I've been putting off contributing to Joe Carter's collaborative project of what's being misnamed Jesus the Logician, but here we go finally. Here's an instance of Jesus' reasoning strategy with his disciples that I think fits what Joe is looking for. John 9:1-3 contains a good example of a false dilemma. Jesus' disciples give him this dilemma, and he responds with the common philosophical practice of going through the horns of the dilemma by denying either of the options presented to him and saying they simply haven't listed all the options. A more exhaustive dilemma would have contained at least a third option, and that third option isn't as problematic as the two they mention.
In this passage, Jesus is presented with a dilemma. A man was born blind. His disciples asked him what caused the man's blindness. Was it his own sin or someone else's? The text leaves out the details of their thinking, but presumably they were thinking that he couldn't have caused it himself because he was blind before he sinned. They could also point to God's statement to Moses that the sins of fathers would be visited on the children (Exodus 34:7), yet they also had to take into account that Ezekiel seems to deny that it's the punishment of sins that gets inherited (Ezekiel 18).
The dilemma is thus as follows. Ezekiel shows why it cannot be the man's parents' fault, but we also know it can't be his. How does this square with the obvious truth that blindness is not God's intent for creation, and thus it must be causes by sin somehow? Jesus goes between the horns of their dilemma and says what amounts to be the main claim of the book of Job. Neither the man nor his parents sinned in such a way as to cause this man's blindness. "This happened so that the word of God might be displayed in his life." (John 9:3b, NIV) He doesn't further specify with words what purpose that would be, but he proceeds to heal the man, showing at least part of that purpose through his deed.