Affirming the Consequent

An Affirming the Consequent is an argument pattern that ...

• See: Abductive Logic, Formal Fallacy, Converse (Logic), Argument Form, Validity, Contraposition, Consequent, Indicative Conditional, Argument Form.

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References

2015

• (Wikipedia, 2015) ⇒ http://en.wikipedia.org/wiki/Affirming_the_consequent Retrieved:2015-1-2.
  • Affirming the consequent, sometimes called converse error or fallacy of the converse, is a formal fallacy of inferring the converse from the original statement. The corresponding argument has the general form:
    1. If P, then Q.
    2. Q.
    3. Therefore, P.
  • An argument of this form is invalid, i.e., the conclusion can be false even when statements 1 and 2 are true. Since P was never asserted as the only sufficient condition for Q, other factors could account for Q (while P was false).

    To put it differently, if P implies Q, the only inference that can be made is non-Q implies non-P. (Non-P and non-Q designate the opposite propositions to P and Q.) This is known as logical contraposition. Symbolically:

    [math]\displaystyle{ (P \to Q)\leftrightarrow (\neg Q \to \neg P) }[/math]

    The name affirming the consequent derives from the premise Q, which affirms the "then" clause of the conditional premise.

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