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Affirming The AntecedentAffirming 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. It is commonly referred to as Modus ponens, or "method of affirming." - If P, then Q.
- P.
- Therefore, Q.
In logical operator notation, this is symbolized -
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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 -
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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).
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