Uma reavaliação do pensamento lógico de George Boole à luz da história da matemática

The aim of the present study is to reevaluate the logical thought of the English mathematician George Boole (1815 - 1864). Thus, our research centers on the mathematical analysis of logic in the context of the history of mathematics. In order to do so, we present various biographical considerations about Boole in the light of events that happened in the 19th century and their consequences for mathematical production. We briefly describe Boole's innovations in the areas of differential equations and invariant theory and undertake an analysis of Boole's logic, especially as formulated in the book The Mathematical Analysis of Logic, comparing it not only with the traditional Aristotelian logic, but also with modern symbolic logic. We conclude that Boole, as he intended, expanded logic both in terms of its content and also in terms of its methods and formal elaboration. We further conclude that his purpose was the mathematical modeling of deductive reasoning, which led him to present an innovative formalism for logic and, because the different ways it can be interpreted, a new conception of mathematics

Atividades comportamentais e comportamento alimentar de rã touro, Lithobates catesbeianus (Shaw, 1802), de pigmentação normal e albina em cativeiro

The behavior of bullfrogs reared in captivity must be well understood to support management practices that use efficient feeding regimes. In general, bullfrogs reared in captivity have normal pigmentation, but to develop an enhanced product, some studies have investigated the introduction of albino individuals in frog farms. The present study characterized the behavior of both pigmented and albino bullfrogs reared in captivity. In an initial experiment, 48 bullfrogs (70.5 ± 25.6 g) housed in small stalls were fed once a day at random times. Frogs were filmed and the images showed that both the pigmented and albino varieties behaved similarly: food intake was more frequent at dawn followed by light periods; moving and resting in dry areas may be associated to feeding events; frogs appeared to anticipate feeding time and to rest in the water more frequently in periods other than feeding time; daylight is the recommended period for feeding both pigmented and albino frogs. In a second experiment, 72 albino bullfrogs were fed at fixed times (10 a.m. or 4 p.m.) in small stalls. An initial weight of 23.8 ± 7.6 g was considered to evaluate frog performance, and after the animals reached 60.0 ± 20.0 g, they were filmed for behavior analyses. Food intake varied as a function of feeding time, and frogs were more likely to eat during the early hours of the day and immediately after receiving fresh food. Frogs fed only in the afternoon changed their behavior. Food supplied twice a day stimulated the albino frogs to eat at different times, but did not increase growth. Although fresh food stimulated feeding behavior, food intake was more frequent at dawn. Food supplied at this time of day should therefore be further investigated. The results did not indicate a more suitable feeding time (10 a.m. or 4 p.m.) for albino bullfrogs, or any advantage in using two feedings per day. The results provide xvi important information about bullfrogs in terms of food supply regime and activity preferences throughout the day. This novel information will contribute to future studies in this area