Why is affirming the consequent invalid?

Affirming the consequent is invalid because it assumes a specific cause for an outcome that can have multiple causes. Consider the formula for affirming the consequent:

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

The above syllogism is fallacious because Q can be true for reasons other than P. The mistake lies in assuming a single cause for an effect or trait.

For example:

  • If a number is a perfect square, then it is positive.
  • The number 14 is positive.
  • Therefore, the number 14 is a perfect square.