Is argumentation a rule-following activity in the sense of the latter as suggested by L.Wittgenstein in his ‘Philosophical Investigations’? In what follows I will argue that it is not, despite of the two issues which appear to support the positive reply to this key question of my paper. These positive insights into the question come from the idea that the very fact that the argumentation is often presented as a rule-following activity implies that the argumentation itself is the rule-following activity in L.Wittgensteinian sense. However, it does not, and this is so for two main reasons: there is no necessary connection between the rule-following activity and the presentation of argumentation in the form of rules; this connection is contingent instead and, if needed, may be maintained in a variety ways three of which I observe here. To this end, I am intended to compare the three basic properties of the rule-following activity, namely, the ostensive names’ imposition, the experimental learning of language use