In this thesis, I investigate the nature of geometric knowledge and its relationship to spatial intuition. My goal is to rehabilitate the Kantian view that Euclid's geometry is a mathematical practice, which is grounded in spatial intuition, yet, nevertheless, yields a type of a priori knowledge about the structure of visual space. I argue for this by showing that Euclid's geometry allows us to derive knowledge from idealized visual objects, i.e., idealized diagrams by means of non-formal logical inferences. By developing such an account of Euclid's geometry, I complete the "standard view" that geometry is either a formal system (pure geometry) or an empirical science (applied geometry), which was developed mainly by the logical positivists and which is currently accepted by many mathematicians and philosophers. My thesis is divided into three parts. I use Hans Reichenbach's arguments against Kant and Edmund Husserl's genetic approach to the concept of space as a means of arguing that the "standard view" has to be supplemented by a concept of a geometry whose propositions have genuine spatial content. I then develop a coherent interpretation of Euclid's method by investigating both the subject matter of Euclid's geometry and the nature of geometric inferences. In the final part of this thesis, I modify Husserl's phenomenological analysis of the constitution of visual space in order to define a concept of spatial intuition that allows me not only to explain how Euclid's practice is grounded in visual space, but also to account for the apriority of its results.

Made available in DSpace on 2014-06-11T19:26:49Z (GMT). No. of bitstreams: 0 Previous issue date: 2010-05-11Bitstream added on 2014-06-13T19:55:12Z : No. of bitstreams: 1 iagallo_po_me_arafcl.pdf: 1020146 bytes, checksum: c7d7dfe99d4620b0abcb306ada80eada (MD5) / O tempo da linguagem é regido por coordenadas gerais. Um modelo descritivo geral do tempo localiza a noção de tempo de um enunciado coerentemente com as informações gramaticais. Partindo-se da hipótese lógica de que o passado deveria ser sempre passado, o futuro sempre futuro e o presente sempre presente, foram investigadas as localizações temporais que servem de momentos de referência ao tempo dos enunciados, sem perder de vista o momento da produção-recepção do ato de enunciar. Os níveis de compreensão do tempo na linguagem foram sistematizados em etapas: investigando o tempo do mundo, depois o tempo da linguagem e, por último, o tempo do discurso entendido como o “mundo possível” criado pela linguagem. Percebe-se que o tempo físico e psicológico interpretável de um modo geral pelo homem possui duas orientações, e que a linguagem também geraria duas formas de tempo, construídas por dois grandes sistemas temporais: o mundo comentado e o mundo narrado, inspirados em Weinrich. Eles podem descrever duas grandes intenções do interlocutor, e não apenas dois grandes grupos de formas modotemporais dos verbos. Descobrindo-se quais são os lugares temporais, e utilizando principalmente construtos inspirados em Reichenbach, foi investigado como se dá a relação entre os momentos dos eventos, os momentos da fala e o momento presente pressuposto da enunciação. Dentro de uma abordagem da semântica formal, da teoria cognitiva e da semiótica francesa, o sistema temporal da linguagem pode ser descrito mais adequadamente. A dissertação analisa vários enunciados orais e escritos / The notion of time is governed by specific coordinates in the languages. A general descriptive model deals with the expression of time by referring it to grammatical information. Based upon the logical assumption that the past should always be the past, the future always be the future and the present always be the present, it has been determined how time is located in an utterance, i.e., the reference moment and its relation to the speaking moment and the enunciation. The level of understanding of time in languages must be organized in two stages: first, by investigating the time from the physic and the linguistic point of view; and second by setting the possible world created by the discourse. Usually, the physical and psychological interpretation of time by ordinary people runs in two directions that matches with the dual linguistic time framework: one that takes into account the commented world and the other that is implemented by the spoken world, according to Weinrich. On the other hand, our time model can describe the speaker's main intentions that is not only the traditional identification of tense from the verbs. Following Reichenbach approach to the expressions of time in the languages, the parameters of event and reference moments were investigated in relation to the parameter of speaking moment, presupposed in the utterance. Moreover, the linguistic temporal system can better understood when we take into account the contributions from semiotics and from the cognitive semantics. Besides the theoretical approach to the subject, this dissertation analyzes several examples from the oral and written Portuguese language

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