Ever since the advent of computerized methods for solving mathematical problems, the concept of surveyability has played a central role in the debate surrounding what constitutes a mathematical proof. Ordinarily, it is by surveying the argument presented that the mathematician ascertains the truth of the conclusion, but with the advent of computer assisted technologies, there are mathematical conclusions known to be true without anyone ever having been able to survey the argument in its entirety. What this seems to suggest is that what is called "mathematical knowledge" encompasses two different types of knowledge: one gained through the act of surveying a proof, and the other through computerized empirical experiments. The goal of this thesis is to investigate the connection between surveyability and the acquisition of mathematical knowledge, thereby elucidating the difference between the two epistemological categories. The claim is that this can be accomplished by applying Heidegger's account of unconcealment to the notion of mathematical truth, supported by a Wittgensteinian analysis of the act of surveying as a type of reproduction of the proof. While much has been written on how his early mathematical training influenced Heidegger's philosophy, attempts at applying elements from his thinking to problems belonging to the philosophy of mathematics are rare. This investigation has the ambition of making a convincing case for the potential in this kind of approach.

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Rule-following has been a controversial issue in professional philosophical literature since Wittgenstein's Philosophical Investigations. Many authors have developed accounts of rule-following along different lines, including those that naturalistically reduce rule-following to non-normative phenomena and those that take rule-following to be an irreducible aspect of cognition and agency. Hannah Ginsborg, a prominent contributor to rule-following literature, has developed a partially reductive account of rule-following, combining features of both reductionist and nonreductionist accounts. But naturalizing or internalistic theories of rule-following, or even Ginsborg's partial reduction of rule-following, ignore important facets of what it is to follow a rule, particularly its social aspect. In this thesis I reject Ginsborg's partial reductionism, holding that her hybrid theory does not escape the particular problems of naturalistic reductionism or nonreductionism about rule-following. I argue instead that certain social concepts are necessary for a satisfactory theory of rule-following. The first concept is how an individual is "enculturated" into her various social and cultural networks. The second is one's "normative identity," the accumulated concepts and behaviors one has as part of a social and cultural network. I develop these notions with inspiration from Wittgenstein and other social contributors to rule-following literature.

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[pt] Este trabalho apresenta uma reflexão sobre a comensurabilidade entre as perspectivas chomskyana e wittgensteiniana da linguagem em geral e, em particular, no que diz respeito à questão do sentido. O objetivo da pesquisa foi examinar, nos textos do Wittgenstein maduro, nos desenvolvimentos mais recentes de Chomsky — levando em consideração as sucessivas mudanças na teoria gerativa — e nas obras de outros autores que se alinham com as ideias de um e outro ou se dedicam a estudá-los, convergências e divergências relevantes entre eles. A pesquisa adotou uma perspectiva pragmática e antiessencialista da linguagem, mais especificamente a versão dessa perspectiva oferecida pela filosofia mais madura de Wittgenstein, sobretudo nas suas Investigações filosóficas. Sem renunciar a essa perspectiva, foram analisadas as teorias sobre a linguagem humana defendidas por Noam Chomsky, geralmente tidas como opostas às do filósofo vienense, partindo da hipótese de que fosse possível encontrar, no diálogo entre elas, possíveis complementações para uma melhor compreensão do funcionamento da linguagem humana. As teses que resultam do trabalho são as seguintes: (1) Que os pontos de vista de Chomsky e Wittgenstein sobre a linguagem não são inteiramente irreconciliáveis e podem existir convergências, divergências e possíveis complementações que valem a pena serem exploradas, (2) Que as versões contemporâneas das teorias de Chomsky estão mais abertas à aproximação com Wittgenstein do que versões passadas, (3) Que algumas contradições entre as análises de Wittgenstein e Chomsky podem ser atribuídas à diferença entre o ponto de vista e os métodos de um filósofo e os de um cientista da linguagem, ou a confusões conceituais