Talk:Zendo

I have edited two things:

1) Buddha-nature is hyphenated and capitalized, per the original rules at wunderland.com. (See Buddha-nature for additional Discussion and a link to those rules.)

2) The Master in Ikkozendo may adjust one or both of the two koans, if needed to disprove a guess. This often occurs when the secret rule is color-based.

David Artman (creator of Ikkozendo)

Clear Zendo Rules

One of the example rules is "if no medium pyramids point at yellow pyramids". I'd like to mention here, for those who check this Talk page, that this rule is not the finest example of a clear rule. Note that the word "pyramids" occurs twice. Perhaps it is useful to realize that each rule can be viewed as a preposition of first-order logic. In fact, that preposition needs to have all variables bound. This means that we need to introduce a quantifier (FOR ALL for the universal quantifier, or THERE IS for the existential quantifier) for each variable used in the rule. To show you what I mean, look at this attempt for an equivalent formulation:

- "FOR ALL pyramids (x) IF size (x) = Medium, THEN x doesn't point at Yellows (y)." It can also be shortened to

- "FOR ALL Medium pyramids (x), they (x) do not point at Yellows (y)."

We notice that in both cases, the reference to Yellow pyramids is not bound. It leaves the question unanswered why the original rule has a plural (Yellow pyramids). Because of this, that there are some possible interpretations of this rule that diverge from its intended meaning. The point is that we can not know what the intended meaning is! We can not ask the Master about his rule, until after the game is played, so it is important that the Master is aware of possible ambiguities; he can not easily correct that after the game has started.

To solve this conundrum, we need to introduce a quantifier for the Yellows. Then you immediately see that you have some choices to make: where is the quantifier (at the beginning or in the middle of the preposition), and which quantifier should we use (universal or existential). There are at least the following 4 alternative variants to consider:

• Variant 1. "FOR ALL Medium pyramids (x), FOR ALL Yellow pyramids (y), they (x) do not point to y."

This means that none of the Mediums point at any Yellow. If this is the intended meaning, then the original wording is confusing.

• Variant 2. "THERE IS a Yellow pyramid (y), such that FOR ALL Medium pyramids (x), they (x) do not point at y."

This means that "none of the Medium pyramids point to a (specific) Yellow"; namely they don't point to the specific Yellow they don't point to . . . Even though some koans that follow this rule may have Mediums that point to some Yellows, they all avoid at least one (specific) Yellow. Again, if this is the intended meaning, then the original formulation is confusing.

• Variant 3. "FOR ALL Medium pyramids (x), THERE IS a Yellow pyramid (y), such that x does not point at y."

This plainly means that even though Mediums can point at Yellows, they never point to all Yellows.

• Variant 4. "FOR ALL Yellow pyramids, FOR ALL Medium pyramids (x), x does not point at y."

Lucky for us, this formulation is equivalent to Variant 1. (Something to remember about universal quantifiers).

Perhaps the English grammar is clear enough to decide if we are talking about Variant 1, 2 or 3, but this example shows that it is sometimes not a trivial matter to decide between them. When you keep this in mind, you can train yourself to formulate your rules with quantifiers for each of the occurrences of "pyramid" therein. Hope this helps. Cuc (talk) 21:15, 28 November 2019 (PST)