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Affirming the consequent

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Affirming the consequent is a logical fallacy often used in the context of trying to establish guilt by association. It is named after the consequent in a conditional statement (Q in "if P, then Q").

Contents

Forms of the argument

Propositional logic

  • If P, then Q.
  • Q.
  • Therefore, P.

In formal terms, the fallacious argument is stated as \left(P\rightarrow Q\right), Q \vDash P.

First-order logic

  • If P is true of x, then Q is true of x.
  • Q is true of x.
  • Therefore, P is true of x.

In formal terms, the fallacious argument is stated as \forall x.\left(P(x)\rightarrow Q(x)\right), Q(a)\vDash P(a).

Examples of the argument

Propositional form

  • If it is sunny today, then I will go swimming.
  • I will go swimming.
  • Therefore, it is sunny today.

First-order form

  • Fascists support a strong military.
  • John Q. Warhawk supports a strong military.
  • Therefore, John Q. Warhawk is a fascist.


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