On the refutation of arguments...

I am still very busy, as I said in my last post.  However, I would like to take a moment to point out something  that has been bugging me for quite some time, which has application to discussions everywhere.

One of the most popular logical fallacies these days (in my experience, anyway) is a particular rhetorical tool known as "denying the antecedent."  Wikipedia describes this as:

[T]he consequent in an indicative conditional is claimed to be false because the antecedent is false; if A, then B; not A, therefore not B.

Let me give an example.  Say you and I are having a debate, and you build your conclusion on the existence of purple polka-dotted people-eaters.  In this case, I have one of several options: I can

1) Ignore your argument entirely, and attack your conclusion from a completely different angle, and show why such a conclusion is impossible, or

2) Accept the logical deduction of your conclusion from the existence of purple polka-dotted people-eaters, but attack the existence of such creatures, or

3) Attack the logical steps by which you get from PPDPE's to your conclusion.

Responses 2 and 3 are wonderful rhetorical tools.  They win debates.  Why?  Because people then assume that the conclusion is therefore false, committing the fallacy mentioned above.

However, the only way that that could be the case is if it can be shown that the argument is "if and only if A, then B".  In other words, that "not A, then necessarily not B" is actually the case.  However, in most debates that is extremely hard to prove.

This fallacy has many and subtle forms to it.  Frequently, "armchair atheists" will be very guilty of this.  They may say, "Prove God's existence to me."  Then, they shoot down each argument that they receive.  They then assume that God does not exist.  They think, because no one can prove it to my satisfaction, then it must not Be.

Also, Christians can be guilty of this as well, with their own argumentation from Scripture.  For example, the article that prompted this post contains a quote from Episcopal bishop Gene Robinson (an openly practicing homosexual):

We have allowed the Bible to be taken hostage, and it is being wielded by folks who would use it to hit us over the head,” he said. “The sin of Sodom had nothing to do with homosexual sex but was a failure to care for the poor, the widows and the orphans. Scripture is not as plainspoken as some would have us believe.

Ok, let's assume that that is in fact the case.  Let's grant the point.  He has pointed out that "A" -- the argument against homosexuality from the "sin of Sodom" -- is invalid.  Let's grant the point, for the sake of argument.  He has encountered the argument "If A, then B" -- where "B" is the Christian assertion that homosexuality is a sin.  To which he has replied "not A".  But his conclusion ("therefore, not B") is the fallacy we've been discussing.

The very best his "not A" assertion can do is to reset the discussion back to the raw assertions -- "B" for Christianity, and "not B" for him.   In order for his argument of "not A, therefore not B" to be valid, he would have to show that "B iff A" (that is, "B if and only if A").  This he has not done.
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(NB: Lest I fall into the same fallacy -- I should mention that proving his argument false does not make his assertion of "not B" necessarily incorrect.  It just means that his assertion is in no way proven or not proven.  I disagree with his conclusion that homosexuality is not a sin.  But it is on other bases that I do not agree, not based on the sin of Sodom.)