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American Catholic Philosophical Quarterly

Volume 96, Issue 1, Winter 2022

David Svoboda
Pages 1-20

Formal Abstraction and its Problems in Aquinas

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.