Mathematics of Totalities: an alternative to mathematics of sets

I dare say, a set is contranatural if some pair of its elements has a nonempty intersection. So, we consider only collections of disjoint nonempty elements and call them totalities. We propose the propositional logicTT, where a proposition letters some totality. The proposition is true if it letters the greatest totality. There are five connectives inTT: , , , , # and the last is called plexus. The truth of # means that any element of the totality has a nonempty intersection with any element of the totality . An imbeddingG of the classical predicate logicCPL inTT is defined. A formulaf ofCPL is a classical tautology if and only ifG(f) is always true inTT. So, mathematics may be expounded inTT, without quantifiers.     

The impact of religion on men's blood pressure

Most clinical studies examining the relation between religion and blood pressure status have focused on church attendance, finding lower pressures among frequent attenders. The present study examines the effect on blood pressure status of a religious meaning variable, importance of religion, both by itself and together with frequency of church attendance. The relation between blood pressure, self-perceived importance of religion, and frequency of church attendance was examined among a rural sample of 407 white men free from hypertension or cardiovascular disease. The data confirmed an interaction between the effects of both religious variables on blood pressure status, with importance of religion having an even greater association with lower pressures than church attendance. Diastolic blood pressures of persons with high church attendance and high religious importance were significantly lower than those in the low attendance, low importance group. These differences persisted after adjusting the analyses for age, socioeconomic status, smoking, and weight-height ratio (Quetelet Index). The difference in mean diastolic pressures based on response to the religious importance variable alone was statistically and clinically significant, particularly among men aged 55 and over (6 mm) and among smokers (5 mm). These findings suggest that both religious attitudes and involvement may interact favorably in their effects on cardiovascular hemodynamics.     

The influence of an audience upon the reactions to filmed violence

In order to examine audience effects when viewing firmed violence, 5 to 6 year old pre-school boys who had been rated as submissive by their teachers watched an aggressive or a neutral movie either alone, accompanied by another submissive classmate, or a dominant one. Subsequent aggression against a frustrating, unknown and unseen boy was delivered via a modified Buss machine, especially adapted for children. Subjects accompanied by a dominant peer were more aggressive than the others but did not react differentially to the movies. Subjects tested alone were more aggressive after the violent film than after the neutral one and the opposite pattern occurred for the boys accompanied by a submissive classmate. These findings stress the importance of the social context when viewing filmed violence. It is suggested that the quality of the audience can have different directional (e.g. fear and aggression) as well as energizing properties. Links with the literature on social facilitation and audience effects are underlined.     

Set theory as modal logic

A logical systemBM ⁺ is proposed, which, is a prepositional calculus enlarged with prepositional quantifiers and with two modal signs, and These modalities are submitted to a finite number of axioms. is the usual sign of necessity, corresponds to transmutation of a property (to be white) into the abstract property (to be the whiteness). An imbedding of the usual theory of classesM intoBM ⁺ is constructed, such that a formulaA is provable inM if and only if(A) is provable inBM ⁺. There is also an inverse imbedding with an analogous property.     

Instructions and group versus individual reinforcement in modifying disruptive group behavior

Head Start children were matched into two groups on the basis of rates of disruptive behavior during rest periods. Attempts were made to modify their behavior using either individual or group token reinforcement procedures. While the reinforcement procedures reduced inappropriate behavior somewhat, the addition of instructions to the reinforcement reduced the inappropriate behavior to near zero for both groups. Instructions alone, however, were ineffective in controlling behavior. Type of reinforcement (group or individual) did not produce differential effects. While experimental control over the target behavior was demonstrated, there was little carryover from the experimental room to the regular classroom. Even when treatment was introduced into the regular class, follow-up results showed that with time the target behavior approximated pretreatment levels. The results suggest that (a) the combination of instructions and reinforcement is much more effective than either one of these alone, (b) behavior change is specific to the environmental contingencies, and (c) the group reinforcement technique, which is much more easily implemented, was at least as effective as individual reinforcement in the present study.     

A study in culturalization of response

The Psychological Record -     

Study of the single channel hypothesis and input regulation within a continuous, simultaneous task situation

Subjects performed simultaneously on an auditory tracking and an auditory discrimination task, with each, task presented to a separate ear. Information transmitted on the tasks was measured as a function of ability to predict task characteristics, input information-rate, and input discriminability. Based on comparison of single-versus simultaneous-task performance, support was found for a single, central decision-type channel in information processing, having as one primary limit the rate at which information can be accepted. Discriminability of inputs also was found to be a limit on information processing rate. Although ability to predict a task's characteristics facilitated performance on that task, in this experiment it did not result in facilitation of performance on the second task. Relevance of these findings to certain aspects of Broadbent's information-processing model is discussed.     

Impaired ranking of semantic attributes in dementia

The present work explored the loss of semantic attributes that is said to occur in dementia. In the first two experiments, subjects had to select attributes that went with concepts like airplane and church. The finding that demented subjects maintained high levels of accuracy when selecting attributes suggested that the semantic content of their concepts was relatively well preserved. The organization of the content was explored in a third experiment by having subjects order attributes according to their relative importance in defining concepts. While demented subjects performed better than chance, they did not rank attributes as well as healthy aged subjects, suggesting a disruption in organization whereby the importance of central attributes is reduced. The hypothesized disruption in organization is viewed in relation to the learning and memory deficit that is the hallmark of the dementias.