Right:

All are "all but one are ___"; all but one are black.

All are "every other is ___"; every other is solid polygons.

All are "gradually becoming ___"; gradually becoming thickly outlined.

Left:

All but one are "all but one are ___".

Every other is "every other is ___".

Gradually becoming "gradually becoming ___".

Here is another way of putting it:

Call it "meta" when the whole imitates its parts, and call it "doubly-meta" when the whole imitates its parts with respect to the way it imitates its parts. Left are doubly-meta, while right are just meta.

Here is a more belabored way of putting it:

Call something like "is star-shaped" a "rule". An object can fit a rule.

Call something like "all but one are ___" a "rule-parametrized rule". A collection of objects, with respect to a particular rule, can fit a rule-parametrized rule.

A drawing on the right shows many collections. Every collection fits the same rule-parametrized rule (with respect to various rules); furthermore the collection of collections fits that same rule-parametrized rule (with respect to some rule collections can fit).

Likewise a drawing on the left shows a collection of collections, with some noticeable recurring rule-parametrized rule. The collection of collections must fit that rule-parametrized rule with respect to the rule of fitting that rule-parametrized rule (with respect to various rule).

An unintended solution to this BP is "not all groups share some noticeable property vs. all do." It is hard to come up with examples foiling this alternative solution because (what was above called) the rule-parametrized rule usually has to do with not all objects in the collection fitting the rule. (See BP568, which is about BP ideas that are always overridden by a simpler solution.)

Some examples would fit left under a certain interpretation: EX8220 "all are 'all are ___' " and EX8222 "palindrome with respect to being a palindrome with respect to ___" (every shown collection is a palindrome with respect to some property, and all things in a list being the same is a palindrome). But those rules are not necessarily the most obvious ways of interpreting these pictures, so they have been marked as ambiguous. Either of these placed on the left would prevent the intended solution being overridden (see the previous paragraph).

Here is a list of left example ideas that would be impossible to make:

- Exhaustive list of all exhaustive lists of all ____.

Right:

All are "all but one are ___"; all but one are black.

All are "every other is ___"; every other is solid polygons.

All are "gradually becoming ___"; gradually becoming thickly outlined.

Left:

All but one are "all but one are ___".

Every other is "every other is ___".

Gradually becoming "gradually becoming ___".

Here is another way of putting it:

Call it "meta" when the whole imitates its parts, and call it "doubly-meta" when the whole imitates its parts with respect to the way it imitates its parts. Left are doubly-meta, while right are just meta.

Here is a more belabored way of putting it:

Call something like "is star-shaped" a "rule". An object can fit a rule.

Call something like "all but one are ___" a "rule-parametrized rule". A collection of objects, with respect to a particular rule, can fit a rule-parametrized rule.

A drawing on the right shows many collections. Every collection fits the same rule-parametrized rule (with respect to various rules); furthermore the collection of collections fits that same rule-parametrized rule (with respect to some rule collections can fit).

Likewise a drawing on the left shows a collection of collections, with some noticeable recurring rule-parametrized rule. The collection of collections must fit that rule-parametrized rule with respect to the rule of fitting that rule-parametrized rule (with respect to various rule).

An unintended solution to this BP is "not all groups share some noticeable property vs. all do." It is hard to come up with examples foiling this alternative solution because (what was above called) the rule-parametrized rule usually has to do with not all objects in the collection fitting the rule. (See BP568, which is about BP ideas that are always overridden by a simpler solution.)

Sorted ambiguously are examples that would fit left by wishful interpretation: EX8220 "all are 'all are ___' " and EX8222 "palindrome with respect to being a palindrome with respect to ___" (every shown collection is a palindrome with respect to some property, and all things in a list being the same is a palindrome). Either of these placed on the left would prevent the intended solution being overridden (as mentioned in the previous paragraph), but they are hard to understand.

Here is a list of left example ideas that would be impossible to make:

- Exhaustive list of all exhaustive lists of all ____.

Right:

All are "all but one are ___"; all but one are black.

All are "every other is ___"; every other is solid polygons.

All are "gradually becoming ___"; gradually becoming thickly outlined.

Left:

All but one are "all but one are ___".

Every other is "every other is ___".

Gradually becoming "gradually becoming ___".

