In this thesis I discuss the problems associated with the epistemological task of arriving at basic logical knowledge. This is knowledge that the primitive rules of inference we use in deductive reasoning are correct. Knowledge of correctness, like all knowledge, is available to us either as the product of inference, or it is available non-inferentially. Success in the campaign to justify the correctness of these rules is mired by opposing views on how to do this properly. Inferential justifications of rules of inference, which are based on reasons, lead to regressive or circular results. Non-inferential justifications, based on something other than reasons, at first do not seem to fare any better: without a basis for these justifications, they appear arbitrary and unfounded. The works of Boghossian and Dummett who argue for an inferentialist approach, and Hale who supports non-inferentialism are carefully examined in this thesis. I conclude by finding superiority in Hale's suggestion that a particular set of basic logical constants are indispensable to deductive reasoning. I suggest that we endorse a principle which states that rules are not premises, and are therefore to be excluded from expression as statements in a deductive argument. I argue that the quality of being indispensable is sufficient for a basic rule of deduction to be countenanced as default-justified, and therefore need not be expressed in argument. By a rule's evading expression in argument, it avoids circular reasoning in deductive arguments about its own correctness. Another important outcome that emerges from my research is the finding that non-inferential knowledge is ontologically prior to the inferential sort. This is because plausible inferential knowledge of basic logical constants shall always be justified by circular reasoning that already assumes the correctness of the rule to be vindicated. This initial assumption is tantamount to non-inferential knowledge, and therefore this latter is more primitive-in fact the only primitive-species of basic logical knowledge.

Made available in DSpace on 2014-12-17T15:12:11Z (GMT). No. of bitstreams: 1 AdrianoMS_DISSERT.pdf: 2088118 bytes, checksum: dd824a46d35773271668ba84f8280fa8 (MD5) Previous issue date: 2009-12-15 / The main goal of this work is to clarify the central concepts involved in the study of formalization of conditional sentences. More specifically, it has been done a comparative analysis of the two greater and more traditional proposals of conditional formalization (Lewis 1973c e Adams 1975). These proposals were responsible for the creation of a way of analysis that still present in the current debate about this subject. This work pursues to explain the principal assumptions held within these proposals. According to certain disambiguation techniques from Bennett (2003) and Lycan (2005), this work tries to explicit how these assumptions connect to the aims sought by the initial approaches. The following results show that there is a not declared presumption, the definition of the object of study of these theories, i.e., the definition of conditional sentence. This work argues that despite of not explicitly declared the definition of the study object has a central role in the intelligibility of the debate itself / estudo da formaliza??o das senten?as condicionais. Mais especificamente, empreendemos uma an?lise comparativa de duas das principais e mais tradicionais propostas de formaliza??o dos condicionais (Lewis (1973c) e Adams (1975)), propostas respons?veis pela inaugura??o de vertentes de an?lise que ainda se fazem presentes no debate contempor?neo sobre o tema. Visamos, fundamentalmente, o esclarecimento das principais assun??es presentes nessas propostas. Com base em certas t?cnicas de desambigua??o presentes em Bennett (2003) e em Lycan (2005), buscamos explicitar como essas assun??es articulam-se, efetivamente, aos objetivos almejados pelas abordagens inaugurais. Os resultados que se seguem mostram que existe um pressuposto, n?o explicitamente declarado, t?cito, a defini??o do objeto de estudo dessas teorias, isto ?, a defini??o de senten?a condicional. Argumentamos que, apesar de n?o claramente declarada, a defini??o do objeto de estudo desempenha um papel fundamental na pr?pria inteligibilidade do debate

