The purpose of this dissertation is to search the primitives of Axiomatic Set Theory in Leibnizian Philolosophy, nourishing, roughly, from Platonic idea of universal-particular distinction, Aristotelian syllogistic propositions of Organon-Categoria and Euclidean Methodology in Elements. The main focus of the dissertation intends to examine the analyticity of Leibnizian Metaphysics and the anologies between the subject-predicate relation in The Philosophy of Leibniz and Axiomatic Method in general and Set Theory in particular. In doing this, special emphasis will be ascribed to the notion of sets as to universality and/or nullness of a class, probable causes of paradoxes and in this context a critical analysis of Russell Paradox.

Made available in DSpace on 2016-06-02T20:12:19Z (GMT). No. of bitstreams: 1 5621.pdf: 971098 bytes, checksum: c5d30431f6d74b2c37a4e7b0a76b6491 (MD5) Previous issue date: 2013-11-28 / Financiadora de Estudos e Projetos / The purpose of this thesis is analyze the changes in the thinking of Rudolf Carnap in relation to the analysis of language before the innovations of the work of Alfred Tarski. To this end, we will seek to explain the syntactic analysis of language presented by Carnap in his work "Logical Syntax of Language". Secondly, the semantic analysis of the language proposed by Alfred Tarski. To then discuss the influence of Tarski in the later work of Rudolf Carnap. / Esta tese tem por finalidade examinar as mudanças do pensamento de Rudolf Carnap em relação à análise da linguagem frente às inovações dos trabalhos de Alfred Tarski. Para tanto, buscaremos esclarecer a análise sintática da linguagem apresentada por Carnap em sua obra a Sintaxe Lógica da Linguagem , e a análise semântica da linguagem proposta por Alfred Tarski, para, então, discutir a influência de Tarski nos trabalhos posteriores de Rudolf Carnap.

Frege wanted to show that arithmetical truths are logical by proving them from purely logical basic laws. But how do we know that these basic laws are logical? Frege uses generality and undeniability to make a prima facie case for logicality—if a truth is general and undeniable, then it's likely logical. I argue that Frege could, did, and had to make a deeper case for why we're right in recognizing his basic laws as logical. Implicit in his work is a view of logical laws as epistemically analytic—his arguments for his basic laws serve to elicit a reflective awareness of the fact that understanding them is sufficient for recognizing them to be true. This view both fits with Frege's comments concerning the connection between logic, truth, and normativity, and serves to explain why and in what sense he took logic to be general and conceptually undeniable. In my view, semantics must play a distinctive role in any rational reconstruction of Frege's case for logicality—the aforementioned “reflective awareness” must be an explicit appreciation of how the truth of formulas expressing Frege's laws follows quickly from his stipulations governing terms which figure in those formulas. Opposing this view is the elucidatory interpretation of Thomas Ricketts, Warren Goldfarb, and Joan Weiner, which holds that Frege's arguments for his basic laws can't be taken at face value, and must serve the merely elucidatory purpose of easing us into the language. Another reading is the correctness interpretation of Richard Heck and Jason Stanley, which holds that Frege's primary purpose in his arguments is justifying the claim that Frege's axioms, qua formulas, are true. I argue against both of these interpretations, and in doing so clarify the role and limits of semantics in Frege's enterprise.

Motivated by the results concerning the regularity of solutions to the fractional Navier-Stokes system and questions about the influence of noise on the formation of singularities in hydrodynamic models, we have explored these two problems in the context of the fractional 1D Burgers equation. First, we performed highly accurate numerical computations to characterize the dependence of the blow-up time on the the fractional dissipation exponent in the supercritical regime. The problem was solved numerically using a pseudospectral method where integration in time was performed using a hybrid method combining the Crank-Nicolson and a three-step Runge-Kutta techniques. A highlight of this approach is automated resolution refinement. The blow-up time was estimated based on the time evolution of the enstrophy (H1 seminorm) and the width of the analyticity strip. The consistency of the obtained blow-up times was verified in the limiting cases. In the second part of the thesis we considered the fractional Burgers equation in the presence of suitably colored additive noise. This problem was solved using a stochastic Runge-Kutta method where the stochastic effects were approximated using a Monte-Carlo method. Statistic analysis of ensembles of stochastic solutions obtained for different noise magnitudes indicates that as the noise amplitude increases the distribution of blow-up times becomes non-Gaussian. In particular, while for increasing noise levels the mean blow-up time is reduced as compared to the deterministic case, solutions with increased existence time also become more likely. / Thesis / Master of Science (MSc)

A glass couldn't contain water unless it contained H2O-molecules. Likewise, a man couldn't be a bachelor unless he was unmarried. Now, the latter is what we would call a conceptual or analytical truth. It's also what we would call a priori. But it's hardly a conceptual or analytical truth that if a glass contains water, then it contains H2O-molecules. Neither is it a priori. The fact that water is composed of H2O-molecules was an empirical discovery made in the eighteenth century. The fact that all bachelors are unmarried was not. But neither is a logical truth, so how do we explain the difference? Two-dimensional semantics is a framework that promises to shed light on these issues. The main purpose of this thesis is to understand and evaluate this framework in relation to various alternatives, to see whether some version of it can be defended. I argue that it fares better than the alternatives. However, much criticism of two-dimensionalism has focused on its alleged inability to provide a proper semantics for certain epistemic operators, in particular the belief operator and the a priori operator. In response to this criticism, a two-dimensional semantics for belief ascriptions is developed using structured propositions. In connection with this, a number of other issues in the semantics of belief ascriptions are addressed, concerning indexicals, beliefs de se, beliefs de re, and the problem of logical omniscience.

