From: Paul Dixon - Ladd Hill Bible Church (firstname.lastname@example.org)
Date: Tue Jun 03 1997 - 21:21:28 EDT
On Tue, 3 Jun 1997 JohnBARACH@aol.com wrote:
> On Jun 3, 3:06pm, Paul Dixon - Ladd Hill Bible Church wrote:
> > I question your differentiation, however, between "not all A is B" and
> > "all A are not B". Concerning the latter, you conclude that no A is B.
> > In doing so, you are equating "All A are not B" to the conditional
> > thought, "A implies not B." The problem, however, is that this does not
> > follow. "All A are not B" can be interpreted to mean that some A are not
> > B. The key may be the meaning of PAS hO (or, PANTES hOI). It is every
> > member of the class individually that is being considered, rather than the
> > class as a whole. Thus, "not every one who is from Israel is a true
> > Israelite" = "every one who is from Israel is not a true Israelite." The
> > former, to be sure, is better, but I fail to see a necessary difference.
> Um ... I realize this is not a logic mailing list, but ...
> There is a world of difference between "All A is not B" and "Not all A is B."
> "All A is not B" can be converted into a conditional statement (as is
> commonly done in logic exercises): "If A then not B." If "All cats are not
> dogs" then "If Fluffy is a cat, then Fluffy is not a dog." On the other
> hand, "Not all A is B" leaves room for *some* A to be B. There is no
> possible way to conclude from "All A is B" that some A might not be B.
John, thanks for your response. The problem is "All A is not B" is
ambiguous. It could be interpreted as:
1. the entire set A is outside of set B (hence, A>~B), or
2. it is not true that the entire set A is a subset of B (hence,
If we assume the second interpretation, then "All A is not B" = "Not all A
is B." This is certainly what Paul had in mind. It is not true, as some
apparently erroneously assumed, that all Israel were elect. Of course, to
say "not all Israel are elect" is saying the same thing.
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