Mémoire numérisé par la Direction des bibliothèques de l'Université de Montréal.

Texte remanié de: Diss.--Fachbereich Philosophie und Sozialwissenschaften I--Berlin--Freie Universität, 1991.

Tarski's semantic conception of truth is arguably the most influential - certainly, most discussed - modern conception of truth. It has provoked many different interpretations and reactions, some thinkers celebrating it for successfully explicating the notion of truth, whereas others have argued that it is no good as a philosophical account of truth. The aim of the thesis is to offer a systematic and critical investigation of its nature and significance, based on the thorough explanation of its conceptual, technical as well as historical underpinnings. The methodological strategy adopted in the thesis reflects the author's belief that in order to evaluate the import of Tarski's conception we need to understand what logical, mathematical and philosophical aspects it has, what role they play in his project of theoretical semantics, which of them hang in together, and which should be kept separate. Chapter 2 therefore starts with a detailed exposition of the conceptual and historical background of Tarski's semantic conception of truth and his method of truth definition for formalized languages, situating it within his project of theoretical semantics, and Chapter 3 explains the formal machinery of Tarski's truth definitions for increasingly more complex languages. Chapters 4-7 form the core of the...

Mémoire numérisé par la Direction des bibliothèques de l'Université de Montréal.

Το παράδοξο Banach-Tarski είναι ένα εντυπωσιακό θεώρημα των καθαρών μαθηματικών που αποδείχθηκε απο τους Πολωνούς μαθηματικούς Banach και Tarski το 1924. Το θεώρημα αυτό λέει ότι μπορούμε να διαμέρισουμε οποιαδήποτε τρισδιάστατη ευκλείδεια μπάλα σε πεπερασμένα το πλήθος κομμάτια και έπειτα απο περιστροφές και μεταφορές αυτών των κομματιών να σχηματίσουμε δύο μπάλες οι οποίες είναι πανομοιότυπες με την αρχική. Το αποτέλεσμα αυτό έχει χαρακτηριστεί ως παράδοξο ακριβώς επειδή είναι ενάντιο στις διαισθήσεις μας. Για την απόδειξη του χρησιμοποιείται ουσιωδώς το Αξίωμα της Επιλογής απο τη Θεωρία Συνόλων, το πλέον επίμαχο αξίωμα της Συνολοθεωρίας. / The Banach-Tarski paradox is a striking theorem of pure mathematics proved by Polish mathematicians Banach and Tarski in 1924. This theorem states that there exists a decomposition of the three-dimensional Euclidean ball in a finite number of non-overlapping pieces, which can then be put back together in a different way to yield two identical copies of the original ball. This result has been described as a paradox precisely because it is highly anti-intuitive. To prove this theorem one must appeal to a set theoretic axiom, the Axiom of Choice, the most controversial axiom of Set theory.

The present study aims at analyzing the so-called Tarski proposal, a proposal about which objects should be considered as logical. My analysis has two parts: the first part, more historically oriented, compares Tarskis evolving methodology to Carnaps and Quines, in particular with the dierent conceptions of these latter two regarding that which they called explication. The second, more argumentative part, attempts to show that the most natural environment for this proposal is a platonic metaphysics of a neo-Fregean variety. / O presente estudo tem por objetivo analisar a assim chamada proposta de Tarski, a qual visa fornecer uma resposta à pergunta: quais objetos são lógicos? Nossa análise consiste em duas partes: uma primeira, mais histórica, compara a metodologia de Tarski àquela de Carnap e de Quine, se atentando principalmente às diferentes acepções que cada um deles atribui à noção de explicação (explication). A segunda parte, mais argumentativa, procura mostrar que um ambiente natural para essa proposta é uma metafísica platônica de franca inspiração neo-fregeana.

The present study aims at analyzing the so-called Tarski proposal, a proposal about which objects should be considered as logical. My analysis has two parts: the first part, more historically oriented, compares Tarskis evolving methodology to Carnaps and Quines, in particular with the dierent conceptions of these latter two regarding that which they called explication. The second, more argumentative part, attempts to show that the most natural environment for this proposal is a platonic metaphysics of a neo-Fregean variety. / O presente estudo tem por objetivo analisar a assim chamada proposta de Tarski, a qual visa fornecer uma resposta à pergunta: quais objetos são lógicos? Nossa análise consiste em duas partes: uma primeira, mais histórica, compara a metodologia de Tarski àquela de Carnap e de Quine, se atentando principalmente às diferentes acepções que cada um deles atribui à noção de explicação (explication). A segunda parte, mais argumentativa, procura mostrar que um ambiente natural para essa proposta é uma metafísica platônica de franca inspiração neo-fregeana.

This thesis presents the strong and weak forms of the Banach-Tarski paradox based on the Hausdorff paradox. It provides modernized proofs of the paradoxes and necessary properties of equidecomposable and paradoxical sets. The historical significance of the paradox for measure theory is covered, along with its incorrect attribution to Banach and Tarski. Finally, the necessity of the axiom of choice is discussed and contrasted with other axiomatic and topological assumptions that enable the paradoxes. / Den här uppsatsen presenterar den starka och svaga formen av Banach-Tarskis paradox baserade på Hausdorffs paradox. Den tillhandahåller moderniserade bevis av paradoxerna och nödvändiga egenskaper av likuppdelningsbara och paradoxala mängder. Den historiska betydelsen av paradoxen på måtteori tas upp samt dess felaktiga tillskrivning till Banach och Tarski. Till sist diskuteras behovet av urvalsaxiomet som ställs i kontrast mot andra axiomatiska och topologiska antaganden som möjliggör paradoxerna.

