A false dilemma, also referred to as false dichotomy or false binary, is an informal fallacy based on a premise that erroneously limits what options are available. The source of the fallacy lies not in an invalid form of inference but in a false premise. This premise has the form of a disjunctive claim: it asserts that one among a number of alternatives must be true. This disjunction is problematic because it oversimplifies the choice by excluding viable alternatives, presenting the viewer with only two absolute choices when, in fact, there could be many.

False dilemmas often have the form of treating two contraries, which may both be false, as contradictories, of which one is necessarily true. Various inferential schemes are associated with false dilemmas, for example, the constructive dilemma, the destructive dilemma or the disjunctive syllogism. False dilemmas are usually discussed in terms of deductive arguments, but they can also occur as defeasible arguments.

The human liability to commit false dilemmas may be due to the tendency to simplify reality by ordering it through either-or-statements, which is to some extent already built into human language. This may also be connected to the tendency to insist on clear distinction while denying the vagueness of many common expressions.

A false dilemma is an informal fallacy based on a premise that erroneously limits what options are available. In its most simple form, called the fallacy of bifurcation, all but two alternatives are excluded. A fallacy is an argument, i.e. a series of premises together with a conclusion, that is unsound, i.e. not both valid and true. Fallacies are usually divided into formal and informal fallacies. Formal fallacies are unsound because of their structure, while informal fallacies are unsound because of their content. The problematic content in the case of the false dilemma has the form of a disjunctive claim: it asserts that one among a number of alternatives must be true. This disjunction is problematic because it oversimplifies the choice by excluding viable alternatives. Sometimes a distinction is made between a false dilemma and a false dichotomy. On this view, the term "false dichotomy" refers to the false disjunctive claim while the term "false dilemma" refers not just to this claim but to the argument based on this claim.

In its most common form, a false dilemma presents the alternatives as contradictories, while in truth they are merely contraries. Two propositions are contradictories if it has to be the case that one is true and the other is false. Two propositions are contraries if at most one of them can be true, but leaves open the option that both of them might be false, which is not possible in the case of contradictories. Contradictories follow the law of the excluded middle but contraries do not. For example, the sentence "the exact number of marbles in the urn is either 10 or not 10" presents two contradictory alternatives. The sentence "the exact number of marbles in the urn is either 10 or 11" presents two contrary alternatives: the urn could also contain 2 marbles or 17 marbles. A common form of using contraries in false dilemmas is to force a choice between extremes on the agent: someone is either good or bad, rich or poor, normal or abnormal. Such cases ignore that there is a continuous spectrum between the extremes that is excluded from the choice. While false dilemmas involving contraries, i.e. exclusive options, are a very common form, this is just a special case: there are also arguments with non-exclusive disjunctions that are false dilemmas. For example, a choice between security and freedom does not involve contraries since these two terms are compatible with each other.

In logic, there are two main types of inferences known as dilemmas: the constructive dilemma and the destructive dilemma. In their most simple form, they can be expressed in the following way:

The source of the fallacy is found in the disjunctive claim in the third premise, i.e. ${\displaystyle P\lor R}$ and ${\displaystyle \lnot Q\lor \lnot R}$ respectively. The following is an example of a false dilemma with the simple constructive form: (1) "If you tell the truth, you force your friend into a social tragedy; and therefore, are an immoral person". (2) "If you lie, you are an immoral person (since it is immoral to lie)". (3) "Either you tell the truth, or you lie". Therefore "[y]ou are an immoral person (whatever choice you make in the given situation)". This example constitutes a false dilemma because there are other choices besides telling the truth and lying, like keeping silent.

A false dilemma can also occur in the form of a disjunctive syllogism: