experiment 1) and thematic (Experiment 2) syllogisms. An atmosphere-based heuristic accounted for most responses with both abstract and thematic syllogisms. With thematic syllogisms, a weaker effect of a belief heuristic was also observed, mainly where the correct response was inconsistent with the atmosphere of the premises. Analytic processes appear to have played little role in the time-constrained condition, whereas their involvement increased in a self-paced, unconstrained condition. From a dual-process perspective, the results further specify how task demands affect the recruitment of heuristic and analytic systems of reasoning. Because the syllogisms and experimental procedure were the same as those used in a previous neuroimaging study by Goel, Buchel, Frith, and Dolan (2000), the result also deepen our understanding of the cognitive processes investigated by that study.     

Systemic-Oriented Psychological Counselling for Caregivers of People with Severe Brain Injury: Reflections on a Clinical Case

Severe brain injuries can have dramatic consequences on family life, often changing rules and routines and fostering intense and prolonged caregiving duties. People affected by the injuries have to face relevant restrictions in their activities and a loss of independence. Thus, primary caregivers are often involved in their assistance, which can entail the help for self-care, movements and many activities of daily living. Furthermore, cognitive and behavioural symptoms can complicate communication, disrupt previous relationships and put an additional strain on all family members. Indeed, caregiving relationships take place in wider familial and societal contexts and are obviously influenced by previous characteristic of such relationships, as they were before the onset of the pathological condition. Therefore, a thorough examination of typical emotions, feelings and thoughts that can emerge during caregiving must be paralleled by an ecological and developmental perspective, in order to appraise the complexity of these cases and provide effective interventions. The present work aims to address such topics taking inspiration from a clinical case.     

Prospective memory and intraindividual variability in ongoing task response times in an adult lifespan sample: the role of cue focality

To contribute to the ongoing conceptual debate of what traditional mean-level ongoing task (OT) costs tell us about the attentional processes underlying prospective memory (PM), we investigated costs to intraindividual variability (IIV) in OT response times as a potentially sensitive indicator of attentional processes. Particularly, we tested whether IIV in OT responses may reflect controlled employment of attentional processes versus lapses of controlled attention, whether these processes differ across adulthood, and whether it is moderated by cue focality. We assessed 150 individuals (19–82 years) in a focal and a nonfocal PM condition. In addition, external measures of inhibition and working memory were assessed. In line with the predictions of the lapses-of-attention/inefficient-executive-control account, our data support the view that costs to IIV in OT trials of PM tasks reflect fluctuations in the efficiency of executive functioning, which was related to failures in prospective remembering, particularly in nonfocal PM tasks, potentially due to their increased executive demands. The additional value of considering costs to IIV over and beyond traditional mean-level OT costs in PM research is discussed.     

Recognition of human faces by dogs (<Emphasis Type="Italic">Canis familiaris</Emphasis>) requires visibility of head contour

Researchers have suggested that dogs are able to recognise human faces, but conclusive evidence has yet to be found. Experiment 1 of this study investigated whether dogs can recognise humans using visual information from the face/head region, and whether this also occurs in conditions of suboptimal visibility of the face. Dogs were presented with their owner’s and a stranger’s heads, protruding through openings of an apparatus in opposite parts of the experimental setting. Presentations occurred in conditions of either optimal or suboptimal visibility; the latter featured non-frontal orientation, uneven illumination and invisibility of outer contours of the heads. Instances where dogs approached their owners with a higher frequency than predicted by chance were considered evidence of recognition. This occurred only in the optimal condition. With a similar paradigm, Experiment 2 investigated which of the alterations in visibility that characterised the suboptimal condition accounted for dogs’ inability to recognise owners. Dogs approached their owners more frequently than predicted by chance if outer head contours were visible, but not if heads were either frontally oriented or evenly illuminated. Moreover, male dogs were slightly better at recognition than females. These findings represent the first clear demonstration that dogs can recognise human faces and that outer face elements are crucial for such a task, complementing previous research on human face processing in dogs. Parallels with face recognition abilities observed in other animal species, as well as with human infants, point to the relevance of these results from a comparative standpoint.     

A Longitudinal Study of Parental Depressive Symptoms and Coparenting in the First 18 Months

Although the negative impact of postpartum depression on parenting behaviors has been well established—albeit separately—for mothers and fathers, the respective and joint impact of both parents' mood on family‐group interactive behaviors, such as coparenting support and conflict behaviors between the parents, have not yet been investigated. The aim of this study was to examine the association between parental depressive symptoms and coparenting behaviors in a low‐risk sample of families with infants, exploring reciprocity between the variables, as well as gender differences between mothers and fathers regarding these links. At 3 (T1), 9 (T2), and 18 months postpartum (T3), we assessed both parents' depressive symptoms with a self‐report questionnaire and observed coparenting support and conflict during triadic mother–father–child interactions. The results revealed that higher maternal depressive symptoms at T1 were associated with lower support at T1 and T2. Conflict at T3 was associated with higher maternal depressive symptoms at T3 and, more surprisingly, with less depressive symptoms in mothers at T2 and fathers at T3. Cross‐lagged associations suggested that parental depressive symptoms were more likely to influence coparenting than the reverse. Moreover, maternal depressive symptoms were more likely to be linked to coparenting behaviors than were paternal depressive symptoms. These results confirm that parental—mostly maternal—depressive symptoms, even of mild intensity, may jeopardize the development of healthy family‐level relations, which previous research has shown to be crucial for child development.     

Who Are the Children Most Vulnerable to Social Exclusion? The Moderating Role of Self-Esteem,Popularity, and Nonverbal Intelligence on Cognitive Performance Following Social Exclusion

Social exclusion has a profound emotional impact on children. However, there is still limited and partly conflicting experimental evidence for the possible effect of social exclusion on children’s cognitive performance. In the present study, we tested the possibility that some children are more vulnerable than others to the negative effects of social exclusion on cognitive performance. We selected 4 potential candidates that could moderate the effects of social exclusion: relational self-esteem, peer ratings of popularity, rejection sensitivity and nonverbal intelligence. Individual differences in these 4 potential moderating factors were first assessed in a sample of 318 children (45.6 % females; mean age = 9.92 years). Then, in a subsequent experimental session, the participants were either socially included or excluded using a typical manipulation (i.e., the Cyberball paradigm). Following the manipulation, the children’s cognitive performance was assessed using a logical reasoning test. The results showed that the children with lower scores for relational self-esteem (the bottom 37.46 % of the sample), lower popularity (43.49 %) or weaker nonverbal intelligence (37.80 %) performed worse on the logical reasoning test following social exclusion. Moreover, children with combined low self-esteem, popularity and nonverbal intelligence were the most affected by social exclusion. This study identified factors that make some children more vulnerable to the negative effects of social exclusion. Overall, the present work underscores the value of considering basic cognitive and relational individual differences when developing interventions aimed at preventing the negative effects of social exclusion among children.