Editing False dilemma (section)

=== 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"/>