Uma investigação sobre os fundamentos da lógica numa perspectiva transcendental idealista da matemática
Date
2022-07-26
Authors
Primon, Gabriel Kiredjian [UNIFESP]
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Castilho, Tiago Nunes [UNIFESP]
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Trabalho de conclusão de curso de graduação
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Abstract
Este trabalho dedica-se a investigação de como se justificam alguns conceitos e definições básicos da matemática, mais detidamente acerca das tabelas-verdade na lógica clássica. Como pergunta norteadora temos: "como é possível justificar os princípios lógicos e as definições das tabelas-verdade da lógica clássica, assim como alguns fundamentos da matemática, usando do referencial fenomenológico?". Procurou-se estabelecer uma justificativa fenomenológica dos princípios lógicos (identidade, não-contradição e bivalência) e das definições de algumas tabelas-verdade básicas (negação, conjunção e condicional). No início da dissertação explicou-se brevemente as escolas de pensamento matemático buscando pontuar como elas se distinguem nos seus princípios. Logo, viu-se que existe, de um certo modo, visões distintas dentre as correntes filosóficas do pensamento matemático. O referencial teórico adotado neste trabalho é o da fenomenologia tal como explicitada na referência Mathematics and Its Applications: A Transcendental-Idealist Perspective (SILVA, 2017). Neste trabalho objetivamos prospectar uma interface dos termos da fenomenologia com os fundamentos da lógica e da matemática. Investigamos uma abordagem fenomenológica buscando verificar como é possível investigar os fenômenos a partir das fontes intencionais. Esta pesquisa também propôs explicitar o uso de alguns conceitos básicos da fenomenologia num contexto do âmbito de ensino da matemática a fim de analisar fenômenos que ali aparecem. Também alguns exercícios de lógica clássica são propostos. Como contribuições desse estudo, podemos potencializar e reavaliar o modo como os alunos veem o mundo intervindo em suas “verdades” já pré-estabelecidas.
This work is dedicated to the investigation of how some basic concepts and definitions of mathematics are justified, with more detail about truth tables in classical logic. As a guiding question we have: "how is it possible to justify the logical principles and the definitions of the truth tables of classical logic, as well as some foundations of mathematics, using the phenomenological framework?". We tried to establish a phenomenological justification of the logical principles (identity, noncontradiction and bivalence) and the definitions of some basic truth tables (negation, conjunction and conditional). At the beginning of the dissertation the schools of mathematical thought were briefly explained, seeking to point out how they differ in their principles. Therefore, it was seen that there are, in a certain way, different views among the philosophical currents of mathematical thought. The theoretical framework adopted in this work is that of phenomenology as explained in the reference Mathematics and Its Applications: A TranscendentalIdealist Perspective (SILVA, 2017). In this work we aim to explore an interface between the terms of phenomenology and the foundations of logic and mathematics. We investigated a phenomenological approach seeking to verify how it is possible to investigate phenomena from intentional sources. This research also proposed to explain the use of some basic concepts of phenomenology in the context of the teaching of mathematics to analyze phenomena that appear there. Also, some classic logic exercises are proposed. As contributions of this study, we can enhance and reevaluate the way students see the world intervening in their preestablished “truths”.
This work is dedicated to the investigation of how some basic concepts and definitions of mathematics are justified, with more detail about truth tables in classical logic. As a guiding question we have: "how is it possible to justify the logical principles and the definitions of the truth tables of classical logic, as well as some foundations of mathematics, using the phenomenological framework?". We tried to establish a phenomenological justification of the logical principles (identity, noncontradiction and bivalence) and the definitions of some basic truth tables (negation, conjunction and conditional). At the beginning of the dissertation the schools of mathematical thought were briefly explained, seeking to point out how they differ in their principles. Therefore, it was seen that there are, in a certain way, different views among the philosophical currents of mathematical thought. The theoretical framework adopted in this work is that of phenomenology as explained in the reference Mathematics and Its Applications: A TranscendentalIdealist Perspective (SILVA, 2017). In this work we aim to explore an interface between the terms of phenomenology and the foundations of logic and mathematics. We investigated a phenomenological approach seeking to verify how it is possible to investigate phenomena from intentional sources. This research also proposed to explain the use of some basic concepts of phenomenology in the context of the teaching of mathematics to analyze phenomena that appear there. Also, some classic logic exercises are proposed. As contributions of this study, we can enhance and reevaluate the way students see the world intervening in their preestablished “truths”.