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On Tue, Apr 06, 2004 at 09:14:05PM +0100, Chris Bates wrote:
> >Actually, if you read Descartes (in the original Latin) you'll
> >discover that the sentence he wrote doesn't contain a "therefore", nor
> >any other connector for that matter. It is "I think, I am", *not* "I
> >think, therefore I am" (a common mistranslation that was already
> >common in his time, and that he fought against all his life). The
> >sentence is *not* a law of logic. It is *not* an implication, it is
> >*not* a cause-and-effect description. The sentence is a declaration of
> >*EQUALITY*: I think = I am.


But an implication *also* says absolutely nothing about cause and
effect!  "A implies B" means only that if A is true, then B is true.
It is not as strong a statement as your equality, since "A implies B"
does not mean that "B implies A"; it is perfectly possible for B to be
true and A be false.  It's just not possible for A to be true and B to be
false.  But by the same token, I don't think Descarte's "ego, sum" is a
bidirectional equality either.  After all, it is possible to exist without
thinking; but it is patently impossible to think without existing.

One particularly effective way to bring this point home is to note that
if A is always false, then "A implies B" is true, for any B whatsoever!
For instance, "if the Earth is flat, then I am its king." is a perfectly
valid statement of predicate logic, because the Earth is not flat.  You
do not have to suppose some complicated Rube-Goldbergian sequence of world
events such that if the Earth were flattened I would wind up crowned its
ruler; none of that has any effect on the statement.  It's just that, to
put it in predicate logic terms, "For all B, (not A) implies (A implies B)."

-Mark