[pt] A dissertação apresenta e discute as idéias desenvolvidas por Crispin Wright no livro Frege´s Conception of Numbers as Objects (1983), em particular, a sua tese de que a aritmética é analítica. Wright deposita toda sua força argumentativa (em relação à analiticidade da aritmética) na derivação dos axiomas da aritmética de segunda ordem de Dedekind-Peano a partir do Princípio de Hume. Assim, é nosso principal objetivo apresentar e discutir em que medida o Princípio de Hume é capaz de fornecer, segundo Wright, um relato da analiticidade da aritmética, assim como, as objeções a esse relato. / [en] The dissertation presents and discusses the ideas developed by Crispin Wright in his book Frege's Conception of Numbers as Objects (1983), in particular his thesis that arithmetic is analytic. Wright concentrates all his argumentative efforts (in relation to the analyticity of arithmetic) on the derivation of the axioms of Dedekind-Peano's second order arithmetic from Hume's Principle. Thus, it is our main goal to present and discuss how Hume's Principle provides, according to Wright, an explanation of the analytic character of arithmetic as well as some objections to this account.

Cette thèse se situe à l'intersection de plusieurs domaines mathématiques particulièrement actifs actuellement : l'analyse fonctionnelle, la théorie des opérateurs, la dynamique complexe et la théorie des semigroupes. Nous étudierons ici les semigroupes d'opérateurs de composition sur quelques espaces de Hardy pondérés, notamment l'espace de Hardy du disque et l'espace de Dirichlet. Dans un premier temps, nous allons voir pourquoi se placer à cette intersection est pertinent, en montrant comment utiliser les propriétés des semigroupes pour calculer explicitement les normes de certains opérateurs de composition. Dans un second temps, nous étudierons les propriétés des semigroupes d'opérateurs de compositions qui sont directement accessibles à partir de la seule donnée du générateur infinitésimal du semigroupe, en nous concentrant tout particulièrement sur les notions d'analyticité et de compacité / This thesis takes place at the intersection of several particularly active mathematical areas : functional analysis, operator theory, complex dynamics and theory of semigroups. Here, we study semigroups of composition operators on some weighted Hardy spaces, in particular the Hardy space of the disk and the Dirichlet space. First, we will show why this intersection is relevant for our study, pointing out how to use the properties of semigroups to explicitly compute the norms of some composition operators. Secondly, we will study the properties of semigroups of composition operators that are directly accessible from the only data of the infinitesimal generator, focusing on analyticity and compactness

Vários módulos funcionais de células ou bactérias são controlados por meio de genes que se regulam através da codificação de proteínas repressoras ou indutoras. A compreensão destas redes gênicas é um problema em aberto da biologia. Nesta dissertação procuramos aplicar o modelo estocástico de spins e bósons para o caso da rede mais simples, contiduída de dois genes, o primeiro reprimindo o segundo. Apresentamos a solução exata para a distribuição de probabilidades sobre o número das proteínas dos dois genes no estado estacionário, e a probabilidade dependente do tempo sobre o estado do segundo gene (ativado ou desativado). Discutimos também maneiras de generalizar os resultados para redes maiores. / Several functional modules in cells or bacteria are controlled by genes that regulate each other by coding repressive or inducer proteins. The understanding of these genetic networks is still an open problem in biology. In this work we apply the stochastic spin-boson model to the simplest interacting network, made of two genes, the first repressing the second. We present the exact solution for the stationary probability distribution over their both protein numbers, and the temporal evolution of the second genes state (on or off). We also discuss ways of generalizing these results to larger networks.

No description available.

Vários módulos funcionais de células ou bactérias são controlados por meio de genes que se regulam através da codificação de proteínas repressoras ou indutoras. A compreensão destas redes gênicas é um problema em aberto da biologia. Nesta dissertação procuramos aplicar o modelo estocástico de spins e bósons para o caso da rede mais simples, contiduída de dois genes, o primeiro reprimindo o segundo. Apresentamos a solução exata para a distribuição de probabilidades sobre o número das proteínas dos dois genes no estado estacionário, e a probabilidade dependente do tempo sobre o estado do segundo gene (ativado ou desativado). Discutimos também maneiras de generalizar os resultados para redes maiores. / Several functional modules in cells or bacteria are controlled by genes that regulate each other by coding repressive or inducer proteins. The understanding of these genetic networks is still an open problem in biology. In this work we apply the stochastic spin-boson model to the simplest interacting network, made of two genes, the first repressing the second. We present the exact solution for the stationary probability distribution over their both protein numbers, and the temporal evolution of the second genes state (on or off). We also discuss ways of generalizing these results to larger networks.