A presente dissertação tem dois objetivos. Em primeiro lugar, pretendemos armar um debate entre Russell e Wittgenstein tendo como questão mestra a relação entre lógica e linguagem. Em especial, procuramos encontrar elementos em The Philosophy of Logical Atomism e no Tractatus Logico-Philosophicus para reconstruir a resposta que consta em cada uma das obras para as questões: qual o estatuto lógico da linguagem corrente? Qual a função do lógico enquanto tal? Em segundo lugar, pretendemos apresentar um jogo de cartas – o jogo da Figuração – que desenvolvemos ao longo da pesquisa e funciona como uma ilustração do Tractatus. Em função do jogo será possível compreender algumas das principais teses da obra. Em especial, o papel da teoria da figuração e a distinção entre dizer e mostrar como pilares da explicação tractariana para a questão sobre o funcionamento lógico da linguagem. Além disso, com base na semelhança entre o nosso jogo da figuração e a explicação de Wittgenstein para o funcionamento lógico da linguagem, apresentaremos uma série de razões que justificam o fracasso do projeto de Wittgenstein. Por fim, defenderemos a tese segundo a qual o nosso pensamento funciona com base em uma série de padrões lógicos distintos e não apenas um único padrão lógico (tal qual defendido no Tractatus). / The present dissertation has two goals. In the first place, we intend to construct a debate between Russell and Wittgenstein having the relation between logic and language as our master question. In particular, we seek to find elements in The Philosophy of Logical Atomism and the Tractatus Logico-Philosophicus to reconstruct the answer in each of the works for the questions: what is the logical status of the current language? What is the role of the logician as such? Secondly, we intend to present a card game – the Picture game- that we developed throughout the research and functions as an illustration of the Tractatus. Based on the game we will be able to understand some of the main theses of the work. In particular, the role of picture theory and the distinction between saying and showing as pillars of the tractarian explanation for the question about the logical functioning of language. Moreover, on the basis of the similarity between our picture game and Wittgenstein's explanation for the logical functioning of language, we will present a number of reasons for the failure of Wittgenstein's project. Finally, we will defend the thesis that our thinking operates on the basis of a series of distinct logical patterns and not just a single logical pattern (as defended in the Tractatus).

A presente dissertação tem dois objetivos. Em primeiro lugar, pretendemos armar um debate entre Russell e Wittgenstein tendo como questão mestra a relação entre lógica e linguagem. Em especial, procuramos encontrar elementos em The Philosophy of Logical Atomism e no Tractatus Logico-Philosophicus para reconstruir a resposta que consta em cada uma das obras para as questões: qual o estatuto lógico da linguagem corrente? Qual a função do lógico enquanto tal? Em segundo lugar, pretendemos apresentar um jogo de cartas – o jogo da Figuração – que desenvolvemos ao longo da pesquisa e funciona como uma ilustração do Tractatus. Em função do jogo será possível compreender algumas das principais teses da obra. Em especial, o papel da teoria da figuração e a distinção entre dizer e mostrar como pilares da explicação tractariana para a questão sobre o funcionamento lógico da linguagem. Além disso, com base na semelhança entre o nosso jogo da figuração e a explicação de Wittgenstein para o funcionamento lógico da linguagem, apresentaremos uma série de razões que justificam o fracasso do projeto de Wittgenstein. Por fim, defenderemos a tese segundo a qual o nosso pensamento funciona com base em uma série de padrões lógicos distintos e não apenas um único padrão lógico (tal qual defendido no Tractatus). / The present dissertation has two goals. In the first place, we intend to construct a debate between Russell and Wittgenstein having the relation between logic and language as our master question. In particular, we seek to find elements in The Philosophy of Logical Atomism and the Tractatus Logico-Philosophicus to reconstruct the answer in each of the works for the questions: what is the logical status of the current language? What is the role of the logician as such? Secondly, we intend to present a card game – the Picture game- that we developed throughout the research and functions as an illustration of the Tractatus. Based on the game we will be able to understand some of the main theses of the work. In particular, the role of picture theory and the distinction between saying and showing as pillars of the tractarian explanation for the question about the logical functioning of language. Moreover, on the basis of the similarity between our picture game and Wittgenstein's explanation for the logical functioning of language, we will present a number of reasons for the failure of Wittgenstein's project. Finally, we will defend the thesis that our thinking operates on the basis of a series of distinct logical patterns and not just a single logical pattern (as defended in the Tractatus).

