Also called Apple Polishing.
An Appeal to Flattery is a fallacy of the following form:
The basic idea behind this fallacy is that flattery is presented in the place of evidence for accepting a claim. This sort of "reasoning" is fallacious because flattery is not, in fact, evidence for a claim.
"My Bill, that is a really nice tie. By the way, it is quite clear that one plus one is equal to forty three."
"Might I say that this is the best philosophy class I've ever taken. By the way, about those two points I need to get an A..."
"That was a wonderful joke about AIDS boss, and I agree with you that the damn liberals are wrecking the country. Now about my raise..."
"That was a singularly brilliant idea. I have never seen such a clear and eloquent defense of Plato's position. If you do not mind, I'll base my paper on it. Provided that you allow me a little extra time past the deadline to work on it."