If P, then Q.
Therefore, not Q.
Informally, this means that arguments of this form do not give good reason to establish their conclusions, even if their premises are true.
Here’s an example:
If someone owned 1,000,000 shares of IBM, then they would be rich!
Bill Gates does not own 1,000,000 shares of IBM.
Therefore, Bill Gates is not rich.
I bring this up because I see this fallacy quite often. It’s the foundation for much of the argument that Barack Obama is not eligible to be President because his father was not a US Citizen.
In the case of the anti-Obama argument “P” in the formal argument is “a person born in the United States to two US Citizen parents” and “Q” is “natural born citizen.”
Two birther examples of the fallacy include their reading of the material supporting Senate Resolution 511 on John McCain and the Supreme Court decision in Minor v Happersett. Secretary of Homeland Security Michael Chertoff testified before the Senate Judiciary Committee (on the subject of McCain’s eligibility) and made this statement that fits nicely in the template for the first premise:
My assumption and my understanding is that if you are born of American parents, you are naturally a natural-born American citizen.
Obama opponents take this statement, or similar ones, and point out (correctly) that one of Barack Obama’s parents was not American. The mistake is drawing the conclusion that he is himself not a natural born American citizen–”that’s the formal fallacy.
Similarly, the decision in Minor v Happersett:
In that sense, women, if born of citizen parents within the jurisdiction of the United States, have always been considered citizens of the United states, as much so before the adoption of the Fourteenth Amendment to the Constitution as since.
Is turned from a conditional statement to a definition through the same fallacy.