What is the name of the rhetorical device where the author says he/she isn't going/or doesn't need to give examples, and then the author goes on to give examples?
The rhetorical device of saying something by claiming that you will not say it is called praeteritio. A classic example is found in Cicero's Against Catiline 1.14 in which Cicero claims to pass over Catiline's having murdered his wife and destroyed his patrimony. The material introduced by an explicit claim that it will be passed over in praeteritio can be anything, not just an example. A valid example of praeteritio could be "I will not allude to X's vicious moral character or lack of personal hygiene in this context, as they have no bearing on his ability to lead an army," a sentence that does not use the rhetorical device of the example or paradeigma. On the other hand, in judicial contexts, examples of previous bad behaviour can be introduced effectively using praeteritio; Cicero is particularly good at this.