Razão: origem, crise e respostas contemporâneas

The philosophical discussion has been present throughout the whole history of reason, for philosophy and reason have been always closely linked. In the following work, Reason, origin, crises and contemporary answers I go into the history of the rational and demonstrative thought, focusing on how rationality can be thought about in contemporary philosophy. To answer this question I discuss the principle of philosophy, the mythical period and the thoughts of Heraclito , Parmenides , Plato and Aristotle in relation to reason and rationality. Also discussed is the medieval period and the philosophical use of logic and the criticism of Aristotle s thoughts, especially focusing on the criticism of Hegel and Luckasiewicz of the non contradiction principle. Lastly I discuss the development of reason in present day philosophy, mainly how modern logics could be putting at stake Aristotle s model of reason

Kant e o fim da modernidade pré-crítica: os sonhos de um visionário

Coordenação de Aperfeiçoamento de Pessoal de Nível Superior (CAPES)

Pedro Damián y la defensa ética del principio de no contradicción

Intentaremos desentrañar uno de los aspectos centrales del De divina omnipotentia de Pedro Damián: la relación entre omnipotencia divina y principio de no contradicción. Para ello, refutaremos una de las hipótesis de lectura más tradicionales que se han hecho del tema, según la cual Pedro Damián considera que la omnipotencia divina es incompatible con el principio de no contradicción, y por tanto éste pierde toda vigencia. Por nuestra parte, afirmaremos que Pedro Damián nunca cuestionó seriamente la validez de la lógica, sino que procuró afianzarla sobre premisas de raigambre ético-metafísica. Para iluminar el sentido de nuestra interpretación, debemos contextualizar la discusión y explicar diversos conceptos del pensamiento damianeano (i.e. voluntas Dei, omnipotentia divina, aeternitas y bondad divina).

El principio de contradicción o el estado de cosas en cuanto estado de cosas

El principio de contradicción tiene su lugar propio en la filosofía griega, concretamente en la Filosofía Primera o Teología de Aristóteles. No es ni un precepto ni una prohibición sobre el ente, abstraído de diversos estados de cosas, sino él mismo un estado de cosas, mejor dicho: el estado de cosas primero para todo el que quiera conocer algo. Su universalidad consiste en que presenta el estado de cosas en cuanto estado de cosas y se expresa en la decisividad de lo que constata: es imposible – que lo es el caso no sea el caso.

La conception platonicienne de la contradiction

Cette thèse se rapporte à la notion de contradiction, entendue en son sens logique ou formel. Plus précisément, elle vise à dégager une conception de la contradiction chez un philosophe qui, du point de vue chronologique, précède l’avènement de la syllogistique et de la logique : Platon. À partir de l’examen des dialogues réfutatifs de Platon, il s’agira de mettre en lumière la forme des propositions contradictoires, de déterminer la terminologie et les métaphores utilisées par Platon pour nommer et décrire la contradiction et d’évaluer le contexte dans lequel avait lieu la réflexion platonicienne. L’analyse révélera que Platon se faisait une idée somme toute assez précise de la contradiction logique et qu’il a même eu une influence sur Aristote lorsque ce dernier élabora son célèbre principe de non-contradiction.

Borderline cases and the collapsing principle

John Broome has argued that value incommensurability is vagueness, by appeal to a controversial ‘collapsing principle’ about comparative indeterminacy. I offer a new counterexample to the collapsing principle. That principle allows us to derive an outright contradiction from the claim that some object is a borderline case of some predicate. But if there are no borderline cases, then the principle is empty. The collapsing principle is either false or empty.

An Extension of the Invariance Principle for a Class of Differential Equations with Finite Delay

An extension of the uniform invariance principle for ordinary differential equations with finite delay is developed. The uniform invariance principle allows the derivative of the auxiliary scalar function V to be positive in some bounded sets of the state space while the classical invariance principle assumes that. V <= 0. As a consequence, the uniform invariance principle can deal with a larger class of problems. The main difficulty to prove an invariance principle for functional differential equations is the fact that flows are defined on an infinite dimensional space and, in such spaces, bounded solutions may not be precompact. This difficulty is overcome by imposing the vector field taking bounded sets into bounded sets.

On Seliger and Whitham`s variational principle for hydrodynamic systems from the point of view of `fictitious particles`

FAPESP, the Sao Paulo State Research Foundation[04/04611-5]

A Separation Principle for the Continuous-Time LQ-Problem With Markovian Jump Parameters

In this paper, we devise a separation principle for the finite horizon quadratic optimal control problem of continuous-time Markovian jump linear systems driven by a Wiener process and with partial observations. We assume that the output variable and the jump parameters are available to the controller. It is desired to design a dynamic Markovian jump controller such that the closed loop system minimizes the quadratic functional cost of the system over a finite horizon period of time. As in the case with no jumps, we show that an optimal controller can be obtained from two coupled Riccati differential equations, one associated to the optimal control problem when the state variable is available, and the other one associated to the optimal filtering problem. This is a separation principle for the finite horizon quadratic optimal control problem for continuous-time Markovian jump linear systems. For the case in which the matrices are all time-invariant we analyze the asymptotic behavior of the solution of the derived interconnected Riccati differential equations to the solution of the associated set of coupled algebraic Riccati equations as well as the mean square stabilizing property of this limiting solution. When there is only one mode of operation our results coincide with the traditional ones for the LQG control of continuous-time linear systems.

Contradiction of quantum mechanics with local hidden variables for quadrature phase amplitude measurements

We demonstrate a contradiction of quantum mechanics with local hidden variable theories for continuous quadrature phase amplitude (position and momentum) measurements. For any quantum state, this contradiction is lost for situations where the quadrature phase amplitude results are always macroscopically distinct. We show that for optical realizations of this experiment, where one uses homodyne detection techniques to perform the quadrature phase amplitude measurement, one has an amplification prior to detection, so that macroscopic fields are incident on photodiode detectors. The high efficiencies of such detectors may open a way for a loophole-free test of local hidden variable theories.

Sobre a imagem rousseauniana da lei acima dos homens

Entre o verbete sobre economia política, de 1755, e o Contrato social, de 1762, a noção rousseauniana de lei passa de "voz celeste" para "declaração da vontade geral". Pretende-se defender aqui a proposição de que tal mudança na definição de lei de um escrito para o outro não implica contradição. Para tanto, será analisada a presença da imagem da "lei acima dos homens" em diversos textos do Cidadão de Genebra, sobretudo no capítulo "Do legislador" no livro II do Contrato, a fim de mostrar-se que ela corresponde a um mesmo princípio de oposição entre a liberdade, associada ao dever de obediência, e a escravidão, associada ao impulso das paixões, expressando-se de modos particulares nos diversos momentos da obra de Rousseau.