A reasoning based upon aporia might be used to destabilize, to confuse your logic.
An example is given by this dialog inspired by the French movie "Garde à vue". The application here is sophistical not rhetorical.
You said that you don't remember what you did last night?
Yes
Then , how can you be sure you didn't do what you where accused of?
Indeed, I am not sure
You recognize that the elements that have been submitted to you are right?
Yes
Since you don't remember what happend, you agree then that it is perfectly possible that you are the author of the accusations?
....
Source: roughly translated from http://fr.wikipedia.org/wiki/Aporie, you tube
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