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In recent years, there has been increasing interest in causal reasoning for designing fair decision-making systems due to its compatibility with legal frameworks, interpretability for human stakeholders, and robustness to spurious correlations inherent in observational data, among other factors. The recent attention to causal fairness, however, has been accompanied with great skepticism due to practical and epistemological challenges with applying current causal fairness approaches in the literature. Motivated by the long-standing empirical work on causality in econometrics, social sciences, and biomedical sciences, in this paper we lay out the conditions for appropriate application of causal fairness under the "potential outcomes framework." We highlight key aspects of causal inference that are often ignored in the causal fairness literature. In particular, we discuss the importance of specifying the nature and timing of interventions on social categories such as race or gender. Precisely, instead of postulating an intervention on immutable attributes, we propose a shift in focus to their perceptions and discuss the implications for fairness evaluation. We argue that such conceptualization of the intervention is key in evaluating the validity of causal assumptions and conducting sound causal analysis including avoiding post-treatment bias. Subsequently, we illustrate how causality can address the limitations of existing fairness metrics, including those that depend upon statistical correlations. Specifically, we introduce causal variants of common statistical notions of fairness, and we make a novel observation that under the causal framework there is no fundamental disagreement between different notions of fairness. Finally, we conduct extensive experiments where we demonstrate our approach for evaluating and mitigating unfairness, specially when post-treatment variables are present.