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

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

Assessing residual reasoning ability in overtly non-communicative patients using fMRI

It is now well established that some patients who are diagnosed as being in a vegetative state or a minimally conscious state show reliable signs of volition that may only be detected by measuring neural responses. A pertinent question is whether these patients are also capable of logical thought. Here, we validate an fMRI paradigm that can detect the neural fingerprint of reasoning processes and moreover, can confirm whether a participant derives logical answers. We demonstrate the efficacy of this approach in a physically non-communicative patient who had been shown to engage in mental imagery in response to simple audi- tory instructions. Our results demonstrate that this individual retains a remarkable capacity for higher cogni- tion, engaging in the reasoning task and deducing logical answers. We suggest that this approach is suitable for detecting residual reasoning ability using neural responses and could readily be adapted to assess other aspects of cognition.

The role of sleep and dreaming in the processing of episodic memory

La présente thèse examine les liens entre le sommeil, la mémoire épisodique et les rêves. Dans une première étude, nous utilisons les technologies de la réalité virtuelle (RV) en liaison avec un paradigme de privation de sommeil paradoxal et de collecte de rêve en vue d'examiner l'hypothèse que le sommeil paradoxal et le rêve sont impliqués dans la consolidation de la mémoire épisodique. Le sommeil paradoxal a été associé au rappel des aspects spatiaux des éléments émotionnels de la tâche RV. De la même façon, l'incorporation de la tâche RV dans les rêves a été associée au rappel des aspects spatiaux de la tâche. De plus, le rappel des aspects factuels et perceptuels de la mémoire épisodique, formé lors de la tâche VR, a été associé au sommeil aux ondes lentes. Une deuxième étude examine l'hypothèse selon laquelle une fonction possible du rêve pourrait être de créer de nouvelles associations entre les éléments de divers souvenirs épisodiques. Un participant a été réveillé 43 fois lors de l'endormissement pour fournir des rapports détaillés de rêves. Les résultats suggèrent qu'un seul rêve peut comporter, dans un même contexte spatiotemporel, divers éléments appartenant aux multiples souvenirs épisodiques. Une troisième étude aborde la question de la cognition lors du sommeil paradoxal, notamment comment les aspects bizarres des rêves, qui sont formés grâce aux nouvelles combinaisons d'éléments de la mémoire épisodique, sont perçus par le rêveur. Les résultats démontrent une dissociation dans les capacités cognitives en sommeil paradoxal caractérisée par un déficit sélectif dans l'appréciation des éléments bizarres des rêves. Les résultats des quatre études suggèrent que le sommeil aux ondes lentes et le sommeil paradoxal sont différemment impliqués dans le traitement de la mémoire épisodique. Le sommeil aux ondes lentes pourrait être implique dans la consolidation de la mémoire épisodique, et le sommeil paradoxal, par l'entremise du rêve, pourrais avoir le rôle d'introduire de la flexibilité dans ce système mnémonique.

Direito de recesso parcial: a permissão silenciosa do legislador societário

A posição majoritária da doutrina societária brasileira entende não ser possível o exercício parcial do direito de recesso. Os argumentos nesse sentido são: (i) não há previsão legal; (ii) o exercício parcial do direito de recesso constituiria forma de abuso de direito; (iii) a possibilidade geraria a aceitação de uma lógica incompatível, afinal: ou a deliberação prejudicou o interesse do acionista em continuar sócio da companhia, ou ele mantém tal interesse e não exerce o recesso. Contudo, as ideias defendidas nesse trabalho buscam descaracterizar esses argumentos, ao mesmo tempo em que pretendem demonstrar que o direito de recesso parcial é possível, permitido, legal e economicamente eficiente. Os argumentos construídos tentaram demonstrar que o recesso não é, necessariamente, uma forma de ruptura total do vínculo societário, não gerando reflexos única e exclusivamente sobre a qualidade de sócio do acionista. Deve-se perceber que o interesse protegido é dual: da companhia e do acionista. E esse interesse do acionista tanto pode ser uma readequação do seu investimento na companhia (decorrente da deliberação que gerou o direito de recesso), como a possibilidade de ruptura do vínculo social. Essa, entretanto, deve ser uma decisão que cabe única e exclusivamente a ele, no exercício de uma faculdade que a lei lhe confere. No mais, defende-se que afastar o recesso parcial significa impedir uma operação economicamente eficiente, visto que nenhuma parte é prejudicada pelo exercício do recesso com apenas parte das ações elegíveis.

