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Why is affirming the consequent a fallacy?

  • A.Implication is not a truth functional connective at all
  • B.The consequent may be true for reasons other than the antecedent
  • C.The implication may not hold in the model concerned
  • D.The antecedent may be false in some models of the premises

Answer: B

From rain implies wet ground and wet ground, one cannot conclude rain, since a burst pipe would serve equally well. The implication holds and the consequent is true, yet the antecedent may be false. Truth functionality holds and the implication is granted. Recognising that a true conditional and a true consequent leave the antecedent undetermined is what separates valid inference from plausible reasoning, and the distinction matters constantly in diagnosis.

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