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Emotional appeal is a logical fallacy, or at least a very bad way of making an objective argument, whereby a debater attempts to win an argument by trying to get an emotional reaction from the opponent(s) and/or audience, e.g. eliciting fear or outrage. It is generally characterized by the use of loaded language and concepts (God, country, and apple pie being good concepts, homosexuality, drugs, and crime common bad ones). In debating terms, it is often effective as a rhetorical device, but is generally considered naive or dishonest as a logical argument, since it often appeals to listeners' prejudices instead of being a sober assessment of a situation.
Emotional appeal overlaps with other fallacies such as argumentum ad populum (i.e. appeal to widely held values), argument from adverse consequences, argument from shame, and poisoning the well (i.e. using the audience's perceived distaste for an opponent against the opponent).
 Acceptable use
There are times when appealing to people's emotion is acceptable. This is usually when attempting to motivate people, rather than influence or alter their beliefs. Occasionally, this may still be unsound, particularly if the emotions being appealled to have little to do with the action that the appeal intends to motivate.
Children are more often than not toddled out as an appeal to emotion. From pictures of starving children to motivate people to give to charity to using them as any excuse to ban things that children shouldn't even be aware of (guns and porn, for example), they are repeatedly paraded in front of audiences to appeal to their emotional protective instincts, often overriding anyone's sense of rationality. "For the children" or "think of the children" as emotional appeals have been used with success in passing political motions such as Proposition Hate in California.
As with children, cute animals override most people's sense. Even if the pictures of animal testing put out by PETA are 50 years out of date, they still provoke an emotional response rather than a reasoned one when trying to assess cruelty in animal testing. This is also the reason PETA tried to rename fish "sea kittens".
The ever-prevalent "hysterical woman" caricature is a particularly ironic form of emotional appeal (combined with poisoning the well) as it automatically dismisses the opponent's argument as being entirely based on it regardless of their actual argument, even more so as most perpetrators of this argument claim to be completely rational. The target doesn't even have to be female, but we all know being motivated by emotion is a female trait.