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Reductio ad Hitlerum, also argumentum ad Hitlerum (Latin for "reduction to" and "argument to" and dog Latin for "Hitler" respectively), is a term coined by conservative philosopher Leo Strauss in 1951. According to Strauss, the Reductio ad Hitlerum is an informal fallacy that consists of trying to refute an opponent's view by comparing it to a view that would be held by Adolf Hitler or the Nazi Party.
According to Strauss, Reductio ad Hitlerum is a form of ad hominem or ad misericordiam, a fallacy of irrelevance, in which a conclusion is suggested based solely on something's or someone's origin rather than its current meaning. The suggested rationale is one of guilt by association. Its name is a variation on the term reductio ad absurdum.
Reductio ad Hitlerum is sometimes called "playing the Nazi card." According to its critics and proponents, it is a tactic often used to derail arguments, because such comparisons tend to distract and anger the opponent.
Reductio ad Hitlerum is a form of association fallacy. The argument is that a policy leads to – or is the same as – one advocated or implemented by Adolf Hitler or the Third Reich and so "proves" that the original policy is undesirable. Although previously acceptable policies (particularly eugenics) have been abandoned in part owing to such comparisons, the fallacious nature of reductio ad Hitlerum is easily illustrated by identifying X as something that Adolf Hitler or his supporters did promote but which is not considered unethical, such as painting (like Sir Winston Churchill), enjoying classical music (like some of the July 20 plotters), owning dogs (like Franklin Delano Roosevelt), advocating good roads (like Dwight Eisenhower), demonstrating nationalistic patriotism (David Ben-Gurion), performing spellbinding oratory (like Martin Luther King), or in some contexts having difficulty with existing authorities (like Mohandas Gandhi), all of whom were either enemies of Hitler or ideological opposites. For example: "Hitler loved animals, so animal protection is a fascist activity [because the things Hitler did were wrong, or because it could lead to results ideologically or morally aligned with Hitler]." Used broadly enough, ad Hitlerum can encompass more than one questionable-cause fallacy type, by both inverting cause and effect and by linking an alleged cause to wholly unrelated consequences. For example, Hitler was fond of children, but to argue that affection for children is wrong on this basis is not persuasive.
Another instance of reductio ad Hitlerum is asking a question of the form "You know who else...?" with the deliberate intent of impugning a certain idea or action by implying Hitler held that idea or performed such action.
An invocation of Hitler or Nazism is not a Reductio ad Hitlerum when it illuminates the argument instead of causing distraction from it.
The phrase reductio ad Hitlerum is first known to have been used in an article written by University of Chicago professor Leo Strauss for "Measure: a critical journal" in Spring 1951; it was made famous in a book by the same author published in 1953  Natural Right and History, Chapter II:
In following this movement towards its end we shall inevitably reach a point beyond which the scene is darkened by the shadow of Hitler. Unfortunately, it does not go without saying that in our examination we must avoid the fallacy that in the last decades has frequently been used as a substitute for the reductio ad absurdum: the reductio ad Hitlerum. A view is not refuted by the fact that it happens to have been shared by Hitler.
The phrase was derived from the legitimate logical argument called reductio ad absurdum. The argumentum variant takes its form from the names of many classic fallacies, such as argumentum ad hominem. The ad Nazium variant may be further derived, humorously, from argumentum ad nauseam.
In 2000 traditionalist Catholic Thomas Fleming described its use against traditional values:
Leo Strauss called it the reductio ad Hitlerum. If Hitler liked neoclassical art, that means that classicism in every form is Nazi; if Hitler wanted to strengthen the German family, that makes the traditional family (and its defenders) Nazi; if Hitler spoke of the "nation" or the "folk," then any invocation of nationality, ethnicity, or even folkishness is Nazi ...
In 1991, Professor Michael André Bernstein alleged reductio ad Hitlerum over a full-page advertisement placed in The New York Times by the Lubavitch community, following the Crown Heights Riot, under the heading "This Year Kristallnacht Took Place on August 19th Right Here in Crown Heights." Henry Schwarzschild, who had witnessed Kristallnacht, wrote to the New York Times that "however ugly were the anti-Semitic slogans and the assaultive behavior of people in the streets [during the Crown Heights riots]... one thing that clearly did not take place was a Kristallnacht."
American conservative radio and television host Glenn Beck is often criticized for his frequent use of reductio ad Hitlerum, including a controversial statement comparing the victims of the 2011 Norway attacks to members of the Hitler Youth. Beck has also compared the National Endowment for the Arts to Joseph Goebbels and ACORN to Hitler's "Brown Shirt" soldiers.
That Nazism and contemporary liberalism both promote healthy living is as meaningless a finding as that bloody marys and martinis may both be made with gin. Repeatedly, Goldberg fails to recognize a reductio ad absurdum. ... In no case does Goldberg uncover anything more ominous than a coincidence.