A presente dissertação tem dois objetivos. Em primeiro lugar, pretendemos armar um debate entre Russell e Wittgenstein tendo como questão mestra a relação entre lógica e linguagem. Em especial, procuramos encontrar elementos em The Philosophy of Logical Atomism e no Tractatus Logico-Philosophicus para reconstruir a resposta que consta em cada uma das obras para as questões: qual o estatuto lógico da linguagem corrente? Qual a função do lógico enquanto tal? Em segundo lugar, pretendemos apresentar um jogo de cartas – o jogo da Figuração – que desenvolvemos ao longo da pesquisa e funciona como uma ilustração do Tractatus. Em função do jogo será possível compreender algumas das principais teses da obra. Em especial, o papel da teoria da figuração e a distinção entre dizer e mostrar como pilares da explicação tractariana para a questão sobre o funcionamento lógico da linguagem. Além disso, com base na semelhança entre o nosso jogo da figuração e a explicação de Wittgenstein para o funcionamento lógico da linguagem, apresentaremos uma série de razões que justificam o fracasso do projeto de Wittgenstein. Por fim, defenderemos a tese segundo a qual o nosso pensamento funciona com base em uma série de padrões lógicos distintos e não apenas um único padrão lógico (tal qual defendido no Tractatus). / The present dissertation has two goals. In the first place, we intend to construct a debate between Russell and Wittgenstein having the relation between logic and language as our master question. In particular, we seek to find elements in The Philosophy of Logical Atomism and the Tractatus Logico-Philosophicus to reconstruct the answer in each of the works for the questions: what is the logical status of the current language? What is the role of the logician as such? Secondly, we intend to present a card game – the Picture game- that we developed throughout the research and functions as an illustration of the Tractatus. Based on the game we will be able to understand some of the main theses of the work. In particular, the role of picture theory and the distinction between saying and showing as pillars of the tractarian explanation for the question about the logical functioning of language. Moreover, on the basis of the similarity between our picture game and Wittgenstein's explanation for the logical functioning of language, we will present a number of reasons for the failure of Wittgenstein's project. Finally, we will defend the thesis that our thinking operates on the basis of a series of distinct logical patterns and not just a single logical pattern (as defended in the Tractatus).

Partant des travaux séminaux de Boole, Frege et Russell, le mémoire cherche à clarifier l‟enjeu du pluralisme logique à l‟ère de la prolifération des logiques non-classiques et des développements en informatique théorique et en théorie des preuves. Deux chapitres plus « historiques » sont à l‟ordre du jour : (1) le premier chapitre articule l‟absolutisme de Frege et Russell en prenant soin de montrer comment il exclut la possibilité d‟envisager des structures et des logiques alternatives; (2) le quatrième chapitre expose le chemin qui mena Carnap à l‟adoption de la méthode syntaxique et du principe de tolérance, pour ensuite dégager l‟instrumentalisme carnapien en philosophie de la Logique et des mathématiques. Passant par l‟analyse d‟une interprétation intuitive de la logique linéaire, le deuxième chapitre se tourne ensuite vers l‟établissement d‟une forme logico-mathématique de pluralisme logique à l‟aide de la théorie des relations d‟ordre et la théorie des catégories. Le troisième chapitre délimite le terrain de jeu des positions entourant le débat entre monisme et pluralisme puis offre un argument contre la thèse qui veut que le conflit entre logiques rivales soit apparent, le tout grâce à l‟utilisation du point de vue des logiques sous-structurelles. Enfin, le cinquième chapitre démontre que chacune des trois grandes approches au concept de conséquence logique (modèle-théorétique, preuve-théorétique et dialogique) forme un cadre suffisamment général pour établir un pluralisme. Bref, le mémoire est une défense du pluralisme logique. / Starting from the seminal work of Boole, Frege and Russell, the dissertation seeks to clarify the issue of logical pluralism in the era of the proliferation of non-classical logics and the developments