Here is another way of putting it:

Call it "meta" when the whole imitates its parts, and call it "doubly-meta" when the whole imitates its parts with respect to the way it imitates its parts. Left are doubly-meta, while right are just meta.

Here is a more explicit way of putting it:

Call something like "is star-shaped" a "rule". An object can fit a rule.

Call something like "all but one are ___" a "rule-parametrized rule". A collection of objects, with respect to a particular rule, can fit a rule-parametrized rule.

A drawing on the right shows many collections. Every collection fits the same rule-parametrized rule (with respect to various rules); furthermore the collection of collections fits that same rule-parametrized rule (with respect to some rule collections can fit).

Likewise a drawing on the left shows a collection of collections, with some noticeable recurring rule-parametrized rule. The collection of collections must fit that rule-parametrized rule with respect to the rule of fitting that rule-parametrized rule (with respect to various rule).

An unintended solution to this BP is "not all groups share some noticeable property vs. all do." It is hard to come up with examples foiling this alternative solution because (what was above called) the rule-parametrized rule usually has to do with not all objects in the collection fitting the rule. (See BP568, which is about BP ideas that are always overridden by a simpler solution.)

Sorted ambiguously are examples that would fit left by wishful interpretation: EX8220 "all are 'all are ___' " and EX8222 "palindrome with respect to being a palindrome with respect to ___" (every shown collection is a palindrome with respect to some property, and all things in a list being the same is a palindrome). Either of these placed on the left would prevent the intended solution being overridden (as mentioned in the previous paragraph), but they are hard to understand.

Here is a list of left example ideas that would be impossible to make:

- Exhaustive list of all exhaustive lists of all ____.

Right:

All are "all but one are ___"; all but one are black.

All are "every other is ___"; every other is solid polygons.

All are "gradually becoming ___"; gradually becoming thickly outlined.

Left:

All but one are "all but one are ___".

Every other is "every other is ___".

Gradually becoming "gradually becoming ___".

Here is another way of putting it:

Call it "meta" when the whole imitates its parts, and call it "doubly-meta" when the whole imitates its parts with respect to the way it imitates its parts. Left are doubly-meta, while right are just meta.

Here is a more explicit way of putting it:

Call something like "star-shaped" a "rule". An object can fit a rule.

Call something like "all but one are ___" a "rule-parametrized rule". A collection of objects, with respect to a particular rule, can fit a rule-parametrized rule.

A drawing on the right shows many collections. Every collection fits the same rule-parametrized rule (with respect to various rules); furthermore the collection of collections fits that same rule-parametrized rule (with respect to some rule collections can fit).

Likewise a drawing on the left shows a collection of collections, with some noticeable recurring rule-parametrized rule. The collection of collections must fit that rule-parametrized rule with respect to the rule of fitting that rule-parametrized rule (with respect to various rule).

An unintended solution to this BP is "not all groups share some noticeable property vs. all do." It is hard to come up with examples foiling this alternative solution because (what was above called) the rule-parametrized rule usually has to do with not all objects in the collection fitting the rule. (See BP568, which is about BP ideas that are always overridden by a simpler solution.)

Sorted ambiguously are examples that would fit left by wishful interpretation: EX8220 "all are 'all are ___' " and EX8222 "palindrome with respect to being a palindrome with respect to ___" (every shown collection is a palindrome with respect to some property, and all things in a list being the same is a palindrome). Either of these placed on the left would prevent the intended solution being overridden (as mentioned in the previous paragraph), but they are hard to understand.

Here is a list of left example ideas that would be impossible to make:

- Exhaustive list of all exhaustive lists of all ____.

Right:

All are "all but one are ___"; all but one are black.

All are "every other is ___"; every other is solid polygons.

All are "gradually becoming ___"; gradually becoming thickly outlined.

Left:

All but one are "all but one are ___".

Every other is "every other is ___".

Gradually becoming "gradually becoming ___".

Here is another way of putting it:

Call it "meta" when the whole imitates its parts, and call it "doubly-meta" when the whole imitates its parts with respect to the way it imitates its parts. Left are doubly-meta, while right are just meta.

Here is a more explicit way of putting it:

Call something like "star-shaped" a "pattern". An object can fit a pattern.

