Doctorat en philosophie et lettres / info:eu-repo/semantics/nonPublished

This dissertation is about the structure of thought. Following Gottlob Frege, I define a thought as the sort of content relevant to determining whether an assertion is true or false. The historical component of the dissertation involves interpreting Frege’s actual views on the structure of thought. I argue that Frege did not think that a thought has a unique decomposition into its component senses, but rather the same thought can be decomposed into senses in a variety of distinct ways. I extend Frege’s position and use it to develop an account of the hierarchy of senses, the senses expressed by indexicals and demonstratives, and the distinction between logical and non-logical structure. I also discuss various connections with the nature of meta-representation, our capacity for reflective judgment, some aspects of the structure of conscious experience, the way we perceive regions of space and durations of time, and our conscious awareness of our own perceptions and events of thinking.

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Frege's arithmetical-platonism is glossed as the first step in developing the thesis; however, it remains silent on the subject of structures in mathematics: the obvious examples being groups and rings, lattices and topologies. The structuralist objects to this silence, also questioning the sufficiency of Fregean platonism is answering a number of problems: e.g. Benacerraf's Twin Puzzles of Epistemic and Referential Access. The development of structuralism as a philosophical position, based on the slogan 'All mathematics is structural' collapses: there is no single coherent account which remains faithful to the tenets of structuralism and solves the puzzles of platonism. This prompts the adoption of a more modest structuralism, the aim of which is not to solve the problems facing arithmetical-platonism, but merely to give an account of the 'obviously structural areas of mathematics'. Modest strucmralism should complement an account of mathematical systems; here, Frege's platonism fulfils that role, which then constrains and shapes the development of this modest structuralism. Three alternatives are considered; a substitutional account, an account based on a modification of Dummett's theory of thin reference and a modified from of in re structuralism. This split level analysis of mathematics leads to an investigation of the robustness of the truth predicate over the two classes of mathematical statement. Focussing on the framework set out in Wright's Truth and Objectivity, a third type of statement is identified in the literature: Hilbert's formal statements. The following thesis arises: formal statements concern no special subject matter, and are merely minimally truth apt; the statements of structural mathematics form a subdiscourse - identified by the similarity of the logical grammar - displaying cognitive command. Thirdly, the statements of mathematics which concern systems form a subdiscourse which has both cognitive command and width of cosmological role. The extensions of mathematical concepts are such that best practice on the part of mathematicians either tracks or determines that extension - at least in simple cases. Examining the notions of response dependence leads to considerations of indefinite extensibility and intuitionism. The conclusion drawn is that discourse about structures and mathematical systems are response dependent but that this does not give rise to any revisionary arguments contra intuitionism.

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

Esta dissertação tem como objetivo compreender como a distinção entre conceito e objeto opera no sistema fregeano de modo a autorizar ou não alguma concepção de inexpressabilidade como característica fundamental da lógica. O problema de fundo é determinar em que sentido distinções entre categorias lógicas, especificamente a distinção entre conceito e objeto, envolvem algum tipo de inexpressabilidade. A questão é abordada com foco no problema do estatuto da proposição “O conceito cavalo não é um conceito”. Tratamos do problema através da apresentação de duas alternativas que envolvem um esforço de formalização da proposição. A primeira alternativa insere-se numa tradição de comentários que aproxima as considerações de Frege sobre essa proposição a certas ideias do Tractatus de Wittgenstein, atribuindo à proposição o estatuto de contrassenso. A segunda alternativa problematiza, pelo menos em parte, a primeira, ao trazer razões para a consideração da afirmação como uma proposição com sentido. Refletindo sobre as duas alternativas, consideramos que há mais de uma maneira de conceber a ideia de inexpressabilidade da lógica presente nas obras de Frege. / This work aims to understand how the distinction between concept and object works in the fregean system in such a way as to authorize some conception of inexpressibility as a fundamental feature of logic. The background problem is to ascertain how distinctions between logical categories, specifically the distinction between concept and object, involve some kind of inexpressibility. Our approach to the question focuses on the problem of the status of the proposition ‘The concept horse is not a concept’. Two alternatives are shown here that involve an effort of formalization of this proposition. The first alternative is part of a tradition of Frege’s exegesis that approximates Frege’s considerations about this proposition to certain ideas of Wittgenstein's Tractatus, assigning to the proposition the status of nonsense. The second alternative probematizes the first one at least in part by bringing reasons to considerate the statement as a proposition with sense. Reflecting on the two alternatives, we believe that there is more than one way of conceiving the idea of inexpressibility of logic in the works of Frege.

