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The fallacy of false dichotomy (aka false dilemma and the black or white fallacy) occurs when one is presented with only some of all the alternatives to choose from.
While at TAM5, the James Randi Educational Foundation's annual reasonfest, I was approached by André Kole, who introduced himself to me as a magician and longtime friend of Randi's. He asked me if I would read a short pamphlet he'd written and give him my opinion of his arguments. I looked at the title of his pamphlet and told him I'd read it but I could see that the main problem is that he's arguing a false dichotomy. The title of his tract is Jesus: Magician or God [sic]? (Kole, it turns out is a "Christian magician" who does "faith-based illusions."*) I told him without reading his tract that there were other possibilities like madman, fraud, and myth. My own view is that the character described in the four gospels accepted as "authentic" by most Christians is a mythical character. A man named Jesus existed but the stories about his miracles are either exaggerations or distortions of actual, non-miraculous, events or confabulations that incorporated myths from other traditions (like the Mithraic tradition). He may have been a faith healer like Benny Hinn or Peter Popov.
I read the tract and told Kole that he did a good job in arguing that Jesus was not a magician, but that it didn't follow that just because he wasn't a magician he was therefore a god. I really had no interest in arguing with Kole about the Bible or the alleged miracles, but he asked me what I thought of his argument and I told him. If he wants to prove Jesus was a god, he has to do more than prove that he wasn't a magician.
Kole was not satisfied with my appraisal and asked me to explain how the Bible could be so accurate about some range of prophecies he rattled off that I'd never heard of. I really had no interest in the topic and told him that I don't think the Bible is much of a guide for anything important but that if he thinks it's true it's of no concern to me. I was being sidetracked into a conversation I had no interest in engaging in. It wasn't my job to prove Jesus wasn't a god. I was asked to evaluate an argument and agreed to do it. Had I been asked to prove to him that Jesus wasn't a god or that the Bible isn't the word of a god, I'd have told him to waste somebody else's time.
There is another lesson here besides the lesson regarding the fallacy of false dichotomy. When someone asks you to evaluate his argument, he may not want you to evaluate his argument.
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complete list of the SD critical thinking mini-lessons