Logical Fallacy #9: Denying the antecedent

-John Dunfee

Inferring that Q is false just because if P is true, Q is also true, but P is false.
 
Logical Form:
f P, then Q.
Not P.
Therefore, not Q.
 
This fallacy is similar to the fallacy of affirming the consequent. Again the problem is that some alternative explanation or cause might be overlooked. Although P is false, some other condition might be sufficient to make Q true.
 
Example: If there is a traffic jam, then a colleague may be late for work. But it is not right to argue in the light of a smooth traffic that the colleague will not be late. Again, his alarm clock may have stopped working.
 
This at first can seem like affirming the consequent, but it’s not. If you one thing is true because of something else, then that is affirming the consequent. If I say something is false because one thing is true, then that would be denying the antecedent. These occur in conditional statements which are if: then statements. Basically if a conditional statement doesn’t logically follow then you would be denying the antecedent or affirming the consequent. If you deny the antecedent, then you can’t deny the consequent.
 
Example: If john doesn’t have a car, then he can’t get to work.
John doesn’t have a car; therefore, he can’t get to work. John could get to work by someone else or walk if he lives close enough to his work place. This example commits the denying the antecedent fallacy.
 
Example: If I didn’t have any water, then I didn’t have anything to drink.
I didn’t have any water; therefore, I didn’t have anything to drink. I clearly could have had a soft drink, coffee, milk, orange juice, or anything other drinkable. It’s not false that that I had anything to drink not based on the fact of not having water. On the fact that I didn’t not consume any form of liquid.
 
Example: If there’s no evidence for God, then he doesn’t exist.
There’s no evidence for God, therefore he doesn’t exist. Evidence of absence is not evidence of absence. If it were the case that there is no evidence for God right now, then it doesn’t follow that he doesn’t exist. There could be evidence in the future that shows the existence of God. Either you have to give a case against the existence of God, or you have to be an agnostic. It’s as simple as that. Of course, I do believe that there is very good evidence for the existence of God.
 
This is another fallacy that you know from reading the article. If you like this on Facebook, then you will be happy!
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