Problemas e modelos que contribuíram com o desenvolvimento do cálculo diferencial e integral: dos gregos à Newton

This article refers to a research which tries to historically (re)construct the conceptual development of the Integral and Differential calculus, taking into account its constructing model feature, since the Greeks to Newton. These models were created by the problems that have been proposed by the history and were being modified by the time the new problems were put and the mathematics known advanced. In this perspective, I also show how a number of nature philosophers and mathematicians got involved by this process. Starting with the speculations over scientific and philosophical natures done by the ancient Greeks, it culminates with Newton s work in the 17th century. Moreover, I present and analyze the problems proposed (open questions), models generated (questions answered) as well as the religious, political, economic and social conditions involved. This work is divided into 6 chapters plus the final considerations. Chapter 1 shows how the research came about, given my motivation and experience. I outline the ways I have gone trough to refine the main question and present the subject of and the objectives of the research, ending the chapter showing the theoretical bases by which the research was carried out, naming such bases as Investigation Theoretical Fields (ITF). Chapter 2 presents each one of the theoretical bases, which was introduced in the chapter 1 s end. In this discuss, I try to connect the ITF to the research. The Chapter 3 discusses the methodological choices done considering the theoretical fields considered. So, the Chapters 4, 5 and 6 present the main corpus of the research, i.e., they reconstruct the calculus history under a perspective of model building (questions answered) from the problems given (open questions), analyzing since the ancient Greeks contribution (Chapter 4), pos- Greek, especially, the Romans contribution, Hindus, Arabian, and the contribution on the Medium Age (Chapter 5). I relate the European reborn and the contribution of the philosophers and scientists until culminate with the Newton s work (Chapter 6). In the final considerations, it finally gives an account on my impressions about the development of the research as well as the results reached here. By the end, I plan out a propose of curse of Differential and Integral Calculus, having by basis the last three chapters of the article

Heráclito na filosofia do jovem Nietzsche

In the early 1870s, the German Philosopher Friedrich Nietzsche, professor of philology in Basel, researches the ancient Greek philosophers. These studies result in texts as The Preplatonic Philosophers, also known as Lessons on Pre-platonic Philosophers, and Philosophy in Greek tragic age. Using both texts as sources, this dissertation aims elucidating the Nietzsche's interpretation about Heraclitus, in other words, comprehend how Nietzsche recognizes in Heraclitus a philosopher with an aesthetic vision of the world, a contemplative and cheerful view of the world, the becoming, defined by the incessant change, as a child's play that builds and destroy sand castles on the shore. This spectacle, as Nietzsche believed, would be unveiled first by Heraclitus and must be contemplated eternally

Agostinho e o ceticismo: um estudo da crítica agostiniana ao ceticismo em Contra Acadêmicos

The assent of the Truth: here's a formula that seems to have puzzled philosophers since antiquity. The possibility of apprehending truth was defended by some philosophers who have been called dogmatic, due to their haste to judge appearances as representations of reality, and refuted by those who chose to continue questioning rather than engage with his predicament. These thinkers were called skeptics. Among those who defended the consent of the truth, is highlighted by St. Augustine in this research, which aims to combat the widespread skepticism in the ancient doctrine of the Academy of Plato in his work Against Academicos. Thus, to conduct this research we ask: What are the main arguments made by St. Augustine against the scholarly skepticism? In order to address the problem identified, we propose to investigate the critical skepticism of St. Augustine, identifying and analyzing the main rebuttals he built. For this purpose, we conducted a survey of aspects of both the skepticism about the life and thought of St. Augustine about this doctrine