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Affirming the antecedent
Affirming the antecedent is an 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.
Many people assume that this works the other way as well, so that one could say:
- If P then Q.
- Q.
- Therefore P.
But this is a Logical fallacy called Affirming the consequent. Since P entails Q, but Q does not necessarily entail 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).
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