Um estudo sobre as origens da Lógica Matemáitca

The present study has as objective to explaining about the origins of the mathematical logic. This has its beginning attributed to the autodidactic English mathematician George Boole (1815-1864), especially because his books The Mathematical Analysis of Logic (1847) and An Investigation of the Laws of Thought (1854) are recognized as the inaugural works of the referred branch. However, surprisingly, in the same time another mathematician called Augutus of Morgan (1806-1871) it also published a book, entitled Formal Logic (1847), in defense of the mathematic logic. Even so, times later on this same century, another work named Elements of Logic (1875) it appeared evidencing the Aristotelian logic with Richard Whately (1787-1863), considered the better Aristotelian logical of that time. This way, our research, permeated by the history of the mathematics, it intends to study the logic produced by these submerged personages in the golden age of the mathematics (19th century) to we compare the valid systems in referred period and we clarify the origins of the mathematical logic. For that we looked for to delineate the panorama historical wrapper of this study. We described, shortly, biographical considerations about these three representatives of the logic of the 19th century formed an alliance with the exhibition of their point of view as for the logic to the light of the works mentioned above. In this sense, we aspirated to present considerations about what effective Aristotelian´s logic existed in the period of Boole and De Morgan comparing it with the new emerging logic (the mathematical logic). Besides of this, before the textual analysis of the works mentioned above, we still looked for to confront the systems of Boole and De Morgan for we arrive to the reason because the Boole´s system was considered better and more efficient. Separate of this preponderance we longed to study the flaws verified in the logical system of Boole front to their contemporaries' production, verifying, for example, if they repeated or not. We concluded that the origins of the mathematical logic is in the works of logic of George Boole, because, in them, has the presentation of a new logic, matematizada for the laws of the thought similar to the one of the arithmetic, while De Morgan, in your work, expand the Aristotelian logic, but it was still arrested to her

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

Uma abordagem histórica para o ensino do princípio da inércia

Placed in the field of Didactic of Science, this paper proposes an approach to the introduction of the History of Science in science education, at high school level. It was designed and implemented a series of activities regarding the history of the Principle of Inertia. The aim of this approach was to give more meaning to scientific education, while opening new avenues for a better understanding of the processes of construction of scientific knowledge. The preparation of the activities involved a study of the historical development of the concept of motion, from the Aristotelian physics through physical movement concepts at medieval period, from Galileo, Gassendi, Descartes, until the first law of Newton. The strategy of teaching was applied to three classes of high school (night period) of a state public school at the city of Natal (RN). The results indicated the difficulty of overcoming alternative conceptions about movement by students. Nevertheless, we consider that the implementation of this strategy of teaching both represented gains for the learning of students, and contributed to the resizing of pedagogical practices of the teacher-researcher

A retórica em Aristóteles: da orientação das paixões ao aprimoramento da eupraxia

This research brings into focus the relationship between the work Rhetoric, from Aristotle, and the conceptions of ethics and practical wisdom of the philosopher from Stageira. Accordingly, it attempts to show that Aristotle's Rhetoric was produced to guide the construction and orientation of oratory passions of the Greek man, setting it as a reference for practices aimed at social ordering of the polis. In other words, the Aristotelian Rhetoric, designed by the author as the study of what is persuasive in every speech, is not composed with the meaning of persuasion at any cost, in another sense it is conceived by Aristotle as a useful knowledge for the improvement eupraxic (the good act in accordance with the fair and true). This research finds that such work has been prepared by Stagirite a time of strong social transformations and upheavals in ancient Greece: The skepticism expanded, with each person wanting to live their own businesses, and especially in Athens, a city that served as intellectual and political reference, there was a lack of collective spirit. In this tumultuous social environment, Aristotle, with a culture of Greeks eager Trusted reviews and socially shareable in the field of verisimilitude, sought with his Rhetoric, contributing to the development of ethics and political science; referrals for legal and organization of inter-social relations in varied environments, including seeking to provide knowledge about human passions and emotional status of active citizens in deliberative meetings

Elementos da ética sexual Tomista

This dissertation aims to present a elementar vision of thomistic thought about human sexuality from knowledges of vices and virtues. Introduce the notion of vice as otherwise to human nature and seek its etymological meaning, approaching with the neotestamentary perspective of sin and malice. This notion is based in aristotelian and augustinian notion, used by Thomas Aquinas. Also present two virtues inside of the christian thought about the sexuality. They are temperance and chastity. The temperance is a virtue that orders the pleasures of tact, and regulates the chastity. Finally, we show that is possible in thomistic thought admit the legitimacy of sexual pleasure and also the natural necessity in relations, and this relations just can be designed inside of legitimate marriage

Acolhimento institucional e desenvolvimento moral: a generosidade em crianças de quatro a seis anos de idade em situação de abrigo

This research has as main proposal to verify how the virtue of generosity, considered as one of the important aspects of moral development on children, shows itself in children between four and six years old in institutional welcome condition. Toward this aim, knowledge in Human Development Psychology, specifically Jean Piaget and his contemporary collaborators, were associated to philosophic knowledge, with emphasis in Kant and Aristotle. The research took place in an institutional welcome service in the town of Natal-RN, between February and May of 2009, witch is responsible to offer care to children from zero till six years old. As procedure were used: the rulebased game Memory Game ; the childhood story One note fight ; and observations of the institution s everyday. The corpus analysis was done by the Thematic Content Analysis method. In general, in the daily observations, children showed themselves more co-operative and generous than in the executed procedures, mainly when the matter subject was other´s well-being. The duty, Kantian perspective, was overcome by the Aristotelian sumo bem, classified as generous act of afford to other what is not posted as right, however guaranteed by solidarity

Of madness and many-valuedness: an investigation into Suszko's Thesis

Suszko’s Thesis is a philosophical claim regarding the nature of many-valuedness. It was formulated by the Polish logician Roman Suszko during the middle 70s and states the existence of “only but two truth values”. The thesis is a reaction against the notion of many-valuedness conceived by Jan Łukasiewicz. Reputed as one of the modern founders of many-valued logics, Łukasiewicz considered a third undetermined value in addition to the traditional Fregean values of Truth and Falsehood. For Łukasiewicz, his third value could be seen as a step beyond the Aristotelian dichotomy of Being and non-Being. According to Suszko, Łukasiewicz’s ideas rested on a confusion between algebraic values (what sentences describe/denote) and logical values (truth and falsity). Thus, Łukasiewicz’s third undetermined value is no more than an algebraic value, a possible denotation for a sentence, but not a genuine logical value. Suszko’s Thesis is endorsed by a formal result baptized as Suszko’s Reduction, a theorem that states every Tarskian logic may be characterized by a two-valued semantics. The present study is intended as a thorough investigation of Suszko’s thesis and its implications. The first part is devoted to the historical roots of many-valuedness and introduce Suszko’s main motivations in formulating the double character of truth-values by drawing the distinction in between algebraic and logical values. The second part explores Suszko’s Reduction and presents the developments achieved from it; the properties of two-valued semantics in comparison to many-valued semantics are also explored and discussed. Last but not least, the third part investigates the notion of logical values in the context of non-Tarskian notions of entailment; the meaning of Suszko’s thesis within such frameworks is also discussed. Moreover, the philosophical foundations for non-Tarskian notions of entailment are explored in the light of recent debates concerning logical pluralism.