O papel da abstração na instanciação da álgebra nas Regulae ad Directionem Ingenii

Analytica (Rio) 15 (1):145-172 (2011)
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In this essay I will defend three points, the first being that Descartes- unlike the aristotelian traditon- maintained that abstraction is not a operation in which the intellect builds the mathematical object resorting to sensible ob- jects. Secondly I will demonstrate that, according to cartesian philosophy, the faculty of understanding has the ability to instatiate- within the process of abstraction- mathematical symbols that represent the relation between quantities, whether magnitude or multitude.And finally I will advocate that the lack of onthological commitment with sensible experience found in cartesian philosophy of mathematics allows for the creation of a mathematical language that regards the objects of geometry and arithmetics through a system of rules and notations, in other words, algebra.
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