The methods of abstraction and idealization are typically examined in connection with their applications in modelling and explanation. This paper investigates how the use of abstract and idealized models in arguments structures the process of argumentation. If a discussant uses an idealized model to justify a thesis, they also adopt an implicit or explicit attitude towards the idealizing assumptions it involves. The precise nature of this attitude determines the argumentation strategies available to the opponent. If the proponent views the assumptions as approximating the actual state of affairs, the opponent can request a de-idealization of the model. On the other hand, if the model is viewed as a non-Galilean idealization, or in a purely instrumental way, the opponent must challenge the relevance of the model with respect to the target system. However, as illustrated by the debate on minimum wage, even empirical evidence need not always provide a clear-cut resolution of the difference in opinion.