Thomas Pavel
The Critical Inquiry essay that helped me most was Badiou’s Number: A Critique of Mathematics as Ontology (2011), coauthored by our former colleague David Nirenberg, intellectual historian, and his father, Ricardo L. Nirenberg, mathematician and writer.
The topic of this essay was French philosopher Alain Badiou’s use of interdisciplinary arguments to reach unexpected, stunning conclusions. Badiou followed the example of thinkers who, inspired by structural linguistics, asserted in the late sixties that since the human condition had ceased to be the main object of philosophy, thinkers should henceforth examine language and its networks of relevant differences. In a stronger, more radical move, in the late eighties Badiou aimed at revolutionizing ontology, the philosophical reflection on being, by identifying it with mathematics.
A simple, elementary, insight tells us that such an identification is probably mistaken. Yes, mathematics does assist natural and social sciences find simple, elegant expressions of their discoveries, provided that empirical observations confirm the predictions reached with its help. Perhaps it could also assist some branches of philosophy formulate their findings in a more rigorous way. But in the case of Badiou’s speculations, prudent insights are not decisive, given that his main theses are remarkably audacious. He states, for instance, that “Situations are nothing more, in their being, than pure multiplicity.” Using the expression “pure multiplicity,” Badiou suggests that ontological reflection should pay no attention to the differences between the beings that populate the world and to the specificity of their mutual interactions. For him, there are no modes of being. Since, moreover, Badiou asserts that this pure multiplicity is the object of set theory, he concludes, after a few intermediary steps, that “insofar as being, qua being, is nothing other than pure multiplicity, it is legitimate to say that ontology, the science of being qua being, is nothing other than mathematics itself.”
A wonderful feature of the Nirenberg paper is the generosity of their approach. Far from just exclaiming “nonsense!,” they patiently, politely, go through Badiou’s claims, explain to readers less familiar with set theory the notions and the operations he uses, and in a kind, respectful tone, indicate their inadequacy. We all are, the paper suggests, inhabitants of the Republic of Letters, a community in which intellectual errors do happen. Such errors should be calmly discussed with the help of clear, detailed arguments, rather than subjected to condemnation, exclusion, interdiction.
Thank you, Nirenberg father and son, for this important lesson.
Thomas Pavel is the Gordon J. Laing Distinguished Service Professor in Romance Languages and Literatures, Comparative Literature, the Committee on Social Thought, and Fundamentals at the University of Chicago. He is also a member of the editorial board of Critical Inquiry.
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