# [b-greek] Re: Does "If A then B mean if not B then not A" ?

From: Daniel L. Christiansen (dlc@multnomah.edu)
Date: Thu Jun 28 2001 - 18:57:23 EDT

rickstamp@gmx.net wrote:

> I have seen it stated that it is a logical fallacy when one assumes that a conditional statement is also true in the reverse as in "If A, then B is not equal to if non-A, then non-B) as described by Wallace on page 687.

This is correct, since there is nothing in the syllogism to indicate the antecedent is a *necessary* rather than a *sufficient* condition. On the other hand, "If and only if A, then B" _does_ imply "If not A, then not B," since the A condition is necessary.

> Could one also state that this is also the case for "if not B then not A"?

"If A, then B" _does_ imply "If not B, then not A." This is so, since in the original syllogism, B is a *necessary* consequent of A, rather than an occasional result.

> Assume a third class conditional with EAN + subjunctive followed by an apodosis in the future.

Such a conditional sentence is found in John 14:15. EAN AGAPATE ME ("A" Sufficient Subseq), TAS ENTOLAS TAS EMAS THRHSETE ("B" Necessary Conseq). One may _not_ infer from this sentence that one who does not love Jesus will not be keeping his commands: in terms of this sentence, we might expect (e.g.) to see people preaching the gospel in hopes of stirring up persecution. However, we _may_
infer from this conditional the following: If one is not keeping his commands, that one is not loving Jesus.

A great resource for understanding and avoiding logical fallacies, BTW, is T. Edward Damer's _Attacking Faulty Reasoning_, published by Wadsworth Publishing.

Daniel
--
Daniel L. Christiansen
Professor of Biblical Languages, Portland Bible College
Adjunct, Multnomah Bible College and Biblical Seminary
(503) 820-0230

---