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Four Terms Fallacy

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Also called the Politician's Syllogism or Equivocation.
A standard three-step syllogism uses three terms — the things that are being linked by the line of reasoning. If A, then B. If B, then C. Therefore if A, then C. The fallacy of four terms occurs when, exactly like it says, four terms are used instead of three. In most cases, a single term (B) is used two (or more) times, in differing contexts with different meanings; and yet the argument treats the two usages as exactly the same, since the same term was used.
It's best explained by this example from Land of the Blind.
This uses two different meanings of the word "nothing." The first line uses "nothing" to mean "a lack of food", while the second line uses "nothing" as "no such thing exists."
This fallacy can often be the core of a joke or pun, such as if someone were to suggest that Batman must be good at baseball, since he's so well-acquainted with bats.
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Shakespeare really loved this trope. In Much Ado About Nothing, Beatrice asks Benedick what happened when he challenged Claudio to a duel to defend Hero.
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The Gilmore Girls episode "The Third Lorelai" has the following exchange between Lorelai and her father.
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In Hamlet, the gravedigger and Hamlet make wordplay on "lying" (physically remaining in one place and fibbing):
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Garfield expresses the philosophy. "If nobody is perfect, I must be nobody."
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In Discworld, libraries warp spacetime because "knowledge=power=energy=matter=mass", and enough mass gives you a blackhole.
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Anyone Can Whistle explains in "simple" terms what's wrong with leftists:
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From The Colbert Report:
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In Twelfth Night, Feste attempts this to make excuse for his lateness:
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An episode of Yes, Minister called this by name, as "The Politician's Syllogism", specifically the form: "Something must be done. This is something. Therefore we must do this." The two different meanings of "something": "A solution to this problem" and "A thing" are mixed and said to be the same.
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The The Secrets of Droon, the Wand of Urik works by making illogical syllogisms true. For example, "Cape is blue/Water is blue/Cape is water" turns a blue cape into a pool of water. Or "Stone is good/Fountain is good/Stone is fountain" turns a demon of stone into an ornate fountain.
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In the Family Guy episode New Kidney In Town, Peter attempts to make his own Red Bull. When Brian objects to using kerosene as an ingredient, Peter explains it thusly:
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Played for laughs in a Histeria! sketch about Rene Descartes (and a number of other jokes on the same topic): After Descartes makes his famous proposition that "I think, therefore I am."Meaning If he can think at all, he must exist., a cavalcade of distractions cause him to proclaim "I can't think!"meaning He is not literally unable to think, he just can't think clearly., whereupon he disappears in a Puff of Logic.
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