Intersectionality is a critical framework that, through inquiry and praxis, allows us to examine how social inequalities persist through domains of structure and discipline. Given AI fairness' raison d'etre of "fairness", we argue that adopting intersectionality as an analytical framework is pivotal to effectively operationalizing fairness. Through a critical review of how intersectionality is discussed in 30 papers from the AI fairness literature, we deductively and inductively: 1) map how intersectionality tenets operate within the AI fairness paradigm and 2) uncover gaps between the conceptualization and operationalization of intersectionality. We find that researchers overwhelmingly reduce intersectionality to optimizing for fairness metrics over demographic subgroups. They also fail to discuss their social context and when mentioning power, they mostly situate it only within the AI pipeline. We: 3) outline and assess the implications of these gaps for critical inquiry and praxis, and 4) provide actionable recommendations for AI fairness researchers to engage with intersectionality in their work by grounding it in AI epistemology.

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