This essay takes an ethical dilemma posed by current technological developments as a point of departure for discussing the phenomenon of mathematisation and demathematisation as a social phenomenon and a challenge for society. Educational ramifications are drawn and the need to promote self-confidence in rejecting mathematics-based argumentation when being confronted with ethical dilemmas is formulated. On his journey towards such an activity that bears such potential, the author develops a critique of prominent examples of activities proposed by Critical Mathematics Education. This critique feeds into the proposition of a new classroom activity called "no reasons to believe in numbers", based on the Žižekian concept of overidentification. The capacity of this activity to to promote self-confidence in rejecting mathematics-based argumentation is discussed and in the conclusion, the prospected outcome of the overidentifying activities is firstly linked back to the critiqued CME-activity and secondly to the initial discussion of de|mathematisation.