Call something like "all but one are ___" a "pattern-parametrized pattern". A collection of objects, with respect to a particular pattern, can fit a pattern-parametrized pattern.

A drawing on the right shows many collections. Every collection fits the same pattern-parametrized pattern (with respect to various patterns); furthermore the collection of collections fits that same pattern-parametrized pattern (with respect to some pattern collections can fit).

Likewise a drawing on the left shows a collection of collections, with some noticeable recurring pattern-parametrized pattern. The collection of collections must fit that pattern-parametrized pattern with respect to the pattern of fitting that pattern-parametrized pattern (with respect to various patterns).

An unintended solution to this BP is "not all groups share some noticeable property vs. all do." It is hard to come up with examples foiling this alternative solution because (what was above called) the pattern-parametrized pattern usually has to do with not all objects in the collection fitting the pattern. (See BP568, which is about BP ideas that are always overridden by a simpler solution.)

Sorted ambiguously are examples that would fit left by wishful interpretation: EX8220 "all are 'all are ___' " and EX8222 "palindrome with respect to being a palindrome with respect to ___" (every shown collection is a palindrome with respect to some property, and all things in a list being the same is a palindrome). Either of these placed on the left would prevent the intended solution being overridden (as mentioned in the previous paragraph), but they are hard to understand.

Here is a list of left example ideas that would be impossible to make:

- Exhaustive list of all exhaustive lists of all ____.

Right:

All are "all but one are ___"; all but one are black.

All are "every other is ___"; every other is solid polygons.

All are "gradually becoming ___"; gradually becoming thickly outlined.

Left:

All but one are "all but one are ___".

Every other is "every other is ___".

Gradually becoming "gradually becoming ___".

Here is another way of putting it:

Call it "meta" when the whole imitates its parts, and call it "doubly-meta" when the whole imitates its parts with respect to the way it imitates its parts. Left are doubly-meta, while right are just meta.

Here is a more explicit way of putting it:

Call something like "star-shaped" a "pattern". An object can fit a pattern.

Call something like "all but one are ___" a "pattern-parametrized pattern". A collection of objects, with respect to a particular pattern, can fit a pattern-parametrized pattern.

A drawing on the right shows many collections. Every collection fits the same pattern-parametrized pattern (with respect to various patterns); furthermore the collection of collections fits that same pattern-parametrized pattern (with respect to some pattern that collections can fit).

Likewise a drawing on the left shows a collection of collections, with some noticeable recurring pattern-parametrized pattern. The collection of collections must fit that pattern-parametrized pattern with respect to the pattern of fitting that pattern-parametrized pattern (with respect to various patterns).

An unintended solution to this BP is "not all groups share some noticeable property vs. all do." It is hard to come up with examples foiling this alternative solution because (what was above called) the pattern-parametrized pattern usually has to do with not all objects in the collection fitting the pattern. (See BP568, which is about BP ideas that are always overridden by a simpler solution.)

Sorted ambiguously are examples that would fit left by wishful interpretation: EX8220 "all are 'all are ___' " and EX8222 "palindrome with respect to being a palindrome with respect to ___" (every shown collection is a palindrome with respect to some property, and all things in a list being the same is a palindrome). Either of these placed on the left would prevent the intended solution being overridden (as mentioned in the previous paragraph), but they are hard to understand.

Here is a list of left example ideas that would be impossible to make:

- Exhaustive list of all exhaustive lists of all ____.

Right:

All are "all but one are ___"; all but one are black.

All are "every other is ___"; every other is solid polygons.

All are "gradually becoming ___"; gradually becoming thickly outlined.

Left:

All but one are "all but one are ___".

Every other is "every other is ___".

Gradually becoming "gradually becoming ___".

Here is another way of putting it:

Call it "meta" when the whole imitates its parts, and call it "doubly-meta" when the whole imitates its parts with respect to the way it imitates its parts. Left are doubly-meta, while right are just meta.

Here is a more explicit way of putting it:

Call something like "star-shaped" a "pattern". An object can match a pattern.

Call something like "all but one are ___" a "pattern-parametrized pattern". A collection of objects, with respect to a particular pattern, can match a pattern-parametrized pattern.

