As with affirming the consequent, the fallacy of denying the antecedent is for those who do not really care if their brain is going forwards or backwards. It does not admit the possibility that different events can produce similar outcomes.
If I eat too much, I’ll be ill. Since I have not eaten too much, I will not be ill.
(So saying, he downed a whole bottle of whisky, cut his hand on a rusty nail and sat out all night in wet clothes.)
The point is, of course, that other events can bring about the same result, even if the event referred to does not take place. With these ‘if … then’ constructions, it is all right to affirm the antecedent (the ‘if’ part) and it is all right to deny the consequent (the ‘then’ part). It is the other two which are fallacious, affirming the consequent or denying the antecedent.
If he’s slow, he’ll lose.
Since he isn’t slow, he won’t lose.
(But he might just be stupid.)
You can affirm the antecedent: ‘He is slow; he will lose.’ You can deny the consequent: ‘He didn’t lose, so he can’t have been slow/ The first of these is a type of argument called the modus ponens, the second is called the modus tollens, and both are valid. It is the other two which are fallacies, even though they resemble the valid forms.
Denying the antecedent is a fallacy because it assigns only one cause to an event for which there might be several. It dismisses other possibilities which could occur.
The fallacy commonly occurs where plans are being laid. It engenders the belief that if those things are avoided which bring harmful consequences, then a pleasant outcome can be expected:
If I smoke, drink or have sex, it will shorten my life-span. I shall give up cigars, booze and women and live another hundred years.
(No. It will just feel like a hundred years.)
It occurs to no lesser degree on the international scale. Countries may calculate the courses of action which bring unpleasant consequences in their wake. What they are not able to do is insure themselves against even worse outcomes simply by avoiding those actions.
If we have a strong army, countries which fear it might attack us. 5o by disarming, we remove that risk.
(Possibly, but they might be more likely to attack because it brings no retaliation.)
You can use the fallacy of denying the antecedent very skilfully in support of the status quo. It is a natural conservative fallacy because most changes we make do not avert all of the evils of the world. By pointing to the likelihood that death and taxes will be the result of the proposed actions, you might lull an audience into rejecting them. The fact that death and taxes will result anyway should not impinge on your success.
The above article is from the book How To Win Every Argument by Madsen Pirie. The article is only for educational and informative purposes to explain and understand formal logic and logical fallacies. It is a great book, definitely worth a read!