On Thu, Mar 12, 2009 at 10:01:33AM -0500, tophu@xxxxxxx wrote:
> "Marc Hartstein" wrote:
> >Here, it is the case that *every* pyramid
> >in the null koan is grounded;
> >if it were false, there would have to be a
> >pyramid which is ungrounded.
>
> Ah, but *every* pyramid in the null koan is ungrounded. ;)
True, but the negation of "For every X, Y" is "For some X, NOT Y"
That is, the logical negation of "Every pyramid is grounded" is "There
is a pyramid which is ungrounded", not "Every pyramid is ungrounded"
Note that the proper negation is false for the null koan; this is one
proof of the vacuous truth of "All pyramids are grounded" for the null
koan.
"aKhtBN iff it contains only grounded pyramids", in FOL, would
conventionally be:
"For Every pyramid in the koan, that pyramid is grounded."
The null koan satisfies this.
Some people, stating the rule, mean:
"The koan contains at least one pyramid AND for Every pyramid in the
koan, that pyramid is grounded."
The null koan fails to satisfy this rule.
The problem is that the English language is frequently ambiguous when
translated to logic. The good thing is that Zendo doesn't care...the
Rule is what matters, not the English-language translation of it; even
if the players all think in English, the "counterexample" rule means
that the game is actually about the intended Boolean logic proposition.
The issue, of course, is that a "simple" statement to someone used to
the assumptions of logic may be hideously complex to somebody who isn't
("What do you mean the rule is 'Either there are no blue pyramids or all
blue pyramids must be flat'? That's too hard!"), and vice versa ("Your
rule was 'There must be at least one blue pyramid AND all blue pyramids
must be flat'? I thought you said it didn't require a compound
statement!")
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