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The Importance of Argumentation in Philosophy
If you disagree with an expert's reasoning, should you be less confident in the fact that you're actually right? Well, you may simply misunderstood or not understood the logic of the argument. In mathematics, there is just as much disagreement among experts on things at the cunning edge as you find in any other field. The question is if you do not have the expertise to engage in a given discussion at that level, your most rational bet is to go with the expert consensus.