It is wonderful when a student in an introductory philosophy course understands for the first time that you can evaluate what passes for an argument in popular discourse in a principled way by formalizing it and then evaluating its logical form and the plausibility of each of its premises.
However, this process can be potentially misleading. Take, for instance, the ontological argument for the existence of God. This argument says (very roughly) that a perfect being must exist because if it did not then it would not be perfect. That argument is absurd on its face, but there are subtle and sophisticated versions of it that are hard to refute (e.g. Plantinga 1974).
Because the ontological argument is so absurd on its face, sophisticated versions of it make me distrust the fancy philosophical machinery they employ rather than making me more inclined to believe in a perfect deity. They could be worth mining for insights about that fancy machinery, but not for insights about whether or not there is a God.
Sophisticated versions of seemingly absurd arguments are fairly common in philosophy. In general, they are potentially useful as test cases for the kind of reasoning they employ, but they are unlikely to be useful for evaluating their conclusions.
Question: There are of course cases in which formal reasoning corrects mistaken intuitions (e.g. the Monty Hall problem). But are there examples of intuitively absurd arguments (as opposed to surprising conclusions) that have been widely accepted upon careful consideration?
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