As origens da teoria dos invariantes na Inglaterra e o Mécanique Analytique de Lagrange (1788)

Pós-graduação em Educação Matemática - IGCE

Labyrinthum capellae. Le "Annotationes in Marcianum" di Giovanni Scoto Eriugena e la fortuna del neoplatonismo cristiano

The labyrinthum Capella quoted in the title (from a Prudentius of Troyes epistle) represents the allegory of the studium of the liberal arts and the looking for knowledge in the early middle age. This is a capital problem in the early Christianity and, in general, for all the western world, concerning the relationship between faith and science. I studied the evolution of this subject from its birth to Carolingian age, focusing on the most relevant figures, for the western Europe, such Saint Augustine (De doctrina christiana), Martianus Capella (De Nuptiis Philologiae et Mercurii) and Iohannes Scotus Eriugena (Annotationes in Marcianum). Clearly it emerges that there were two opposite ways about this relatioship. According to the first, the human being is capable of get a knowledge about God thanks to its own reason and logical thought processes (by the analysis of the nature as a Speculum Dei); on the other way, only the faith and the grace could give the man the possibility to perceive God, and the Bible is the only book men need to know. From late antiquity to Iohannes Scotus times, a few christian and pagan authors fall into line with first position (the neoplatonic one): Saint Augustine (first part of his life, then he retracted some of his views), Martianus, Calcidius and Macrobius. Other philosophers were not neoplatonic bat believed in the power of the studium: Boethius, Cassiodorus, Isidorus of Seville, Hrabanus Maurus and Lupus of Ferriéres. In order to get an idea of this conception, I finally focused the research on Iohannes Scotus Eriugena's Annotationes in Marcianum. I commented Eriugena's work phrase by phrase trying to catch the sense of his words, the reference, philosophical influences, to trace antecedents and its clouts to later middle age and Chartres school. In this scholastic text Eriugena comments the Capella's work and poses again the question of the studium to his students. Iohannes was a magister in schola Palatina during the time of Carl the Bald, he knew Saint Augustine works, and he knew Boethius, Calcidius, Macrobius, Isidorus and Cassiodorus ones too. He translated Pseudo-Dionysius the Areopagite and Maximus the Confessor. He had a neoplatonic view of Christianity and tried to harmonize the impossibility to know God to man's intellectual capability to get a glimpse of God through the study of the nature. According to this point of view, Eriugena's comment of Martianus Capella was no more a secondary work. It gets more and more importance to understand his research and his mystic, and to understand and really grasp the inner sense of his chief work Periphyseon.

Essays in experimental logic,

Chapter 1 was written especially for this volume; chapter 2-5 are reprinted (with editorial revisions) from the author's Studies in logical theory; "the other essays are in part reprinted and in part rewritten, with additions, from various contributions to philosophical periodicals" cf. Pref. note.

Humanism is a violence typical of the beasts. Philosozing with a Hammer, using Levinas and Derrida, the Measure of the Human and the Human as a measure

Levinas’s reflections arose as a critique of traditional philosophy which, since it was based on presence and identity, leads to the exclusion of the other. Instead of an onto-logical thought the Lithuanian proposes that the ipseity of the human being be constituted by alterity, and that it be so ethically, because the subject is sub-ject, that is, that which upholds, responsibility. In an attempt to take the obligatory attention to the otherness of the other even further, Derrida would develop a radical critique of the Levinasian posture. Deconstruction of every trace of ipseity and sovereignty in the relationship with the other, the reading that we have done of the work of Derrida opts for a no definable understanding of the human. That is why every de-limitation of an ethical field as a properly human implies a brutal violence that the levinasian humanism of the other tried to exceed.

Elements of logic : comprising the doctrine of the laws and products of thought, and the doctrine of method, together with a logical praxis /

Mode of access: Internet.

A treatise on logic, or, The laws of pure thought : comprising both the Aristotelic and Hamiltonian analyses of logical forms, and some chapters of applied logic /

Mode of access: Internet.

An investigation of the laws of thought, on which are founded the mathematical theories of logic and probabilities.

Mode of access: Internet.

A treatise on logic : or, The laws of pure thought; comprising both Aristotelic and Hamiltonian analyses of logical forms, and some chapters of applied logic /

Mode of access: Internet.