In order to understand the implications of Frege's Grundlagen der Arithmetik, we must bear in mind that Frege saw logic as an overarching discipline, necessary for all scientific enquiry. This consideration allows us to make sense of his logicism, the idea that arithmetic is embedded in logic, and his platonism, the commitment to the mind-independent nature of arithmetic objects, such as numbers. In 1902, Russell generated a paradox from Basic Law (V), found in the first volume of Grundgesetze, which suggested that Frege's entire logical system was inconsistent. Recent work by Boolos and Wright, have fenced off the damage and shown that the bulk of Frege's work is consistent. I shall argue, however, that their proposed solutions prove unsatisfactory with respect to Frege's view of logic and especially his logicism.

El Enigma de Frege es considerado como uno de los principales problemas al que se enfrenta el millianismo. Como se sabe, el millianismo sostiene que el significado de un nombre propio es simplemente su referente. Dicho brevemente, el problema consiste en explicar por qué dos oraciones de identidad que contienen nombres propios co-referenciales (por ejemplo, “Mark Twain es Samuel Clemens” y “Mark Twain es Mark Twain”) parecen tener distinto valor informativo, esto es, por qué una de las oraciones parece ser trivial mientras que la otra parece ser informativa. El propósito del presente trabajo es mostrar que el millianismo puede responder de manera plausible al Enigma de Frege haciendo uso de la distinción entre la proposición semánticamente expresada por una oración y la(s) proposición(es) pragmáticamente impartida(s) por el uso o la emisión de una oración. El trabajo consta de tres capítulos. En el primer capítulo planteo el Enigma de Frege, explico cuáles son los principios presupuestos al plantear el problema y expongo qué respuesta le dio Frege al Enigma de Frege. En el segundo capítulo expongo los argumentos anti-descriptivistas de Kripke que pusieron en duda la respuesta que dio Frege al Enigma de Frege. En el tercer capítulo expongo un intento milliano por responder al Enigma de Frege que consiste en distinguir entre la proposición semánticamente expresada por una oración y la(s) proposición(es) pragmáticamente impartida(s) por el uso o la emisión de una oración, y, finalmente, evalúo si haciendo uso de esta distinción el millianismo responde de manera plausible al Enigma de Frege. / Tesis

Esta dissertação tem como objetivo compreender como a distinção entre conceito e objeto opera no sistema fregeano de modo a autorizar ou não alguma concepção de inexpressabilidade como característica fundamental da lógica. O problema de fundo é determinar em que sentido distinções entre categorias lógicas, especificamente a distinção entre conceito e objeto, envolvem algum tipo de inexpressabilidade. A questão é abordada com foco no problema do estatuto da proposição “O conceito cavalo não é um conceito”. Tratamos do problema através da apresentação de duas alternativas que envolvem um esforço de formalização da proposição. A primeira alternativa insere-se numa tradição de comentários que aproxima as considerações de Frege sobre essa proposição a certas ideias do Tractatus de Wittgenstein, atribuindo à proposição o estatuto de contrassenso. A segunda alternativa problematiza, pelo menos em parte, a primeira, ao trazer razões para a consideração da afirmação como uma proposição com sentido. Refletindo sobre as duas alternativas, consideramos que há mais de uma maneira de conceber a ideia de inexpressabilidade da lógica presente nas obras de Frege. / This work aims to understand how the distinction between concept and object works in the fregean system in such a way as to authorize some conception of inexpressibility as a fundamental feature of logic. The background problem is to ascertain how distinctions between logical categories, specifically the distinction between concept and object, involve some kind of inexpressibility. Our approach to the question focuses on the problem of the status of the proposition ‘The concept horse is not a concept’. Two alternatives are shown here that involve an effort of formalization of this proposition. The first alternative is part of a tradition of Frege’s exegesis that approximates Frege’s considerations about this proposition to certain ideas of Wittgenstein's Tractatus, assigning to the proposition the status of nonsense. The second alternative probematizes the first one at least in part by bringing reasons to considerate the statement as a proposition with sense. Reflecting on the two alternatives, we believe that there is more than one way of conceiving the idea of inexpressibility of logic in the works of Frege.