Conditional Random Quantities and Compounds of Conditionals

In this paper we consider conditional random quantities (c.r.q.’s) in the setting of coherence. Based on betting scheme, a c.r.q. X|H is not looked at as a restriction but, in a more extended way, as \({XH + \mathbb{P}(X|H)H^c}\) ; in particular (the indicator of) a conditional event E|H is looked at as EH +  P(E|H)H ^c . This extended notion of c.r.q. allows algebraic developments among c.r.q.’s even if the conditioning events are different; then, for instance, we can give a meaning to the sum X|H + Y|K and we can define the iterated c.r.q. (X|H)|K. We analyze the conjunction of two conditional events, introduced by the authors in a recent work, in the setting of coherence. We show that the conjoined conditional is a conditional random quantity, which may be a conditional event when there are logical dependencies. Moreover, we introduce the negation of the conjunction and by applying De Morgan’s Law we obtain the disjoined conditional. Finally, we give the lower and upper bounds for the conjunction and disjunction of two conditional events, by showing that the usual probabilistic properties continue to hold.     

Numerical acuity of fish is improved in the presence of moving targets,but only in the subitizing range

There is controversy in comparative psychology about whether on the one hand non-symbolic number estimation of small (≤4) and large numbers involves a single mechanism (an approximate number system), or whether on the other hand enumeration of the numbers 1–4 is accomplished by a separate mechanism, an object tracking system. To date, support for the latter hypothesis has come only from the different ratio-dependency of performance seen in the two numerical ranges, a reading that has been criticized on several grounds. In humans, the two-system hypothesis is supported by evidence showing that manipulation of the physical properties of the stimuli (e.g., the motion of the items) has dissimilar effects on small- and large-number discrimination. In this research, we studied this effect on guppies. Initially, fish were trained to simultaneously discriminate two numerical contrasts having the same easy ratio (0.50): one in the small-number (2 vs. 4) range and one in the large-number (6 vs. 12) range. Half of the fish were presented with moving items; the other half were shown the same stimuli without motion. Fish were then subjected to non-reinforced probe trials in the presence of a more difficult ratio (0.75: 3 vs. 4 and 9 vs. 12). Under both static and moving conditions, the fish significantly discriminated 6 versus 12, but not 9 versus 12 items. As regards small numbers, both groups learned to discriminate a 0.50 ratio, but only fish tested with moving stimuli also discriminated 3 and 4 items. This differential effect suggests that fish may possess two separate systems for small- and large-number discrimination.     

Extensive training extends numerical abilities of guppies

Recent studies on animal mathematical abilities suggest that all vertebrates show comparable abilities when they are given spontaneous preference tests, such as selecting the larger number of food items, but that mammals and birds generally achieve much better performance than fish when tested with training procedures. At least part of these differences might be due to the fact that fish are usually trained with only one or two dozen trials while extensive training, sometimes with thousands of trials, is normally performed in studies of mammals and birds. To test this hypothesis, female guppies were trained on four consecutive numerical discriminations of increasing difficulty (from 2 vs. 3 to 5 vs. 6 items), with up to 120 trials with each discrimination. Five out of eight subjects discriminated all contrasts up to 4 versus 5 objects at levels significantly better than chance, a much higher limit than the 2 versus 3 limit previously reported in studies that provided fish with only short training sequences. Our findings indicate that the difference in numerical cognition between teleosts and warm-blooded vertebrates might be smaller than previously supposed.     

Explaining social norm compliance. A plea for neural representations

How should we understand the claim that people comply with social norms because they possess the right kinds of beliefs and preferences? I answer this question by considering two approaches to what it is to believe (and prefer), namely: representationalism and dispositionalism. I argue for a variety of representationalism, viz. neural representationalism. Neural representationalism is the conjunction of two claims. First, what it is essential to have beliefs and preferences is to have certain neural representations. Second, neural representations are often necessary to adequately explain behaviour. After having canvassed one promising way to understand what neural representations could be, I argue that the appeal to beliefs and preferences in explanations of paradigmatic cases of norm compliance should be understood as an appeal to neural representations.     

