>
> 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!")
Which is why Kory made the (IMO) excellent choice to disallow the null koan.
Timothy