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Special pleading

Special pleading is a logical fallacy wherein a double standard is employed by the person making the assertion. Special pleading typically happens when one insists upon less strict treatment for the argument one is making than one would make when evaluating another's argument. For a completely non-controversial example:

John: "I think the chicken crossed the road because somebody put food at the other side."
Mary: "You have no evidence that someone put food there. I think the chicken crossed the road because someone pushed it."

In that example, Mary was using special pleading on John. For John's argument, Mary required that everyone involved be specified, while she didn't do the same for her argument.