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Dependence and independence of mathematical entities on sensitive substances: ontological and logical aspect of abstraction in Aristotle

Grant number: 20/00155-8
Support type:Scholarships in Brazil - Master
Effective date (Start): June 01, 2020
Effective date (End): February 28, 2022
Field of knowledge:Humanities - Philosophy - History of Philosophy
Principal Investigator:Lucas Angioni
Grantee:Rafael Cavalcanti de Souza
Home Institution: Instituto de Filosofia e Ciências Humanas (IFCH). Universidade Estadual de Campinas (UNICAMP). Campinas , SP, Brazil

Abstract

This project investigates how the notion of abstraction (or subtraction) (aphairesis) can be articulated as much to the criticisms exposed to Plato in Metaphysics M 2 1076b11-1077b11, as to the method exposed in Posterior Analytics I. There is the interpretation that aristotle in his criticisms of Plato about mathematics would not take into account epistemological issues (BOSTOCK, 2012). Against this interpretation, we intend to argue that Aristotle in these criticisms, in fact, was not directly debating such questions in this context, but his exposed ideas may also assist questions about knowledge in the mathematical sciences. To better understand these issues, we divide them into two distinct aspects of the process of abstraction of mathematical objects: (1) what we call 'ontological dependence' on sensitive substances, which refers to Aristotle's critiques of Plato, and, ( 2) what we call 'logical independence' in terms of an autonomous science referring to the mathematical sciences. For the first, we will first investigate Aristotle's critiques exposed in Metaphysics M 2 and also investigate the operation qua (hei) exposed in M 3 to understand how this relationship between perceptible objects and mathematical objects occurs. For the second part, we will investigate how abstraction, which considers an object X qua Y, relates to the subject criteria of predication and the demonstrative method set forth in Posterior Analytics.