in theoretical computer science and proof theory. Two “historical” chapters are scheduled: the first chapter articulate the absolutism of Frege and Russell, taking care to show how it condemns the possibility to consider alternative structures and logics; the fourth chapter describes the path that led Carnap from the adoption of the syntactic method to the formulation of the principle of tolerance, then goes on to display Carnap‟s instrumentalism in philosophy of Logic and mathematics. Opening with the analysis of an intuitive interpretation of linear logic, the second chapter then turns to the establishment of a form of logico-mathematical pluralism with the help of order theory and category theory. The third chapter delineates the playground of revisionism (philosophical positions surrounding the debate between monism and pluralism) and then provides an argument against the thesis that denies the reality of the conflict between rival logics, all this being done by adopting the substructural logic point of view. The fifth chapter shows that each of the three main approaches to the concept of logical consequence (model-theoretic, proof-theoretic and dialogical) supplies a framework sufficiently general to establish pluralism. In short, the dissertation is a defence of logical pluralism.

Partant des travaux séminaux de Boole, Frege et Russell, le mémoire cherche à clarifier l‟enjeu du pluralisme logique à l‟ère de la prolifération des logiques non-classiques et des développements en informatique théorique et en théorie des preuves. Deux chapitres plus « historiques » sont à l‟ordre du jour : (1) le premier chapitre articule l‟absolutisme de Frege et Russell en prenant soin de montrer comment il exclut la possibilité d‟envisager des structures et des logiques alternatives; (2) le quatrième chapitre expose le chemin qui mena Carnap à l‟adoption de la méthode syntaxique et du principe de tolérance, pour ensuite dégager l‟instrumentalisme carnapien en philosophie de la Logique et des mathématiques. Passant par l‟analyse d‟une interprétation intuitive de la logique linéaire, le deuxième chapitre se tourne ensuite vers l‟établissement d‟une forme logico-mathématique de pluralisme logique à l‟aide de la théorie des relations d‟ordre et la théorie des catégories. Le troisième chapitre délimite le terrain de jeu des positions entourant le débat entre monisme et pluralisme puis offre un argument contre la thèse qui veut que le conflit entre logiques rivales soit apparent, le tout grâce à l‟utilisation du point de vue des logiques sous-structurelles. Enfin, le cinquième chapitre démontre que chacune des trois grandes approches au concept de conséquence logique (modèle-théorétique, preuve-théorétique et dialogique) forme un cadre suffisamment général pour établir un pluralisme. Bref, le mémoire est une défense du pluralisme logique. / Starting from the seminal work of Boole, Frege and Russell, the dissertation seeks to clarify the issue of logical pluralism in the era of the proliferation of non-classical logics and the developments in theoretical computer science and proof theory. Two “historical” chapters are scheduled: the first chapter articulate the absolutism of Frege and Russell, taking care to show how it condemns the possibility to consider alternative structures and logics; the fourth chapter describes the path that led Carnap from the adoption of the syntactic method to the formulation of the principle of tolerance, then goes on to display Carnap‟s instrumentalism in philosophy of Logic and mathematics. Opening with the analysis of an intuitive interpretation of linear logic, the second chapter then turns to the establishment of a form of logico-mathematical pluralism with the help of order theory and category theory. The third chapter delineates the playground of revisionism (philosophical positions surrounding the debate between monism and pluralism) and then provides an argument against the thesis that denies the reality of the conflict between rival logics, all this being done by adopting the substructural logic point of view. The fifth chapter shows that each of the three main approaches to the concept of logical consequence (model-theoretic, proof-theoretic and dialogical) supplies a framework sufficiently general to establish pluralism. In short, the dissertation is a defence of logical pluralism.