Orientador: Marcelo Esteban Coniglio / Dissertação (mestrado) - Universidade Estadual de Campinas, Instituto de Filosofia e Ciencias Humanas / Made available in DSpace on 2018-08-10T04:02:35Z (GMT). No. of bitstreams: 1 BatistaNeto_AlbertoLeopoldo_M.pdf: 764702 bytes, checksum: 38e943aef1a6e4a5f892916208eca7a5 (MD5) Previous issue date: 2007 / Resumo: Visando a atingir um esclarecimento sobre os conceitos fundamentais envolvidos no estudo das combinações entre lógicas, empreendemos uma alise do problema da representação geral de sistemas lógicos (com ênfase no conceito central de conseqüência lógica), juntamente com o do estabelecimento de uma noção apropriada de tradução ou morfismo entre os sistemas definidos de um determinado modo, com base em que podemos fundamentar algumas técnicas de combinação, especialmente a fibrilação algébrica. Tais técnicas são definidas e apresentadas em suas propriedades mais relevantes, sendo encontrados, no caso particular da fibrilação, problemas tais como o colapso e o anti-colapso. Para estes, a solução parece residir na escolha de formas adequadas de representar lógicas em geral e de traduzir lógicas umas nas outras. Uma apresentação modelo-teorética mostra-se apropriada para algumas representações de lógicas em geral (como, por exemplo, sistemas de Hilbert), embora não o seja para outras (como sistemas de conseqüências múltiplas). No entanto, duas das mais promissoras tentativas de solucionar, em particular, o problema do anti-colapso da fibrilação algébrica as meta-traduções e os transfers elementares podem ser definidas dentro desse arcabouço. Os transfers incluindo os transfers elementares - foram definidos em [17] - e aqui apresentamos uma representação das meta-traduções como tipo específico de transfer / Abstract: In order to accomplish an elucidation of the fundamental concepts involved in the study of the combinations between logics, we undertake an analysis of the problem of the general representation of logical systems (with an emphasis on the central concept of logical consequence) together with that of the establishment of an appropriate notion of translation or morphism between the logical systems defined in a certain fashion, on which basis we can ground some of the combination techniques, specially that of algebraic fibring. Such techniques are defined and presented in their most relevant features, and we find, in the particular case of fibring, problems such as collapsing and anticollapsing. The solution for these seem to rest on the choice of adequate forms of representing logics in general and translating logics into others. A modeltheoretic presentation shows itself appropriate for some representations of logics in general (such as Hilbert calculi), although they are not for some others (such as multipleconclusion systems). Notwithstanding, two of the most promising attempts to solve, in particular, the problem of the anticollapsing of algebraic fibring metatranslations and elementary transfers , are definable within that framework. Transfers including elementary transfers have been defined in [17] and we here present a representation of metatranslations as an specific kind of transfers / Mestrado / Logica / Mestre em Filosofia

Made available in DSpace on 2016-04-27T17:27:13Z (GMT). No. of bitstreams: 1 Carlos Roberto Teixeira Alves.pdf: 1331347 bytes, checksum: cebe03a83120937101a3595710844df2 (MD5) Previous issue date: 2015-12-14 / Coordenação de Aperfeiçoamento de Pessoal de Nível Superior / This work aims to show the current treatment of the semantic notion of satisfiability to the logic of the first order, the relevant problems of Tarski's solution to define this notion - in this case, the use of infinite sequences to satisfy the formulas - and propose an alternative to circumvent this problem. The notion established by Tarski became, in discussions on the subject, standard solution and resulted in rich tools to work with the languages, in particular tools such as the Theory of Models. However, from a philosophical point of view, it is very important to broaden perspectives and look at the problem from a new dimension. Our proposal is to avoid the counterintuitive idea of using infinite sequences of objects to satisfy the finite formulas, knowing that these infinite sequences are composed almost entirely of 'superfluous terms', expendable in the process of satisfaction, but they should and are listed and indexed in the process. It would be interesting to solve the issue involving sequences without 'superfluous terms'. We propose a structure of first-order language that dispenses variables and constants. The notion of satisfaction in this case is distinct, which increases the possibilities and provides an alternative to the satisfaction of infinite sequences. In the end, we show how our solution can produce the satisfaction of formulas of a first-order language within a framework where satisfaction is interpreted according to certain specific criteria and can be performed by finite sequences, differing essentially from Tarski solution / Este trabalho tem por objetivo mostrar o tratamento atual da noção semântica de satisfatibilidade para as lógicas de primeira ordem, os problemas relevantes da solução de Tarski para definir essa noção no caso, o uso de sequências infinitas para a satisfação das fórmulas , e propor uma alternativa que contorne esse problema. A noção estabelecida por Tarski tornou-se, nas discussões a respeito do tema, a solução padrão e resultou em ferramentas ricas para operar com as linguagens, em especial ferramentas como a Teoria dos Modelos. No entanto, de um ponto de vista filosófico, é sadio ampliar as perspectivas e olhar o problema sob uma dimensão nova. Nossa proposta é superar a ideia contraintuitiva de elencarmos sequências infinitas de objetos para satisfação das formulas finitas, sabendo que essas sequências infinitas são compostas quase que totalmente de termos supérfluos , dispensáveis no processo de satisfação, mas que devem e são enumerados e indexados no processo. Seria interessante solucionar a questão envolvendo sequências sem termos supérfluos . Proporemos uma estrutura de linguagem de primeira ordem que dispensa variáveis e constantes. A noção de satisfação nesse caso é distinta, o que amplia as possibilidades e fornece uma alternativa à satisfação por sequências infinitas. No fim, mostraremos como nossa solução consegue produzir a satisfação de fórmulas de uma linguagem de primeira ordem dentro de uma estrutura interpretada onde a satisfação ocorre segundo certos critérios específicos e consegue ser realizada por sequências finitas, diferindo essencialmente da solução de Tarski