This paper argues that deductive arguments are "powerful" when the goal is to stimulate reflection on one's own reasoning. Powerful arguments are defined as arguments that leave only one choice for a potential opponent: either to accept the conclusion or to defeat one of its premises. In the first part, the paper presents an argument for the thesis that so defined powerful arguments are possible when we do not only provide reasons as premises of an argument, but also what is called an "enabler." An "enabler" is that premise in an argument that guarantees that the reason provided in this argument is sufficient to justify the claim or conclusion. In the second part an argument is provided for the theses that powerful arguments promote mutual understanding and self-reflexivity. The paper introduces Logical Argument Mapping (LAM) as a way to present powerful arguments and it describes the LAM approach by means of a reconstruction of Thomas Nagel's core argument in "The Problem of Global Justice."