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

• Grant number: 20/00155-8
• Support Opportunities: Scholarships in Brazil - Master
• Start date: June 01, 2020
• End date: February 28, 2022
• Field of knowledge: Humanities - Philosophy - History of Philosophy
• Principal Investigator: Lucas Angioni
• Grantee: Rafael Cavalcanti de Souza
• Host 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. (AU)

Academic Publications

(References retrieved automatically from State of São Paulo Research Institutions)

SOUZA, Rafael Cavalcanti de. The Aristotelian conception of geometric demonstration from the Posterior Analytics. 2022. Master's Dissertation - Universidade Estadual de Campinas (UNICAMP). Instituto de Filosofia e Ciências Humanas Campinas, SP.