Formal Conditioning between Mathematics and Philosophy: Reassessing Alain Badiou’s Ontology and Event

Muhammad Irfan Syaebani (Department of Management, Faculty of Economics and Business, Universitas Indonesia)
Untung Yuwono (Department of Linguistics, Faculty of Humanities, Universitas Indonesia)
Embun Kenyowati Ekosiwi (Department of Philosophy, Faculty of Humanities, Universitas Indonesia)

Melintas An International Journal of Philosophy and Religion
Vol. 41 No. 2 (2025): Melintas - An International Journal of Philosophy and Religion

Alain Badiou's mathematical philosophy generated sustained controversy because it assigned axiomatic set theory a constitutive role in ontology and used mathematical concepts to rethink being, multiplicity, truth, and event. Previous debates had often evaluated these issues separately, leaving the relationship between mathematical rigor and philosophical appropriation insufficiently clarified. This study aimed to critically reconstruct the major controversies surrounding Badiou's mathematical philosophy by examining three interconnected problems: mathematics as ontology, being as multiplicity, and the event. The study employed a qualitative philosophical-textual design using conceptual analysis, critical textual interpretation, and comparative philosophical analysis. Being and Event and Badiou's published responses to critics were examined alongside mathematically informed critiques and philosophical commentaries. The sources were analyzed through close reading, comparative conceptual analysis, and source triangulation. The findings showed that the main disputes arose from differences between the technical meanings of mathematical concepts and the philosophical functions Badiou assigned to them. The study found that mathematics as ontology did not entail a literal identity between mathematical objects and beings, that Badiou's rejection of the One concerned ontological unity rather than numerical singularity, and that the contingency of the event did not necessarily imply political fatalism because transformation also depended on fidelity and sustained construction. The study concluded that Badiou's philosophy was best understood through formal conditioning, rather than literal equivalence or unrestricted metaphorization, between mathematics and philosophy. The study contributed an integrated interpretation of Badiou's ontology by connecting debates on mathematics, being, and event within a single analytical framework and clarifying how mathematical formalization could condition philosophical thought without collapsing the distinction between the two domains.