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.

In broadest terms, this thesis is concerned to answer the question of whether the view that arithmetic is analytic can be maintained consistently. Lest there be much suspense, I will conclude that it can. Those who disagree claim that accounts which defend the analyticity of arithmetic are either unable to give a satisfactory account of the foundations of mathematics due to the incompleteness theorems, or, if steps are taken to mitigate incompleteness, then the view loses the ability to account for the applicability of mathematics in the sciences. I will show that this criticism is not successful against every view whereby arithmetic is analytic by showing that the brand of "conventionalism" about mathematics that Rudolf Carnap advocated in the 1930s, especially in Logical Syntax of Language, does not suffer from these difficulties. There, Carnap develops an account of logic and mathematics that ensures the analyticity of both. It is based on his famous "Principle of Tolerance", and so the major focus of this thesis will to defend this principle from certain criticisms that have arisen in the 80 years since the book was published. I claim that these criticisms all share certain misunderstandings of the principle, and, because my diagnosis of the critiques is that they misunderstand Carnap, the defense I will give is of a primarily historical and exegetical nature. Again speaking broadly, the defense will be split into two parts: one primarily historical and the other argumentative. The historical section concerns the development of Carnap's views on logic and mathematics, from their beginnings in Frege's lectures up through the publication of Logical Syntax. Though this material is well-trod ground, it is necessary background for the second part. In part two we shift gears, and leave aside the historical development of Carnap's views to examine a certain family of critiques of it. We focus on the version due to Kurt Gödel, but also explore four others found in the literature. In the final chapter, I develop a reading of Carnap's Principle - the `wide' reading. It is one whereby there are no antecedent constraints on the construction of linguistic frameworks. I argue that this reading of the principle resolves the purported problems. Though this thesis is not a vindication of Carnap's view of logic and mathematics tout court, it does show that the view has more plausibility than is commonly thought.

A pesquisa que ora se apresenta consiste em uma investigação sobre o recente trabalho de reavaliação das obras de membros do chamado Círculo de Viena, que foi o primeiro e principal grupo representativo da perspectiva filosófica conhecida como positivismo lógico. Nossa pesquisa compreende três partes: a primeira parte voltada para a reconstrução histórico-conceitual do período entre o alvorecer das idéias neopositivistas e os primeiros momentos posteriores à recepção norte-americana da imigração intelectual vienense; na segunda parte do trabalho, por sua vez, lançaremos luz propriamente à natureza de tal perspectiva contemporânea, a partir de uma descrição sobre o método e o escopo temático de tal projeto revisionista; à terceira parte, por fim, além de tecer uma avaliação geral sobre o que foi feito nas duas partes que a antecedem, coube conjecturar as possibilidades de se encontrar em tal trabalho uma agenda filosófica e política própria. / The present work consists on an inquiry concerning the recent re-evaluation in the works of members of the so-called Vienna Circle, which became the first and main representative of the philosophical movement known as Logical Positivism. Our research comprises three parts: the first one is devoted to a historical-conceptual reconstruction of the period between the uprising of the first Neopositivist ideas and the years immediately following the North-American reception of the intellectual immigration from Vienna; the second part of the work concerns the nature of such contemporary reappraisal researches on the positivists legacy, through a description of the method and scope of such re-evaluation project; finally, the third part comprises a general review of the previous parts, and was worked out in order to conceive conjectures about the possibility of finding out in this re-evaluation project a philosophical and political agenda of its own.

A pesquisa que ora se apresenta consiste em uma investigação sobre o recente trabalho de reavaliação das obras de membros do chamado Círculo de Viena, que foi o primeiro e principal grupo representativo da perspectiva filosófica conhecida como positivismo lógico. Nossa pesquisa compreende três partes: a primeira parte voltada para a reconstrução histórico-conceitual do período entre o alvorecer das idéias neopositivistas e os primeiros momentos posteriores à recepção norte-americana da imigração intelectual vienense; na segunda parte do trabalho, por sua vez, lançaremos luz propriamente à natureza de tal perspectiva contemporânea, a partir de uma descrição sobre o método e o escopo temático de tal projeto revisionista; à terceira parte, por fim, além de tecer uma avaliação geral sobre o que foi feito nas duas partes que a antecedem, coube conjecturar as possibilidades de se encontrar em tal trabalho uma agenda filosófica e política própria. / The present work consists on an inquiry concerning the recent re-evaluation in the works of members of the so-called Vienna Circle, which became the first and main representative of the philosophical movement known as Logical Positivism. Our research comprises three parts: the first one is devoted to a historical-conceptual reconstruction of the period between the uprising of the first Neopositivist ideas and the years immediately following the North-American reception of the intellectual immigration from Vienna; the second part of the work concerns the nature of such contemporary reappraisal researches on the positivists legacy, through a description of the method and scope of such re-evaluation project; finally, the third part comprises a general review of the previous parts, and was worked out in order to conceive conjectures about the possibility of finding out in this re-evaluation project a philosophical and political agenda of its own.