In this paper, I provide an interpretation of Frege's logicist project, drawing a connection between it and his idiosyncratic view of truth.

In the first half of the thesis I investigate David Hilbert's early ontology of mathematics around the period 1899-1916. Hilbert's early views are of significant philosophical interest and have been largely ignored due to his later, more influential work. I suggest that, in this period Hilbert, can be understood as an early structuralist. In the second half of the thesis, I connect two important debates in the foundations of mathematics: Hale and Wright's neo-Fregean logicism and the Frege-Hilbert controversy. Using this connection, I adapt Frege's objections to Hilbert and apply them to Hale and Wright's account. By doing this, I show that the neo-Fregean logicists have long abandoned the Fregean element of their program in favor of a structuralist ontology. I conclude that our ontological conception of what exists in mathematics and what it is like constrains the foundations we use to characterise mathematical reality.

In this thesis I argue forin re structuralism in the philosophy of mathematics. In the first chapters of the thesis I argue that there is a genuine epistemic access problem for Platonism, that the semantic challenge to nominalism may be met by paraphrase strategies, and that nominalizations of scientific theories have had adequate success to blunt the force of the indispensability argument for Platonism. In the second part of the thesis I discuss the development of logicism and structuralism as methodologies in the history of mathematics. The goal of this historical investigation is to lay the groundwork for distinguishing between the philosophical analysis of the content of mathematics and the analysis of the breadth and depth of results in mathematics. My central contention is that the notion of logical structure provides a context for the latter not the former. In turn, this contention leads to a rejection of ante rem structuralism in favor of in re structuralism. In the concluding part of the dissertation the philosophy of mathematical structures developed and defended in the preceding chapters is applied to the philosophy of science.

Orientador: Irineu Bicudo / Banca: Itala Maria Loffredo D'Otaviano / Banca: Paulo Isamo Hiratsuka / Resumo: Neste trabalho apresentamos e analisamos o conceito fregiano de função, presente nos três livros de Frege: Begriffsschrift, Os Fundamentos da Aritmética e Leis Fundamentais da Aritmética. Discutimos ao longo dele o que Frege entendia por função e argumento, as modificações conceituais que tais noções sofreram no período de publicação de seus livros e a importância dessas noções para a sua filosofia. Para tanto, analisamos a linguagem artificial do primeiro livro, a definição de número do segundo, e os casos particulares de funções que são definidos no terceiro, bem como as considerações contidas em outros escritos do filósofo alemão. Verificamos uma caracterização puramente sintática de função em Begriffsschrift, uma distinção entre o sinal de uma função e aquilo que ele denota em Os Fundamentos da Aritmética, e a associação de dois elementos distintos a uma expressão funcional em Leis Fundamentais da Aritmética: o seu sentido e a sua referência. Finalmente, constatamos que a originalidade do sistema fregiano reside na possibilidade de considerar esse ou aquele termo de uma proposição como o argumento (ou os argumentos) de uma função. / Abstract: In this work we present and analyze the fregean concept of function, present in the three books by Frege: Begriffsschrift, The Foundations of the Arithmetic and Fundamental Laws of the Arithmetic. We discuss what Frege understood by function and argument, the conceptual modifications that such notions suffered in the period of publication of those books and the importance of these notions for his philosophy. For so much, we analyze the artificial language of the first book, the definition of number in the second, and the particular cases of functions that are defined in the third, as well as the considerations contained in other works by the philosopher. We verify a purely syntactic characterization of function in Begriffsschrift, a distinction between the sign of a function and what it denotes in The Foundations of the Arithmetic, and the association of two different elements to a functional expression in Fundamental Laws of the Arithmetic: its sense and its reference. Finally, we verify that the originality of the Frege's system is based on the possibility of considering one or other term of a proposition as the argument (or the arguments) of a function. / Mestre

Made available in DSpace on 2016-04-27T17:27:06Z (GMT). No. of bitstreams: 1 Arthur Heller Britto.pdf: 403242 bytes, checksum: 9ea7d542e4846499fab1760b30fe2a33 (MD5) Previous issue date: 2013-11-08 / The objective of this dissertation is first to present the fundamental part of Frege's logicist project - that became known as Frege's theorem - as an independent mathematical result in order to then evaluate its philosophical significance through a discussion of Frege's concept of logic. Besides, there are two appendixes in which a general recursion theorem is proven inside a classical second-order logical system and a neofregean construction of the real numbers from Cauchy sequences is presented / O objetivo desta dissertação e, em primeiro lugar, apresentar o núcleo fundamental do projeto logicista fregeano - o que ficou conhecido pelo nome de teorema de Frege - como um resultado matemático independente para, em seguida, avaliar o seu significado filosófico por meio da discussão acerca do conceito fregeano de logica. Além disso, este trabalho contém dois anexos, nos quais se demonstra um teorema geral de recursão dentro de um sistema clássico de logica de segunda ordem e se apresenta uma construção neofregeana dos números reais por meio de sequências de Cauchy