provocadas pelas armadilhas da própria linguagem — termos usados por eles próprios ou por seus mais destacados comentadores de formas que parecem altamente contraditórias, podendo nos levar à conclusão de que existe uma incompatibilidade insuperável entre seus pontos de vista, (4) Que, ao menos parcialmente, algumas dessas contradições podem ser atribuídas ao choque entre a tese chomskyana da autonomia da sintaxe e a preocupação quase exclusiva de Wittgenstein pelo sentido. Entre outros aspectos relevantes das ideias de ambos os pensadores, analisamos o uso que eles fazem de termos como representação, mente, descrição e explicação; de questões fundamentais para ambos, como suas ideias sobre o que seja aprender uma língua e seguir uma regra, e de algumas noções distintivas do pensamento de cada um, como a noção wittgensteiniana de forma de vida e a hipótese inatista de Chomsky. Por último, analisamos de forma mais aprofundada duas controvérsias explícitas entre Chomsky e Wittgenstein, a partir de dois textos do primeiro que fazem detalhadas críticas a aspectos importantes da filosofia do segundo: o argumento da linguagem privada e a crítica à ideia de que existem processos cerebrais correlacionados com o pensamento. / [en] This work reflects on the commensurability between the Chomskyan and the Wittgenstenian perspectives of language in general, and in particular it deals with issues on meaning. The goal of the research was to examine, in the mature texts of Wittgenstein, in the most recent developments of Chomsky — taking into consideration the successive changes in generative theory — and in the works of other authors that align themselves with the ideas of one or the other or devote themselves to study them, convergences and divergences relevant to them. The research adopted a pragmatic and anti-essentialist approach to language, more specifically the version of this approach offered by Wittgenstein s more mature philosophy, mostly in his Philosophical Investigations. Without renouncing this approach, the theories of human language supported by Noam Chomsky were analyzed, which are generally considered as opposed to those of the Viennese philosopher, starting from the hypothesis that it is possible to find, in the dialog between them, possible complementarities for a better understanding of how human language works. The present work are guided by following thesis: (1) Chomsky s and Wittgenstein s points of view about language are not completely irreconcilable and there can be convergences, divergences and possible complementarities that are worth exploring; (2) the contemporary versions of Chomsky s theories can be more open to a rapprochement with Wittgenstein than past versions; (3) some contradictions between the analysis of Chomsky and Wittgenstein can be attributed to the difference between the points of view and methods of a philosopher and those language of a scientist, or to conceptual confusions originated in the tricks of language itself – terms used by them or by their more outstanding commentators in ways that seem highly contradictory, leading us to the conclusion that there is an insurmountable incompatibility between their points of view; (4) at least partially, some of those contradictions can be attributed to the conflict between the Chomskyan hypothesis about the Autonomy of Syntax and the almost exclusive preoccupation of Wittgenstein for the meaning. Among other relevant aspects of the ideas of both authors, we will analyze how they use terms like representation, mind, description and explanation; fundamental questions for both, like their ideas about what it is to learn a language and follow a rule, and about distinctive notions of their thought, like the Wittgenstenian notion of form of life and the Chomskyan innate hypothesis. Finally, we analyze in deep two explicit disputes between Chomsky and Wittgenstein, taking as a starting point two texts of the former that formulate detailed criticism to important aspects of the latter s philosophy: the argument of private language and the criticism of the idea that there are brain processes correlated to thought. / [es] Este trabajo presenta una reflexión sobre la conmensurabilidad entre las perspectivas chomskyana y wittgensteiniana del lenguaje en general y, en particular, en lo que se refiere a la cuestión del sentido. El objetivo de la investigación fue examinar, en los textos del Wittgenstein maduro, en los desarrollos más recientes de Chomsky —teniendo en cuenta los sucesivos cambios en la teoría generativa— y en las obras de otros autores que se alinean con las ideas de uno y otro o se dedican a estudiarlos, convergencias y divergencias relevantes entre ellos. La investigación adoptó una perspectiva pragmática y antiesencialista