Editing False dilemma (section)

=== 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"/>