On Thu, 28 Jun 2001 21:17:49 EDT DJNordlund@aol.com writes:
>
> Rick,
>
> when you have a valid implication such as
>
> (1) if A then B
>
> you are correct in understanding that it is NOT logically valid to
> claim
>
> (2) if not-A then not-B
>
> However, if (1) above is valid, then it IS valid to conclude
>
> (3) if not-B then not-A
>
> regardless of the Greek you are analyzing.
Exactly. This is referred to as the contrapositive of the conditional
and is the only valid inference of the conditional. Neither the negation
(if not A, then not B), nor the converse (if B, then A) follow from "if
A, then B."
One can visualize the rationale for this by envisioning circle A within
circle B (A implies B). Non-B then means a point outside the larger
circle which by necessity also is non-A (outside circle A).
How does this relate to the Greek? 1 Cor 15:12-29 is a splendid example.
Therein, Paul is refuting the charge that the dead are not raised. His
thesis is that if Christ is raised, then so also are the dead in Christ
(if A, then B). He establishes this point by a proof by contradiction.
He assumes the opponents' position, that the dead are not raised (not-B).
If so, he reasons, then not even Christ is raised (v. 13; not-B implies
not-A). He could have stopped here, of course, but to drive the point
even harder he draws further consequences (14-19).
The point is that Paul recognizes that the contrapositive is essentially
equivalent to the conditional itself. But, it has never been shown that
neither he nor any other author of scripture ever violated the rules of
formal logic by assuming the negation or the converse of a conditional.
We have gone over this in the context of wondering whether there is a
legitimate difference between conversational logic and formal logic in
scripture (cf Acts 2:38, for example).
Paul Dixon
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