Formal Abstraction and its Problems in Aquinas

0557429 - FLÚ 2023 RIV US eng J - Journal Article
Svoboda, David
Formal Abstraction and its Problems in Aquinas.
American Catholic Philosophical Quarterly. Roč. 96, č. 1 (2022), s. 1-20. ISSN 1051-3558
R&D Projects: GA ČR(CZ) GA18-05838S
Institutional support: RVO:67985955
Keywords : Aquinas * formal abstraction * Aristotelian science * mathematics
OECD category: Philosophy, History and Philosophy of science and technology
Impact factor: 0.2, year: 2022
Method of publishing: Limited access
https://doi.org/10.5840/acpq20211223243

Formal abstraction is a key instrument Aquinas employs to secure the possibility of mathematics conceived as a theoretical Aristotelian science. In this concept, mathematics investigates quantitative beings, which are grasped by means of formal abstraction in their necessary, universal, and changeless properties. Based on this, the paper divides into two main parts. In the first part (section II) I explicate Aquinas’s conception of (formal) abstraction against the background of the Aristotelian theory of science and mathematics. In the second part (section III) I present and critically assess the problems associated with formal abstraction in mathematics. With all due respect to Aquinas’s genius, I find his conception of formal abstraction (as well as mathematics) unsatisfactory and list the main reasons for its failure in the conclusion.
Permanent Link: http://hdl.handle.net/11104/0331481