del lenguaje, más específicamente la versión de esta perspectiva ofrecida por la filosofía más madura de Wittgenstein, sobre todo en sus Investigaciones filosóficas. Sin renunciar a esa perspectiva, fueron analizadas las teorías sobre el lenguaje humano defendidas por Noam Chomsky, generalmente consideradas como opuestas a las del filósofo vienés, partiendo de la hipótesis de que fuese posible encontrar, en el diálogo entre ellas, posibles complementaciones para una mejor comprensión del funcionamiento del lenguaje humano. Las tesis que resultan de este trabajo son las siguientes: (1) Que los puntos de vista de Chomsky y Wittgenstein sobre el lenguaje no son completamente irreconciliables y pueden existir convergencias, divergencias y posibles complementaciones que vale la pena explorar, (2) Que las versiones contemporáneas de las teorías de Chomsky están más abiertas a la aproximación con Wittgenstein que las versiones pasadas, (3) Que algunas contradicciones entre los análisis de Wittgenstein y Chomsky pueden ser atribuidos a la diferencia entre el punto de vista y los métodos de un filósofo y los de un científico del lenguaje, o a confusiones conceptuales provocadas por las armadillas del propio lenguaje — términos utilizados por ellos mismos o por sus más destacados comentadores de maneras que parecen altamente contradictorias, pudiendo llevarnos a la conclusión de que existe una incompatibilidad insuperable entre sus puntos de vista, (4) Que, al menos parcialmente, algunas de esas contradicciones pueden ser atribuidas al choque entre la tesis chomskyana de la autonomía de la sintaxis y la preocupación casi exclusiva de Wittgenstein por el sentido. Entre otros aspectos relevantes de las ideas de ambos pensadores, analizamos el uso que realizan de términos como representación, mente, descripción y explicación; de cuestiones fundamentales para ambos, como sus ideas sobre lo que sea aprender una lengua y seguir una regla, y de algunas nociones distintivas del pensamiento de cada uno, como la noción wittgensteiniana de forma de vida y la hipótesis innatista de Chomsky. Por último, analizamos más profundamente dos controversias explícitas entre Chomsky y Wittgenstein, a partir de dos textos del primero que hacen detalladas críticas a aspectos importantes de la filosofía del segundo: el argumento del lenguaje privado y la crítica a la idea de que existan procesos cerebrales correlacionados con el pensamiento.

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The following inquiry pursues two interlinked aims. The first is to understand Wittgenstein's idea of non-foundational certainty in the context of a reading of On Certainty that emphasizes its Pyrrhonian elements. The second is to read Wittgenstein's remarks on idealism/radical skepticism in On Certainty in parallel with the discussion of rule-following in Philosophical Investigations in order to demonstrate an underlying similarity of philosophical concerns and methods. I argue that for the later Wittgenstein, what is held certain in a given context of inquiry or action is a locally transcendental condition of the inquiry or action in question. In On Certainty, Wittgenstein's analysis of the difference between knowledge and certainty forms the basis of his critique of both Moore's "Proof" and radical skepticism. This critique takes the shape of rejection of a presupposition shared by both parties, and utilizes what I identify as a Pyrrhonian-style argument against opposed dogmatic views. Wittgenstein's method in this text involves describing epistemic language-games. I demonstrate that this is consistent with the rejection of epistemological theorizing, arguing that a Wittgensteinian "picture" is not a theory, but an impressionistic description that accomplishes two things: (i) throwing into relief problems with dogmatic theories and their presuppositions, and (ii) describing the provenance of linguistic and epistemic practices in terms of norms grounded in convention. Convention, in turn, is not arbitrary, but grounded in the biological and social natures of human beings--in what Wittgenstein calls forms of life. Thus there is a kind of naturalism in the work of the later Wittgenstein. It is a naturalism that comes neatly dovetailed with Pyrrhonism--a combination of strategies traceable to Hume's work in the Treatise. I read Hume as someone who develops the Pyrrhonian method to include philosophy done "in a careless manner," and argue that Wittgenstein adopts a similar method in his later works. Finally, I explain the deference to convention in the work of both Hume and Wittgenstein by reference to a passage in Sextus' Outlines, on which I provide a gloss in the final chapter of this work.

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