The expression counter-argumentation can be used to refer to any kind of discourse, argued refutation or objection, going openly against an argumentation. A mere “No!” can be considered as a counter-argumentative move, even a nonverbal expression of rejection clearly interpretable as such.
Unlike direct refutation, a specific “argumentation vs. counter-argumentation” situation occurs when the refutation is reciprocal and indirect:
— Speaker S1 argues for proposition M.
— Speaker S2 counter-argues for proposition R, incompatible with M:
S1 — Let’s built the new school here, the land is cheaper.
S2 — Let’s built the new school there, the students will waste less time commuting
S2 makes a counter-proposition R, providing an alternative to M.
Argumentation and counter-argumentation play a reciprocal role in refutation. In such a polarized situation, the fact of providing a reason for doing R, incompatible with M, serves as a reason for not doing M. Any good reason for supporting R is seen as a counter-argument to M.
The argumentation / counter-argumentation structure may correspond to an emerging argumentative situation, or to the moments when the participants present and argue their position without considering the antagonist’s proposal, which can occur at any time in a concrete argumentative situation.
An argued position can be presented in isolation in an autonomous text without refuting or even mentioning any existing counter-argumentation. Adopting such a strongly assertive strategy avoids the paradoxes of refutation, but can be seen as a kind of contempt for the argument put forward by an opposing party. S. Question; Contradiction; Antithesis; Dismissal.
As is the case with weak refutations, a weak counter-argumentation will reinforce the attacked position. In the following passage, Noam Chomsky considers that his opponent, the philosopher Hillary Putnam, has failed to develop a counter-argumentation, even a counter-proposal, and argues that this shows that he, Chomsky, must be right:
So far, in my view, not only [Putnam] has not justified his positions, but he has not been able to clarify what these positions are. The fact that even such an outstanding philosopher fails to do so, may allow us to conclude that…
Noam Chomsky, [Discussion on Putnam’s Comments], 1979.
The praise of the opponent as an « exceptional philosopher » is a characteristically eulogistic and perfidious accompaniment to this kind of refutation:
By refuting you, I’m refuting not just any philosopher, but a Master – and therefore, a fortiori, all the philosophers who are opposed to my views.
 Noam Chomsky, Discussion sur les Commentaires de Putnam. In Piattelli-Palmarini M. (ed.). Théorie du Langage, Théorie de l’Apprentissage. Paris: Le Seuil. 1979. P. 461.