Affirming the antecedent
Affirming the antecedent is a valid
argument form which proceeds by affirming the truth of the first part (the "if" part, commonly called the antecedent) of a
conditional, and concluding that the second part (the "then" part, commonly called the consequent) is true.
- If P, then Q.
- P.
- Therefore, Q.
In
logical operator notation, this is symbolized
-
-
Many people assume that this works the other way as well, so that one could say:
- If P then Q.
- Q.
- Therefore P.
In
logical operator notation, this is symbolized
-
-
-
where represents the
logical assertion.
But this is a Logical fallacy called Affirming the consequent. Since P implies Q, but Q does not necessarily imply P.
You can see this if we simply substitute in actuall statements for P. and Q.
- If there is fire here, then there is oxygen here.
- There is oxygen here.
- Therefore, there is fire here.
Sometimes P and Q entail each other, in that case we can say P if and only if Q. (Sometimes the shorthand P
iff Q is used rather than writing out if and only if).