A drawing on the right shows many collections. Every collection matches the same pattern-parametrized pattern (with respect to various patterns); furthermore the collection of collections matches that same pattern-parametrized pattern (with respect to some pattern that collections can match).

Likewise a drawing on the left shows a collection of collections, with some noticeable recurring pattern-parametrized pattern. The collection of collections must match that pattern-parametrized pattern with respect to the pattern of matching that pattern-parametrized pattern (with respect to various patterns).

An unintended solution to this BP is "not all groups share some noticeable property vs. all do." It is hard to come up with examples foiling this alternative solution because (what was above called) the pattern-parametrized pattern usually has to do with not all objects in the collection fitting the pattern. (See BP568, which is about BP ideas that are always overridden by a simpler solution.)

Sorted ambiguously are examples that would fit left by wishful interpretation: EX8220 "all are 'all are ___' " and EX8222 "palindrome with respect to being a palindrome with respect to ___" (every shown collection is a palindrome with respect to some property, and all things in a list being the same is a palindrome). Either of these placed on the left would prevent the intended solution being overridden (as mentioned in the previous paragraph), but they are hard to understand.

Here is a list of left example ideas that would be impossible to make:

- Exhaustive list of all exhaustive lists of all ____.

Right:

All are "all but one are ___"; all but one are black.

All are "every other is ___"; every other is solid polygons.

All are "gradually getting more like ___"; gradually getting more like black triangles.

Left:

All but one are "all but one are ___".

Every other is "every other is ___".

Gradually getting more like "gradually getting more like ___".

Here is another way of putting it:

Call it "meta" when the whole imitates its parts, and call it "doubly-meta" when the whole imitates its parts with respect to the way it imitates its parts. Left are doubly-meta, while right are just meta.

Here is a more explicit way of putting it:

Call something like "star-shaped" a "pattern". An object can match a pattern.

Call something like "all but one are ___" a "pattern-parametrized pattern". A collection of objects, with respect to a particular pattern, can match a pattern-parametrized pattern.

A drawing on the right shows many collections. Every collection matches the same pattern-parametrized pattern (with respect to various patterns); furthermore the collection of collections matches that same pattern-parametrized pattern (with respect to some pattern that collections can match).

Likewise a drawing on the left shows a collection of collections, with some noticeable recurring pattern-parametrized pattern. The collection of collections must match that pattern-parametrized pattern with respect to the pattern of matching that pattern-parametrized pattern (with respect to various patterns).

An unintended solution to this BP is "not all groups share some noticeable property vs. all do." It is hard to come up with examples foiling this alternative solution because (what was above called) the pattern-parametrized pattern usually has to do with not all objects in the collection fitting the pattern. (See BP568, which is about BP ideas that are always overridden by a simpler solution.)

Sorted ambiguously are examples that would fit left by wishful interpretation: EX8220 "all are 'all are ___' " and EX8222 "palindrome with respect to being a palindrome with respect to ___" (every shown collection is a palindrome with respect to some property, and all things in a list being the same is a palindrome). Either of these placed on the left would prevent the intended solution being overridden (as mentioned in the previous paragraph), but they are hard to understand.

Here is a list of left example ideas that would be impossible to make:

- Exhaustive list of all exhaustive lists of all ____.

Right:

All are "all but one are ___"; all but one are black.

All are "every other is ___"; every other is solid polygons.

All are "gradually getting more like ___"; gradually getting more like black triangles.

Left:

All but one are "all but one are ___".

Every other is "every other is ___".

Gradually getting more like "gradually getting more like ___".

Here is another way of putting it:

Call it "meta" when the whole imitates its parts, and call it "doubly-meta" when the whole imitates its parts with respect to the way it imitates its parts. Left are doubly-meta, while right are just meta.

Here is a more explicit way of putting it:

Call something like "star-shaped" a "pattern". An object can match a pattern.

Call something like "all but one are ___" a "pattern-parametrized pattern". A collection of objects, with respect to a particular pattern, can match a pattern-parametrized pattern.

A drawing on the right shows many collections. Every collection matches the same pattern-parametrized pattern (with respect to various patterns); furthermore the collection of collections matches that same pattern-parametrized pattern (with respect to some pattern that collections can match).

