Logic: Denying the Antecedent
My favorite part of the introductory philosophy course I took at the University of Winnipeg was the segment on logic, especially on logical fallacies. One of the most common logical fallacies is “denying the antecedent.”
Here’s the example used in my old logic text, Joseph G. Brennan, A Handbook of Logic, Harper and Row, 1957:
If Bill Nietman is a Princeton graduate, he cuts his own hair. (If p, then q.)
Bill Nietnam is not a Princeton graduate. (Not p.)
Therefore he does not cut his own hair. (Not q.)
As you can see, the fact that p is not true does not mean that q is not true. Many people besides Princeton graduates cut their own hair.
In his response as a commenter this morning, Nathan Smith commits that fallacy. He writes:
“[Carpenter] contends that preserving NATO is unnecessary because the West European nations now have the economic and military resources to protect their own security.” Logically, “p because q” implies “if not-q, then not-p.” Logically, “NATO is unnecessary because Western European nations can defend themselves” would seem to imply “if Western European nations couldn’t defend themselves, NATO would be necessary.”
Notice that he writes:
Logically, “p because q” implies “if not-q, then not-p.”
In other words, he is denying the antecedent.
I would get more into his substantive argument about foreign policy, but I’m going to stick to my Econlog knitting and focus, as I almost always do, on economics.
I want to reassure readers, though, that we at Econlog do not block people as commenters simply because they disagree with us. I say this because Nathan wrote:
I wouldn’t want to provoke Arnold and Dave and Bryan into blocking me from posting comments in future!
There are two misunderstandings packed into one sentence. First, the webmaster, not Arnold or Bryan or I, has the main say about what gets blocked. Second, she has always been clear about the criteria for blocking and among those criteria there’s not even a hint that one gets blocked simply for disagreeing.