Denying the antecedent 49
second meaning all along, and only your critic has been so
finicky as to ignore it:
Everybody knows that when we talk of trains being punctual, we use the
railway definition of being within ten minutes of the timetable.
(They do now, anyway.)Denying the antecedent
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