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The form of the fallacy of false dichotomy as an argument map with the conclusion at the top of the tree.

The informal fallacy of false dilemma—also known as false choice, false dichotomy, falsified dilemma, fallacy of the excluded middle, black and white thinking, false correlative, either/or fallacy, and bifurcation—involves a situation in which two alternative statements are held to be the only possible options, when in reality there exists one or more other options which have not been considered.

The dilemma need not be limited to two choices; it may involve three possibilities, in which case it is known as a trifurcation.^{[citation needed]} There may be even more choices involved, in which case the fallacy may arise simply by accidental omission—possibly through a form of wishful thinking—rather than by deliberate deception.

When two alternatives are presented, they are often, though not always, two extreme points on some spectrum of possibilities. This can lend credence to the larger argument by giving the impression that the options are mutually exclusive, even though they need not be. Furthermore, the options are typically presented as being collectively exhaustive, in which case the fallacy can be overcome, or at least weakened, by considering other possibilities, or perhaps by considering the whole spectrum of possibilities, as in fuzzy logic.

An example of a false dichotomy appearing on the Australian Broadcasting Corporation radio programme hosted by Michael Duffy, Counterpoint.^[1]

A simple example of a false dilemma is the following:

"You are either with us or against us. You have refused to join our cause, therefore you must be working against our cause."

This argument is a false dilemma, because it denies the possibility that there is someone who has no interest or is unaware of that cause.

Very often a Morton's Fork, a choice between two equally unpleasant options, is a false dilemma. The phrase originates from an argument for taxing English nobles:

"Either the nobles of this country appear wealthy, in which case they can be taxed for good; or they appear poor, in which case they are living frugally and must have immense savings, which can be taxed for good." ^[2]

This is a false dilemma, because some members of the nobility may in fact lack liquid assets.

The presentation of a false choice often reflects a deliberate attempt to eliminate the middle ground on an issue. Rhetorically, this often takes the form of a statement such as "Either you are with us, or you are against us."

A common form of the false dilemma in public discourse is black and white thinking. As an example, consider the following three patterns of reasoning, the first valid, the others invalid.

• Example 1: Three is an odd number. Only even numbers are divisible by two. Therefore three is not divisible by two. (valid)

• Example 2: John says that three is an odd number. John is a liar. Therefore three is not an odd number. (invalid)

• Example 3: John says that two is an odd number. John is a liar. Therefore two is not an odd number. (invalid)

The first example is valid because natural numbers are either even or odd. The two classes are exhaustive and mutually exclusive. The second example is invalid because the categories "liar" and "truth teller" are neither exhaustive nor mutually exclusive. Anyone may tell some lies and some truths. The third example is invalid reasoning for the same reason as the second (even though its conclusion is true).

The assertion that there is no alternative is an example of the false dichotomy taken to its ultimate extreme, in which the alternatives are reduced to one, the proposal of the speaker. Of course the speaker does not believe there are no alternatives otherwise he would not bother to argue the point; rather he opposes the alternatives and seeks to dismiss them by denying their existence.

"This was the mantra chanted by 'dries' during the prime ministerial reign of Margaret Thatcher, by which they demonstrated their belief that free-market capitalism was the only possible economic theory. It was said so often amongst them that it was shortened to TINA. The hard-right Thatcherites called themselves 'dries' to demonstrate their opposition to the 'wets', i.e. the One-Nation Tories whom Thatcher despised. Wet was the public school nickname for any boy who showed any sign of caring for his fellow beings."

• Correlative-based fallacies
• Descartes' Error
• Law of the excluded middle, whose misapplication is sometimes the cause of this fallacy
• Pascal's Wager
• Nolan chart
• Half-truths

1. ^ ABC Counterpoint transcript (accessed 22 Oct 2006)
2. ^ Ivor H. Evans, editor, Brewer's Dictionary of Phrase & Fable, 14th edition, Harper & Row, 1989, ISBN 0-06-016200-7,