A difícil aceitação dos números negativos: um estudo da teoria dos números de Peter Barlow (1776-1862)

The present study seeks to present a historico-epistemological analysis of the development of the mathematical concept of negative number. In order to do so, we analyzed the different forms and conditions of the construction of mathematical knowledge in different mathematical communities and, thus, identified the characteristics in the establishment of this concept. By understanding the historically constructed barriers, especially, the ones having ontologicas significant, that made the concept of negative number incompatible with that of natural number, thereby hindering the development of the concept of negative, we were able to sketch the reasons for the rejection of negative numbers by the English author Peter Barlow (1776 -1862) in his An Elementary Investigation of the Theory of Numbers, published in 1811. We also show the continuity of his difficulties with the treatment of negative numbers in the middle of the nineteenth century

Fundamentos da filosofia moral de Peter Singer

This research aims to reconstruct and explain the argument proposed by Peter Singer to justify the principle of equal consideration of interests (PECI). The PECI is the basic normative principle according to people should consider the interests of all sentient beings affected when somebody taking a moral decision. It is the join that Singer proposes between universalizability and the principle of equal consideration of interests that constitutes a compelling reason to justify it. The universalizability requires to disregard the numerical differences, putting yourself in other people s shoes, and to consider preferences, interests, desires and ideals of those affected. Singer joins universalizability to normative principle and molds the form and content of his theory. The first chapter introduces the discussion will be developed in this essay. The second chapter deals the historical and philosophical viewpoint from which Singer starts his studies. The third chapter is about the Singer s critiques of naturalism, intuitionism, relativism, simple subjectivism and emotivism. The fourth chapter exposes the design of universal prescriptivism proposed by R. M. Hare. The universal prescriptivism indicates, in the Singer s viewpoint, a consistent way to create the join between the universalizability and PECI. It highlights also the criticism designed by J. L. Mackie and Singer himself to universal prescriptivism. The second part of this chapter shows briefly some of the main points of the classical conception of utilitarianism and its possible relationship with the theory of Singer. The fifth chapter introduces the Singer s thesis about the origin of ethics and the universalizability as a feature necessary to the point of view of ethic, and the way which this argument is developed to form the PECI. The sixth chapter exposes the main distinctions that characterize the PECI. Finally the seventh chapter provides a discussion about the reasons highlighted by Singer for one who wants orient his life according to the standpoint of ethics. This structure allows explaining the main ideas of the author concerning the theoretical foundations of his moral philosophy

Distribuição diária das atividades comportamentais dos camarões marinhos Farfantepenaeus subtilis (Pérez Farfante, 1967) e Litopenaeus schmitti (Burkenroad, 1938) em condições laboratoriais

Marine aquaculture has developed in the last decades all over the world, especially related to shrimp management. In Brazil, the introduction of the species Litopenaeus vannamei has contributed to the success of the activity, even if there are problems associated with the management of a exotic species, such as new diseases and ecological pressure on native species. It has been emphasized the need of research for developing new methodology that will allow native species management, being the most important Farfantepenaeus subtilis and Litopenaeus schmitti. Most knowledge obtained from research with those species has generally used a technical approach and mainly focused feeding process. There are no specific behavioral data on their activity pattern which should be of great importance for the use of native species on commercial culture farms. So, it was our objective to study and compare the daily distribution of behavioral activities of the marine shrimp species Litopenaeus schmitti and Farfantepenaeus subtilis. Forty animals of each species, 5 individuals per aquarium, were maintained in aquaria containing 200L of sea water under continuous aeration and filtration. They were marked individually and were observed by the instantaneous focal time sampling, along 10 continuous days, in 6 daily 15 min observation windows, every two hour. In each window, behaviors and location position of the animals in the aquarium were registered at 1 min intervals. Food was offered 3 times a day, representing 10% of each aquarium biomass. Aquaria were maintained in artificial photoperiod, 12hour light/l2 hour dark, 4 aquaria in light cycle equivalent to the environmental one (light from 06:00 to 17:59 h and dark from 18:00 to 05:59 h) and the other 4 in the reverse light cycle (light from 18:00 to 05:59 h and dark from 06:00 to 17:59 h) to allow sequential behavioral observation in both phases of the 24 hour cycle. There was a clear distinction between the distribution of behavioral activities of F. subtilis and L. schmitti in the two phases. The activity pattern of Farfantepenaeus subtilis demonstrates that species has prominently night habits and a burying pattern during the light cycle. Exploration, inactivity and swimming were the most common activities. The behavioral pattern of Litopenaeus schmitti indicates that species is active along both phases of the light cycle, and the most evident behaviors were exploration, inactivity and swimming