Action simulation in the human brain: Twelve questions

Although the idea of action simulation is nowadays popular in cognitive science, neuroscience and robotics, many aspects of the simulative processes remain unclear from empirical, computational, and neural perspectives. In the first part of the article, we provide a critical review and assessment of action simulation theories advanced so far in the wider literature of embodied and motor cognition. We focus our analysis on twelve key questions, and discuss them in the context of human and (occasionally) primate studies. In the second part of the article, we describe an integrative neuro-computational account of action simulation, which links the neural substrate (as revealed in neuroimaging studies of action simulation) to the components of a computational architecture that includes internal modeling, action monitoring and inhibition mechanisms.     

Mereology and mathematics: Christian Wolff's foundational programme

ABSTRACT

How did the traditional doctrine of parts and wholes evolve into contemporary formal mereology? This paper argues that a crucial missing link may lie in the early modern and especially Wolffian transformation of mereology into a systematic sub-discipline of ontology devoted to quantity. After some remarks on the traditional scholastic approach to parts and wholes (Sect. 1), Wolff's mature mereology is reconstructed as an attempt to provide an ontological foundation for mathematics (Sects. 2–3). On the basis of Wolff's earlier mereologies (Sect. 4), the origin of this foundational project is traced back to one of Wolff's private conversations with Leibniz (Sect. 5) and especially to the former's appropriation of the latter's notion of similarity as a means to define quantity (Sect. 6). Despite some hesitancy concerning the ultimate characterization of quantity (Sect. 7), Wolff's contribution was historically significant and influential. By developing a quantitative, extensional account of mereological relations, Wolff departed from the received doctrine and paved the way for the later revival of mereology at the intersection of ontology and mathematics.     

Systematic review of instruments measuring homophobia and related constructs

Since its conceptualization, the construct of homophobia has been the subject of many speculations about its specificity, reach, and possibility of empirical assessment. Several instruments have been created aiming to measure the prejudice against homosexuals. Peer‐reviewed articles of studies using measures to assess homophobia and related constructs were systematically reviewed in 4 databases (Medline, PsycINFO, ERIC, JSTOR). The articles were classified as they displayed evidence of the instrument's validity, reliability, or both. Finally, the instruments were rated according to that evidence. Out of 1076 results, 115 studies between 1993 and 2010 were identified as relevant. Those studies used 47 different instruments. This review focused in 5 instruments that concentrated the majority of the citations. Psychometric properties were acceptable.     

Pacifism and Punishment

This article seeks to expose some of the implications of certain versions of pacifism for matters of criminal punishment, arguing that the plausibility of these versions of pacifism depend on the extent to which their implicit denials of certain central punishment-related concepts are themselves reasonable.     

The Case of Online Trust

This paper contributes to the debate on online trust addressing the problem of whether an online environment satisfies the necessary conditions for the emergence of trust. The paper defends the thesis that online environments can foster trust, and it does so in three steps. Firstly, the arguments proposed by the detractors of online trust are presented and analysed. Secondly, it is argued that trust can emerge in uncertain and risky environments and that it is possible to trust online identities when they are diachronic and sufficient data are available to assess their reputation. Finally, a definition of trust as a second-order property of first-order relation is endorsed in order to present a new definition of online trust. According to such a definition, online trust is an occurrence of trust that specifically qualifies the relation of communication ongoing among individuals in digital environments. On the basis of this analysis, the paper concludes by arguing that online trust promotes the emergence of social behaviours rewarding honest and transparent communications.     

US Responsibility for War Crimes in Iraq

This paper examines the recent actions by the United States in Iraq in the light of just war principles, and sets forth a program for holding accountable those most responsible for war crimes in Iraq.