The Formal Fallacies
A formal fallacy is an error in reasoning which is inherent in the structure of the argument itself. There are two formal fallacies, which are the “evil twins” of modus ponens and modus tollens. The first is called Denying the Antecedent, which we will call “DA” for short. Modus tollens is a valid argument because it denies what’s called the consequent i.e. the Q in “if P then Q”. DA is the invalid evil twin of modus tollens because it denies the antecedent i.e the P in “if P then Q”.
Denying the Antecedent (DA)
Because it is possible to have two true premises and a false conclusion with this inference form, DA is a fallacy.
If John Coltrane could play every instrument in the world, he could play the saxophone. (true)
John Coltrane cannot play every instrument in the world. (true)
Therefore, John Coltrane cannot play the saxophone.(false)
A similar example:
If Barack Obama can solve all the world’s problems, he would make a good president
Barack Obama cannot solve all the world’s problems
Therefore, he would not make a good president
Even if you think the conclusion of this argument is true, I’m sure you will agree that the premises do not support the conclusion, even though both premises are true.