Likewise a drawing on the left shows a collection of collections, with some noticeable recurring pattern-parametrized pattern. The collection of collections must match that pattern-parametrized pattern with respect to the pattern of matching that pattern-parametrized pattern (with respect to various patterns).

An unintended solution to this BP is "not all groups share some obvious property vs. all do." It is hard to come up with examples foiling this alternative solution because (what was above called) the pattern-parametrized pattern usually has to do with not all objects in the collection fitting the pattern. (See BP568, which is about BP ideas that are always overridden by a simpler solution.)

Sorted ambiguously are examples that would fit left by wishful interpretation: EX8220 "all are 'all are ___' " and EX8222 "palindrome with respect to being a palindrome with respect to ___" (every shown collection is a palindrome with respect to some property, and all things in a list being the same is a palindrome). Either of these placed on the left would prevent the intended solution being overridden (as mentioned in the previous paragraph), but they are hard to understand.

Here is a list of left example ideas that would be impossible to make:

- Exhaustive list of all exhaustive lists of all ____.

Right:

All are "all but one are ___"; all but one are black.

All are "every other is ___"; every other is solid polygons.

All are "gradually getting more like ___"; gradually getting more like black triangles.

Left:

All but one are "all but one are ___".

Every other is "every other is ___".

Gradually getting more like "gradually getting more like ___".

Here is another way of putting it:

Call it "meta" when the whole imitates its parts, and call it "doubly-meta" when the whole imitates its parts with respect to the way it imitates its parts. Left are doubly-meta, while right are just meta.

Here is a more explicit way of putting it:

Call something like "star-shaped" a "pattern". An object can match a pattern.

Call something like "all but one are ___" a "pattern-parametrized pattern". A collection of objects, with respect to a particular pattern, can match a pattern-parametrized pattern.

A drawing on the right shows many collections. Every collection matches the same pattern-parametrized pattern (with respect to various patterns); furthermore the collection of collections matches that same pattern-parametrized pattern (with respect to some pattern that collections can match).

Likewise a drawing on the left shows a collection of collections, with some noticeable recurring pattern-parametrized pattern. The collection of collections must match that pattern-parametrized pattern with respect to the pattern of matching that pattern-parametrized pattern (with respect to various patterns).

An unintended solution to this BP is "not all groups share some obvious property vs. all do." It is hard to come up with examples foiling this alternative solution because (what was above called) the pattern-parametrized pattern usually has to do with not all objects in the collection fitting the pattern. (See BP568, which is about BP ideas that are always overridden by a simpler solution.)

Sorted ambiguously are examples that would fit left by wishful interpretation: EX8220 "all are 'all are ___' " and EX8222 "palindrome with respect to being a palindrome with respect to ___" (every shown collection is a palindrome with respect to some property, and all things in a list being the same is a palindrome). Either of these would prevents the intended solution from being overridden (as mentioned in the previous paragraph), but they are hard to understand.

Here is a list of left example ideas that would be impossible to make:

- Exhaustive list of all exhaustive lists of all ____.

"Odd one out with respect to what property is the odd one out" would not fit left in this Problem: even though this example does seem doubly-meta, it is not doubly-meta in the right way. There is no odd one out with respect to the property of having an odd one out.

Similarly, consider "gradual transition with respect to what the gradual transition is between", etc. Instead of having the form "X 'X __' ", this is more like "X [the _appearing in 'X_'] ". Examples like these two could make for a different Bongard Problem.

Right:

All are "all but one are ___"; all but one are black.

All are "every other is ___"; every other is solid polygons.

All are "gradually getting more like ___"; gradually getting more like black triangles.

Left:

All but one are "all but one are ___".

Every other is "every other is ___".

Gradually getting more like "gradually getting more like ___".

Here is another way of putting it:

Call it "meta" when the whole imitates its parts, and call it "doubly-meta" when the whole imitates its parts with respect to the way it imitates its parts. Left are doubly-meta, while right are just meta.

Here is a more explicit way of putting it:

Call something like "star-shaped" a "pattern". An object can match a pattern.

Call something like "all but one are ___" a "pattern-parametrized pattern". A collection of objects, with respect to a particular pattern, can match a pattern-parametrized pattern.

