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Re: ANNOUNCE: First longer sentence in S7

From:Mark J. Reed <markjreed@...>
Date:Tuesday, April 6, 2004, 21:01
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