Mathematical Substances in Aristotle’s Metaphysics B.5: Aporia 12 Revisited

Abstract: Metaphysics B considers two sets of views that hypostatize mathematicals. Aristotle discusses the first in his B.2 treatment of aporia 5, and the second in his B.5 treatment of aporia 12. The former has attracted considerable attention; the latter has not. I show that aporia 12 is more significant than the literature suggests, and specifically that it is directly addressed in M.2 – an indication of its importance. There is an immediate problem: Aristotle spends most of M.2 refuting the view that mathematicals are separate; but the B.5 mathematicals are inherent. I argue that the B.5 inherence is compatible with the M.2 separateness, and further, that aporia 12 is more than just a puzzle about the hypostatization of mathematicals. It is also a puzzle about the ontological status of mathematicals relative to sensibles.

Object Details

• Location: Deutsche Nationalbibliothek Frankfurt am Main
• Extent: Online-Ressource
• Language: Englisch

References and Relationships

• Bibliographic citation: Mathematical Substances in Aristotle’s Metaphysics B.5: Aporia 12 Revisited ; volume:100 ; number:2 ; year:2018 ; pages:113-145 ; extent:33 ; Archiv für Geschichte der Philosophie ; 100, Heft 2 (2018), 113-145 (gesamt 33)

Contributors, Places and Time

• Creator: Katz, Emily

Further information

• DOI: 10.1515/agph-2018-2001
• URN: urn:nbn:de:101:1-2024041118085165830947
• Rights: Open Access; Der Zugriff auf das Objekt ist unbeschränkt möglich.
• Last update: 14.08.2025, 10:46 AM CEST