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  1. Euclid’s Fourth Postulate: Its authenticity and significance for the foundations of Greek mathematics.Vincenzo De Risi - 2022 - Science in Context 35 (1):49-80.
    ArgumentThe Fourth Postulate of Euclid’s Elements states that all right angles are equal. This principle has always been considered problematic in the deductive economy of the treatise, and even the ancient interpreters were confused about its mathematical role and its epistemological status. The present essay reconsiders the ancient testimonies on the Fourth Postulate, showing that there is no certain evidence for its authenticity, nor for its spuriousness. The paper also considers modern mathematical interpretations of this postulate, pointing out various anachronisms. (...)
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  • A definição aristotélica do tempo incorre em uma transgressão de gênero?Rafael Cavalcanti de Souza - 2021 - Anais de Filosofia Clássica 30:61-73.
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  • A Concepção Aristotélica de Demonstração Geométrica a partir dos Segundos Analíticos.Rafael Cavalcanti de Souza - 2022 - Dissertation, University of Campinas
    Nos Segundos Analíticos I. 14, 79a16-21 Aristóteles afirma que as demonstrações matemáticas são expressas em silogismos de primeira figura. Apresento uma leitura da teoria da demonstração científica exposta nos Segundos Analíticos I (com maior ênfase nos capítulo 2-6) que seja consistente com o texto aristotélico e explique exemplos de demonstrações geométricas presentes no Corpus. Em termos gerais, defendo que a demonstração aristotélica é um procedimento de análise que explica um dado explanandum por meio da conversão de uma proposição previamente estabelecida. (...)
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  • Can the Pyrrhonian Sceptic Suspend Belief Regarding Scientific Definitions?Benjamin Wilck - 2020 - History of Philosophy & Logical Analysis 23 (1):253-288.
    In this article, I tackle a heretofore unnoticed difficulty with the application of Pyrrhonian scepticism to science. Sceptics can suspend belief regarding a dogmatic proposition only by setting up opposing arguments for and against that proposition. Since Sextus provides arguments exclusively against particular geometrical definitions in Adversus Mathematicos III, commentators have argued that Sextus’ method is not scepticism, but negative dogmatism. However, commentators have overlooked the fact that arguments in favour of particular geometrical definitions were absent in ancient geometry, and (...)
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