Boèce prétend avoir apporté une solution définitive aux deux grandes apories du corpus logique aristotélicien, l'aporie de l'universel et l'aporie des futurs contingents. Nous montrons qu'Abélard, à travers sa critique des reales, met en question ces deux solutions et leur substitue deux distinctions voulues comme aporétiques - entre res et status d'un côté et entre res et dictum propositionis de l'autre - qui naissent de la reconnaissance par Abélard du caractère fictif des solutions boéciennes aux grandes apories du corpus logique aristotélicien. Ces deux distinctions organisent une réflexion philosophique profondément novatrice que nous nous efforçons de décrire. / Boethius claims to have definitively solved the two great aporias of the corpus of Aristotelian Iogic, the universal aporia and the aporia of contingent futures. l demonstrate that Abelard,Through his critique of reales calls into question these two solutions and substitutes two distinctions that he wanted to he aporetique - between res and status on the one band andand dictum propositionis on the other hand - born of Abelard's recognition of the fictional character of the two Boetian solutions to the great aporias of the Aristotelician logical corpus. The two. distinctions pave the way for a profoundly new kind of philosophical reasoning,which this text mtends to describe.

No description available.

<p>In what is supposed to have been a radical break with neo-Hegelian idealism, Bertrand Russell, alongside G.E Moore, advocated the analysis of propositions by their decomposition into constituent concepts and relations. Russell regarded this as a breakthrough for the analysis of the propositions of mathematics. However, it would seem that the decompositional-analytic approach is singularly unhelpful as a technique for the clarification of the concepts of mathematics. The aim of this thesis will be to clarify Russell’s early conception of the analysis of mathematical propositions and concepts in the light of the philosophical doctrines to which his conception of analysis answered, and the demands imposed by existing mathematics on Russell’s logicist program. Chapter 1 is concerned with the conception of analysis which emerged, rather gradually, out of Russell’s break with idealism and with the philosophical commitments thereby entrenched. Chapter 2 is concerned with Russell’s considered treatment of the significance of relations for analysis and the overturning of his “doctrine of internal relations” in his work on Leibniz. Chapter 3 is concerned with Russell’s discovery of Peano and the manner in which it informed the conception of analysis underlying Russell’s articulation of logicism for arithmetic and geometry in PoM. Chapter 4 is concerned with the philosophical and logical differences between Russell’s and Frege’s approaches to logical analysis in the logicist definition of number. Chapter 5 is concerned with connecting Russell’s attempt to secure a theory of denoting, crucial to mathematical definition, to his decompositional conception of the analysis of propositions.</p> / Doctor of Philosophy (PhD)

[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.

Submitted by JOSIANE SANTOS DE OLIVEIRA (josianeso) on 2017-06-27T17:05:47Z No. of bitstreams: 1 Rafael Godolphim Feijó_.pdf: 1835499 bytes, checksum: 9b7410f8b42d5a741ecbd275052ab216 (MD5) / Made available in DSpace on 2017-06-27T17:05:47Z (GMT). No. of bitstreams: 1 Rafael Godolphim Feijó_.pdf: 1835499 bytes, checksum: 9b7410f8b42d5a741ecbd275052ab216 (MD5) Previous issue date: 2017-03-31 / CAPES - Coordenação de Aperfeiçoamento de Pessoal de Nível Superior / FAPERGS - Fundação de Amparo à Pesquisa do Estado do Rio Grande do Sul / A filosofia kantiana da matemática é fundamentada sobre uma estrutura epistemológica intuicionista. As categorias do espaço e do tempo constituem as formas da sensibilidade, formas estas manifestadas por meio de uma intuição pura a priori. O presente trabalho busca realizar uma defesa razoável de tal intuição frente aos críticos contemporâneos, os quais propõem um programa logicista desprovido de estrutura epistêmica no que tange ao raciocínio matemático. Tais críticos afirmam que a aritmética não necessita da intuição pura do tempo para que as operações numéricas possam ser realizadas. Buscaremos demonstrar que a lógica quantificacional constitui um expediente meramente formalista que deixa de lado os problemas epistemológicos da cognição matemática e, por esse motivo, pode ambicionar desconsiderar a intuição pura kantiana. Portanto, buscaremos demonstrar que a intuição pura kantiana ainda pode lançar luz sobre a natureza dos cálculos da matemática. / The Kantian philosophy of mathematics is based on an intuitionist epistemological structure. The categories of space and time are the forms of sensibility, these forms manifested through a pure intuition a priori. The present work seeks to make a reasonable defense of such intuition in the face of contemporary critics, who propose a logicist program devoid of epistemic structure regarding mathematical reasoning. Such critics claim that arithmetic does not need the pure intuition of time for numerical operations to be performed. We will try to demonstrate that the quantificational logic constitutes a merely formalistic expedient that leaves aside the epistemological problems of the mathematical cognition and, for this reason, it can ambition to disregard the pure Kantian intuition. Therefore, we shall try to demonstrate that pure Kantian intuition can still shed light on the nature of mathematical calculations.