How do Luke, Annabeth, and Grover go “way back”? How are they linked by a fourth character?
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A false dilemma is a type of informal fallacy in which something is falsely claimed to be an "either/or" situation, when in fact there is at least one additional option.
The false dilemma fallacy can also arise simply by accidental omission of additional options rather than by deliberate deception. For example, "Stacey spoke out against capitalism, therefore she must be a communist" (she may be neither capitalist nor communist). "Roger opposed an atheist argument against Christianity, so he must be a Christian" (When it's assumed the opposition by itself means he's a Christian). Roger might be an atheist who disagrees with the logic of some particular argument against Christianity. Additionally, it can be the result of habitual tendency, whatever the cause, to view the world with limited sets of options.
Some philosophers and scholars believe that "unless a distinction can be made rigorous and precise it isn't really a distinction". An exception is analytic philosopher John Searle, who called it an incorrect assumption that produces false dichotomies.Searle insists that "it is a condition of the adequacy of a precise theory of an indeterminate phenomenon that it should precisely characterize that phenomenon as indeterminate; and a distinction is no less a distinction for allowing for a family of related, marginal, diverging cases."Similarly, when two options are presented, they often are, although not always, two extreme points on some spectrum of possibilities; this may lend credence to the larger argument by giving the impression that the options are mutually exclusive of each other, even though they need not be. Furthermore, the options in false dichotomies typically are presented as being collectively exhaustive, in which case the fallacy may be overcome, or at least weakened, by considering other possibilities, or perhaps by considering a whole spectrum of possibilities, as in fuzzy logic.
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