Does "If A then B mean if not B then not A" ?

Dave Reigle dlrgrk at
Thu Jun 28 19:46:23 EDT 2001

All grammar aside, If " A implies B"  is a true statement, then, "NotB
implies NotA is also a true statement.  However we can not say that If "A
implies B" then "NotA implies NotB" is true.
To diagram the situation:
A --> B  (True)  Then
NotB --> NotA (True) [This is called the contrapositive]
B --> A (Not necessarily True) [This is called the Converse]
NotA --> NotB (Not necessarily True) [This is called the Inverse]

I hope this helps, ignore it if not.  Of the logic I'm sure, the rest?
David L. Reigle
Elizabethtown, PA
----- Original Message -----
From: <rickstamp at>
To: "Biblical Greek" <b-greek at>
Sent: Thursday, June 28, 2001 1:17 PM
Subject: [b-greek] Does "If A then B mean if not B then not A" ?

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.   Could
one also state that this is also the case for "if not B then not A"?
Assume a third class conditional with EAN + subjunctive followed by an
apodosis in the future.

Rick Stamp

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