False dilemma

Even crazier than golf, though, is modern American politics, where, thanks to TV and for the convenience of TV, you can only be one of two kinds of human beings, either a liberal or a conservative. A false dilemma (also known as a false dichotomy) is a logical fallacy which involves presenting two opposing views, options, or outcomes in such a way that they seem to be the only possibilities: that is, if one is true, the other must be false, or, more typically, if you do not accept one, then the other must be accepted. The reality in most cases is that there are many in-between or other alternative options, not just two mutually exclusive ones.

In other words, there are two ways in which one can commit a false dilemma. First, one can assume that there are only two (or three, though in that case it is, strictly speaking, a "false trilemma") options when there really are many more. Second, one can take the options to be mutually exclusive when they really are not.

The fallacy is a syllogistic fallacy and a formal fallacy.

Alternate names

 * black-or-white
 * denying a conjunct
 * disjunctive syllogism
 * either/or fallacy
 * excluded middle
 * fallacy of exhaustive hypotheses
 * false dichotomy
 * no middle ground
 * rathering

Form
You commit this fallacy if you interpret the negation of a conjunction (e.g. "not both A and B") as implying that at least one conjunct (either A or B) must be true.

In other words, confusing a contradiction (where one or the other must be true, but not both) with a contrary (where both could be false, but both cannot be true).

For example:

The above example is fallacious, as it is possible for both creationism and evolution to be untrue (life suddenly appeared one day) or true (god created evolution).

Assuming only two options
As an example of the first, here is Reed Heustis’s attempt to prove that the Founding Fathers were deeply influenced by John Calvin:

Since the founding fathers were clearly not Marxists, they must have been Calvinists. The rest of us may be inclined to think that, surely, there are more options here (and especially given Marxism is separated from Calvinism by centuries) than presented.

Assuming mutual exclusion
It is very simple. If I am wrong, they are right. Thus I should be doing the opposite of what I was doing, as that will be the right thing to do. I do not need to think about it. I do not need to introduce complexity where there is none. As an example of the second, here is Joel Richardson, in the WND, criticizing Ron Paul's foreign policies:

But of course, adopting one causal factor does not – despite what Richardson assumes – entail rejecting the other (though of course Richardson's caricatures are also strawmen, even regarding an ideologue like Paul).

It is worth noting that it is not a false dilemma to present two options out of many if no conclusion is drawn based on their exclusivity: "you can have tea or coffee" is not a false dilemma, a fallacious form would require it to be presented as an argument such as "you don't want tea, therefore you must want coffee." Though even this is not necessarily a false dilemma if those are the only two options and it has been established "you" want a drink.

Rathering
Daniel Dennett coined the term rathering as a "way of sliding you swiftly and gently past a false dichotomy". It was inspired by Stephen Jay Gould's usage of the word rather; Dennett provides an example (emphases added):

Of course, both statements can be true.

Some ratherings don't use the word rather, but (for example) not:

Not all usages of the word rather are a false dilemma (or rathering), rather it is a useful technique to detect (possible) false dilemmas.

Alternative Advance
This is a term coined by Dr Bo Bennett of Logically Fallacious fame, to refer to a false dilemma in which two options, essentially the same but with different wording, are present to the subject. They would be committing fallacious reasoning if they accepted the options as the only ones in existence, because, given more thought, there are in fact other choices. For example, a salesperson asking a potential client if they would rather be contacted by telephone or e-mail. This is alternative advance, since another option would be to not be contacted at all (and I would strongly encourage this). Alternative advance creates a lose-lose situation in which the subject, whatever they do, remains in the thrall of the speaker.

