A false dilemma occurs whenever someone suggests that we must choose between a certain number of options on an issue when there are actually other possible options to choose from. Generally, it works by raising a couple of options and giving us reason to think that we shouldn't accept one of them hopes that we will therefore accept the other option the person has mentioned. But of course, if there are additional options besides the two the speaker has mentioned, then we shouldn't jump to his/her favored conclusion even if we agree that we should reject one of those options.
Example #1:
This Obama campaign ad attacks Romeny for not making more of his tax records public (which makes it an ad hominem fallacy too). It commits the false dilemma fallacy by assuming that the only two options here are either (a) Romney has nothing to hide and is therefore willing to release his taxes, or (b) Romney is unwilling to release his taxes because he has something bad to hide. Since Romney has been unwilling to release his taxes, the video wants us to conclude that therefore option (b) is true. However, there are other possible options to consider such as the option (c) that Romney does not have anything to hide but doesn't want to release his taxes because he thinks it's important to maintain his privacy as a matter of principle, or perhaps (d) he doesn't have anything to hide but is afraid his opponents might misconstrue facts about his taxes to an audience of uncritical thinkers in ways that would be undesirable.
Example #1:
This Obama campaign ad attacks Romeny for not making more of his tax records public (which makes it an ad hominem fallacy too). It commits the false dilemma fallacy by assuming that the only two options here are either (a) Romney has nothing to hide and is therefore willing to release his taxes, or (b) Romney is unwilling to release his taxes because he has something bad to hide. Since Romney has been unwilling to release his taxes, the video wants us to conclude that therefore option (b) is true. However, there are other possible options to consider such as the option (c) that Romney does not have anything to hide but doesn't want to release his taxes because he thinks it's important to maintain his privacy as a matter of principle, or perhaps (d) he doesn't have anything to hide but is afraid his opponents might misconstrue facts about his taxes to an audience of uncritical thinkers in ways that would be undesirable.