  Counterfactual post-hoc interpretability approaches have been proven to be
useful tools to generate explanations for the predictions of a trained blackbox
classifier. However, the assumptions they make about the data and the
classifier make them unreliable in many contexts. In this paper, we discuss
three desirable properties and approaches to quantify them: proximity,
connectedness and stability. In addition, we illustrate that there is a risk
for post-hoc counterfactual approaches to not satisfy these properties.