Examples
Spotted in the wild:
 * One of the most common false dilemmas espoused by creationists, especially in the United States, is that if there is any flaw at all in the theories of evolution, then creation science is the only other possible truth. (Not even mainstream Christians accepting theistic evolution is acceptable.)
 * This same kind of wooish reasoning is employed, albeit less frequently, by many pseudoscience promoters, taking the form of "since science has not perfectly explained phenomena X yet, my pet goat claim must be true." The obvious rebuttal to this false dilemma is that the science only needs to be tweaked (or explored more) in order to provide an explanation. Even if it can't provide an answer to everything immediately, of course, that is not proof of the "alternate" claim.
 * "America — Love It Or Leave It" is a popular false dilemma. The dilemma suggests that a "true patriot" must embrace everything ever done by America, or become un-American. However, since America as a nation was founded on the concept of respectful political dissent, one must doubt the premise of this false dilemma very seriously.
 * Many (but not all!) "if you're for A, you're against B"-statements are a false dilemma. President George W. Bush’s famous statement "Either you are with us, or you are with the terrorists." is a good example. Believing that some measures taken by the Dubya (or Obama, or any other) government were unnecessary, excessive or morally suspect obviously doesn't entail a murderous disregard for human life — quite the opposite, in many cases. However, if such a statement is backed with a threat of action ("either you support us, or you're our enemy") it is not a false dilemma, since the speaker is the one who decides who their enemy is.
 * A false dichotomy similar to the last two surrounds discussions about Israel. One example of this is how some persons insist that being critical of the state of Israel or Israeli policies amounts to a) anti-Zionism and b) anti-Semitism. Another example is how persons both on the "pro-Palestinian side" and the "pro-Israeli side" claim that you cannot both support Israel's right to exist and Israel's right to self-defense and also support an independent Palestine or criticize Israeli policies towards the Palestinians. Similarly you cannot dislike Hamas and Benjamin Netanyahu at the same time.
 * Ted Cruz said, after being booed and heckled during an appearance at a Defense of Christians unity dinner celebrating Christians facing persecution in the Middle East, "If you will not stand with Israel, then I will not stand with you," then walked off the stage in a petulant frenzy. This could also be seen as a form of argumentum ad baculum.
 * Pascal's Wager states that it is more reasonable to believe in God and be wrong than to risk burning in Hell &mdash; which would be a pretty safe bet if one assumes that Jehovah is the one and only true God and that He has supreme power and ultimate authority over all of the multitude of other deities that have been proposed over the millennia. Pascal simply dismissed all other possibilities.
 * The concept, from both sides of the "debate", that science and religion are mutually exclusive and one cannot believe in both.(NOMA is an attempt to resolve this.) On the other hand, "God exists or god does not exist" is a true dichotomy.
 * Speaking of which, from the atheist side, one either totally accepts Non-overlapping magisteria, or one is a misogynistic, Islamophobic New Atheist.
 * C. S. Lewis perpetrated the famous "Lord, Liar, Lunatic" false trilemma: "A man who was merely a man and said the sort of things Jesus said would not be a great moral teacher. He would either be a lunatic — on the level with the man who says he is a poached egg — or else he would be the Devil of Hell. You must make your choice. Either this man was, and is, the Son of God, or else a madman or something worse." This trilemma is itself based on a false dilemma: either the claim of divinity attributed to the man Jesus is to be accepted as true and right and good, or that claim attributed to the man Jesus must be rejected as false: either insanely wrong (though this horn has the problem that “lunatics” can still say things that prove “true and right and good” or conversely that he did teach “good” morals but messiahhood was the “insane” belief he would allow his followers to never really give up) or morally evil. Either you accept Jesus as "the Son of God," or you think this is no more valid than "I am a poached egg," and "I am God" is a lie from "the Devil of Hell."
 * Some anti-abortionists present a dilemma between "life begins at conception" and "life begins at birth", taking a denial of the latter to imply support for the former.
 * Texas governor Rick Perry issued a debate challenge to House Minority Leader Nancy Pelosi during his 2012 GOP presidential candidate campaign, despite the fact that Pelosi wasn't running and is a Democrat. Performing poorly in debates against other GOP candidates, he asked Pelosi to debate his own plan to reformat Washington, D.C. versus (his version of) the status quo — and if she refused, declined or did not respond, he told her that "I will take it to mean you will continue your obstructionist ways in the face of much needed Washington reform." Pelosi reportedly laughed at the request and declined, saying she was unavailable to debate due to a busy schedule.
 * Darth Vader in Star Wars III: Revenge of the Sith told Obi-Wan Kenobi "If you're not with me, then you're my enemy," to which Obi-Wan replies, with some irony, "Only a Sith deals in absolutes."
 * Another common false dilemma is "kill or be killed". In almost all circumstances there are alternatives to either killing or being killed. Nonetheless, the Nuremberg defense in its most absurd and untrue application says, "I had to kill those people otherwise I would have been killed next" is demonstrably bullshit since no Wehrmacht soldier or SS member who refused to partake in executions was executed. Pay was cut and transfers to the (rather unpleasant) Eastern Front were issued, but no death warrant was ever found with "refusal to execute prisoners" as the reason.
 * Many supporters of alternative medicine will claim that one must choose between "allopathy" and whatever magic potions the particular individual happens to believe in. Often, this is accompanied with claims that all scientific studies are rigged and can't be trusted; if the science on which evidence-based medicine is based is false, then the anecdotal evidence behind homeopathy (or whatever) must be good! The trouble with this is that of the hundreds of different and all anecdotally supported alternative therapies, theories, and diets, many are contradictory and cannot possibly all work. Even if the results of all medical studies were made up, that does not somehow make the anecdotes in favor of all the totally contradictory ideas of alternative medicine valid. In the words of Ben Goldacre, "pharma being shit does not mean magic beans cure cancer.
 * The very common claim that one must be either completely against all government regulations (and in favor of tax cuts for the wealthy) or else a staunch communist who believes the Eastern bloc was right all along and the Cold War was won by the wrong side. The possibility that some restrictions on capitalism can exist in a society that defends human rights and allows prosperity is treated as utterly chimerical, despite the existence of Scandinavia. Note that both the radical left and radical right have a vested interest in promoting this false dilemma.
 * The entire two-party system in America is a false dilemma, where it is often assumed that liberal and conservative are the only two political beliefs, often ignoring other views such as leftism. And that's not to mention that "conservative" and "liberal" aren't even mutually exclusive terms to begin with.
 * And lest we forget, . (For the Biblically challenged, it starts with "He that is not with me is against me" and continues in the same direction.)

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