Editing False dilemma (section)

== Types ==
=== Disjunction with contraries ===
In its most common form, a ''false dilemma'' presents the alternatives as [[contradictories]], while in truth they are merely [[contraries]].<ref name="Engel"/><ref name="fallacyfiles"/> 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.<ref name="Engel"/> Contradictories follow the [[law of the excluded middle]] but contraries do not.<ref name="fallacyfiles"/> 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.<ref name="Engel"/> While ''false dilemmas'' involving contraries, i.e. [[Exclusive or#Exclusive or in natural language|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.<ref name="Tomić"/> For example, a choice between security and freedom does not involve contraries since these two terms are compatible with each other.<ref name="Engel"/>

=== Logical forms ===
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:<ref name="Honderich">{{cite book |last1=Honderich |first1=Ted |title=The Oxford Companion to Philosophy |date=2005 |publisher=Oxford University Press |url=https://philpapers.org/rec/HONTOC-2 |chapter=Dilemmas |access-date=13 March 2021 |archive-date=29 January 2021 |archive-url=https://web.archive.org/web/20210129082636/https://philpapers.org/rec/HONTOC-2 |url-status=live }}</ref><ref name="fallacyfiles"/><ref name="Tomić"/>
* simple constructive: <math>\frac{(P \to Q), (R \to Q), (P \lor R)}{\therefore Q}</math>
* simple destructive: <math>\frac{(P \to Q), (P \to R), (\lnot Q \lor \lnot R)}{\therefore \lnot P}</math>
The source of the fallacy is found in the disjunctive claim in the third premise, i.e. <math>P \lor R</math> and <math>\lnot Q \lor \lnot R</math> 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)".<ref name="Tomić"/> 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]]:<ref name="fallacyfiles">{{cite web |title=The Black-or-White Fallacy |url=http://www.fallacyfiles.org/eitheror.html |website=www.fallacyfiles.org |access-date=13 March 2021 |archive-date=6 December 2020 |archive-url=https://web.archive.org/web/20201206222117/http://www.fallacyfiles.org/eitheror.html |url-status=live }}</ref>
* disjunctive [[syllogism]]: <math>\frac{(P \lor Q), (\lnot P)}{\therefore Q}</math>
In this form, the first premise (<math>P \lor Q</math>) is responsible for the fallacious inference. [[Lewis's trilemma]] is a famous example of this type of argument involving three disjuncts: "Jesus was either a liar, a lunatic, or Lord".<ref name="Vleet"/> By denying that Jesus was a liar or a lunatic, one is forced to draw the conclusion that he was God. But this leaves out various other alternatives, for example, that Jesus was a prophet.<ref name="Vleet"/>

=== Deductive and defeasible arguments ===
False dilemmas are usually discussed in terms of [[deductive reasoning|deductive arguments]]. But they can also occur as [[defeasible reasoning|defeasible arguments]].<ref name="Tomić"/> A valid argument is deductive if the truth of its premises ensures the truth of its conclusion. For a valid defeasible argument, on the other hand, it is possible for all its premises to be true and the conclusion to be false. The premises merely offer a certain degree of support for the conclusion but do not ensure it.<ref>{{cite web |last1=Koons |first1=Robert |title=Defeasible Reasoning |url=https://plato.stanford.edu/entries/reasoning-defeasible/ |website=The Stanford Encyclopedia of Philosophy |publisher=Metaphysics Research Lab, Stanford University |access-date=13 March 2021 |date=2017 |archive-date=15 March 2023 |archive-url=https://web.archive.org/web/20230315044949/https://plato.stanford.edu/entries/reasoning-defeasible/ |url-status=live }}</ref> In the case of a defeasible false dilemma, the support provided for the conclusion is overestimated since various alternatives are not considered in the disjunctive premise.<ref name="Tomić"/>