Affirming the consequent

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").

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.