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

Ciência e racionalidade em Thomas Kuhn

The work aims to explore the impact that Thomas Kuhn‟s philosophical work had on the philosophy of science, especially on the common idea of scientific rationality. Besides this, it aims to make clear the position of the author about his understanding of what is to be rational in science. In order to achieve this goal we start giving a panoramic view of the philosophical scientific scene of the first half os the twentieth century, to evince the main character of the concept of rationality more accepted at Kuhn‟s time. In a second moment we show how the ideas of this author contrast with that concept, which gives rise to a series of criticisms of irrationalism. Lastly, we show how Kuhn circumvents these accusations by pointing to a new rationality concept, through which we can conciliate his philosophy with a description of the rational development of science