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  1. Visualization as an Intuitive Process in Mathematical Practice.Lina María Peña-Páez - 2024 - Conatus 9 (2):195-221.
    In the field of the philosophy of mathematics, in recent years, there has been a resurgence of two processes: intuition and visualization. History has shown us that great mathematicians in their inventions have used these processes to arrive at their most brilliant proofs, theories and concepts. In this article, we want to defend that both intuition and visualization can be understood as processes that contribute to the development of mathematical knowledge as evidenced in the history of mathematics. Like intuition, visualization (...)
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  • (1 other version)The geometrical basis of arithmetical knowledge: Frege & Dehaene.Sorin Costreie - 2018 - Theoria : An International Journal for Theory, History and Fundations of Science 33 (2):361-370.
    Frege writes in Numbers and Arithmetic about kindergarten-numbers and “an a priori mode of cognition” that they may have “a geometrical source.” This resembles recent findings on arithmetical cognition. In my paper, I explore this resemblance between Gottlob Frege’s later position concerning the geometrical source of arithmetical knowledge, and some current positions in the literature dedicated to arithmetical cognition, especially that of Stanislas Dehaene. In my analysis, I shall try to mainly see to what extent logicism is compatible with intuitionism.
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