- Affirming the consequent
- If P, then Q.
- 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).
One way to demonstrate the invalidity of this argument form is with a counterexample with true premises but an obviously false conclusion. For example:
- If Bill Gates owns Fort Knox, then he is rich.
- Bill Gates is rich.
- Therefore, Bill Gates owns Fort Knox.
Owning Fort Knox is not the only way to be rich. There are any number of other ways to be rich.
Arguments of the same form can sometimes seem superficially convincing, as in the following example:
- If I have the flu, then I have a sore throat.
- I have a sore throat.
- Therefore, I have the flu.
But having the flu is not the only cause of a sore throat since many illnesses cause sore throat, such as the common cold or strep throat.
The following is a more subtle version of the fallacy embedded into conversation.
- A: All Republicans are against gun control.
- B: That's not true. My uncle's against gun control and he's not a Republican.
B attempts to falsify A's conditional statement ("if Republican then against gun control") by providing evidence he believes would contradict its implication. However, B's example of his uncle does not contradict A's statement, which says nothing about non-Republicans. What would be needed to disprove A's assertion are examples of Republicans who support gun control.
- Modus ponens
- Modus tollens
- Post hoc ergo propter hoc
- Denying the antecedent
- Fallacy of the undistributed middle
- Inference to the best explanation
- ELIZA effect
Formal fallacies In propositional logic In quantificational logic Syllogistic fallacyOther types of formal fallacy · List of fallacies This logic-related article is a stub. You can help Wikipedia by expanding it.