A note on mathematical pluralism and logical pluralism

Mathematical pluralism notes that there are many different kinds of pure mathematical structures—notably those based on different logics—and that, qua pieces of pure mathematics, they are all equally good. Logical pluralism is the view that there are different logics (consequence relations), which are, in an appropriate sense, equally good. Some, such as Shapiro (Varieties of logic, Oxford University Press, Oxford, 2014), have argued that mathematical pluralism entails logical pluralism. In this brief note I argue that this does not follow. There is a crucial distinction to be drawn between the preservation of truth (simpliciter) and the preservation of truth-in-a-structure; and once this distinction is drawn, this suffices to block the argument. The paper starts by clarifying the relevant notions of mathematical and logical pluralism. It then explains why the argument from the first to the second does not follow. A final section considers a few objections.

     

The impact of novel labels on visual processing during infancy

The impact of novel labels on visual processing was investigated across two experiments with infants aged between 9 and 21 months. Infants viewed pairs of images across a series of preferential looking trials. On each trial, one image was novel, and the other image had previously been viewed by the infant. Some infants viewed images in silence; other infants viewed images accompanied by novel labels. The pattern of fixations both across and within trials revealed that infants in the labelling condition took longer to develop a novelty preference than infants in the silent condition. Our findings contrast with prior research by Robinson and Sloutsky (e.g., Robinson & Sloutsky, 2007a ; Sloutsky & Robinson, 2008 ) who found that novel labels did not disrupt visual processing for infants aged over a year. Provided that overall task demands are sufficiently high, it appears that labels can disrupt visual processing for infants during the developmental period of establishing a lexicon. The results suggest that when infants are processing labels and objects, attentional resources are shared across modalities.     

Pregnancy-specific stress, prenatal health behaviors, and birth outcomes

OBJECTIVE: Stress in pregnancy predicts earlier birth and lower birth weight. The authors investigated whether pregnancy-specific stress contributes uniquely to birth outcomes compared with general stress, and whether prenatal health behaviors explain this association. DESIGN: Three structured prenatal interviews (N = 279) assessing state anxiety, perceived stress, life events, pregnancy-specific stress, and health behaviors. MAIN OUTCOME MEASURES: Gestational age at delivery, birth weight, preterm delivery (<37 weeks), and low birth weight (<2,500 g). RESULTS: A latent pregnancy-specific stress factor predicted birth outcomes better than latent factors representing state anxiety, perceived stress, or life event stress, and than a latent factor constructed from all stress measures. Controlling for obstetric risk, pregnancy-specific stress was associated with smoking, caffeine consumption, and unhealthy eating, and inversely associated with healthy eating, vitamin use, exercise, and gestational age at delivery. Cigarette smoking predicted lower birth weight. Clinically-defined birth outcomes were predicted by cigarette smoking and pregnancy-specific stress. CONCLUSION: Pregnancy-specific stress contributed directly to preterm delivery and indirectly to low birth weight through its association with smoking. Pregnancy-specific stress may be a more powerful contributor to birth outcomes than general stress.     

Equity, justice, and altruism

According to traditional equity theory, justice is motivated by selfishness. However, critics of equity have argued that it is only one rule of justice that people can apply, and that sometimes other rules of justice are used, such as equality and need, that appear to be altruistically based; that is, they involve sharing and caring in a way that ignores contributions or “inputs” and the probability of receiving outcomes in return. Disagreements have arisen, however, as to the status of these alternative rules as elements of justice, the roles of altruism and selfishness within them, and the relative status of altruism and justice as moral principles. The main aim of this article is to help resolve some of these difficulties by examining the relationship between altruism and justice from the perspective of Wagstaff s theory of Equity as Desert (EAD). This theory integrates a number of allocation rules (including those related to the treatment of offenders) with the concepts of equal opportunity and personal responsibility. One of the advantages of this position is that it enables a conceptual and an empirical distinction to be made between helping and responsiveness to need as altruistic norms, and helping and responsiveness to need as justice norms. It is concluded that there may be something to be gained from viewing core rules of justice in the form of EAD as the sophisticated descendants of the sociobiological concept of reciprocal altruism, that is, a set of algorithms designed to limit both unbridled selfishness and indiscrimi-nate altruism.