A drawing on the right shows many collections. Every collection matches the same pattern-parametrized pattern (with respect to various patterns); furthermore the collection of collections matches that same pattern-parametrized pattern (with respect to some pattern that collections can match).

Likewise a drawing on the left shows a collection of collections, with some noticeable recurring pattern-parametrized pattern. The collection of collections must match that pattern-parametrized pattern with respect to the pattern of matching that pattern-parametrized pattern (with respect to various patterns).

An unintended solution to this BP is "not all groups share some obvious property vs. all do." It is hard to come up with examples foiling this alternative solution because (what was above called) the pattern-parametrized pattern usually has to do with not all objects in the collection fitting the pattern. (See BP568, which is about BP ideas that are always overridden by a simpler solution.)

Sorted ambiguously are examples that would fit left by wishful interpretation: EX8220 "all are 'all are ___' " and EX8222 "palindrome with respect to being a palindrome with respect to ___" (every shown collection is a palindrome with respect to some property, and all things in a list being the same is a palindrome).

Here is a list of left example ideas that would be impossible to make:

- Exhaustive list of all exhaustive lists of all ____.

Right:

All are "all but one are ___"; all but one are black.

All are "every other is ___"; every other is solid polygons.

All are "gradually getting more like ___"; gradually getting more like black triangles.

Left:

All but one are "all but one are ___".

Every other is "every other is ___".

Gradually getting more like "gradually getting more like ___".

Here is another way of putting it:

Call it "meta" when the whole imitates its parts, and call it "doubly-meta" when the whole imitates its parts with respect to the way it imitates its parts. Left are doubly-meta, while right are just meta.

Here is a more explicit way of putting it:

Call something like "star-shaped" a "pattern". An object can match a pattern.

Call something like "all but one are [pattern]" a "pattern-parametrized pattern". A collection of objects, with respect to a particular pattern, can match a pattern-parametrized pattern.

A drawing on the right shows many collections. Every collection matches the same pattern-parametrized pattern (with respect to various patterns); furthermore the collection of collections matches that same pattern-parametrized pattern (with respect to some pattern that collections can match).

Likewise a drawing on the left shows a collection of collections, with some noticeable recurring pattern-parametrized pattern. The collection of collections must match that pattern-parametrized pattern with respect to the pattern of matching that pattern-parametrized pattern (with respect to various patterns).

An unintended solution to this BP is "not all groups share some obvious property vs. all do." It is hard to come up with examples foiling this alternative solution because (what was above called) the pattern-parametrized pattern usually has to do with not all objects in the collection fitting the pattern. (See BP568, which is about BP ideas that are always overridden by a simpler solution.)

Sorted ambiguously are examples that would fit left by wishful interpretation: EX8220 "all are 'all are ___' " and EX8222 "palindrome with respect to being a palindrome with respect to ___" (every shown collection is a palindrome with respect to some property, and all things in a list being the same is a palindrome).

Here is a list of left example ideas that would be impossible to make:

- Exhaustive list of all exhaustive lists of all ____.

Right:

All are "all but one are ___"; all but one are black.

All are "every other is ___"; every other is solid polygons.

All are "gradually getting more like ___"; gradually getting more like black triangles.

Left:

All but one are "all but one are ___".

Every other is "every other is ___".

Gradually getting more like "gradually getting more like ___".

Here is another way of putting it:

Call it "meta" when the whole imitates its parts, and call it "doubly-meta" when the whole imitates its parts with respect to the way it imitates its parts. Left are doubly-meta, while right are just meta.

Here is a more specific way of putting it:

Call something like "star-shaped" a "pattern". An object can match a pattern.

Call something like "all but one are [pattern]" a "pattern-parametrized pattern". A collection of objects, with respect to a particular pattern, can match a pattern-parametrized pattern.

A drawing on the right shows many collections. Every collection matches the same pattern-parametrized pattern (with respect to various patterns); furthermore the collection of collections matches that same pattern-parametrized pattern (with respect to some pattern that collections can match).

Likewise a drawing on the left shows a collection of collections, with some noticeable recurring pattern-parametrized pattern. The collection of collections must match that pattern-parametrized pattern with respect to the pattern of matching that pattern-parametrized pattern (with respect to various patterns).

An unintended solution to this BP is "not all groups share some obvious property vs. all do." It is hard to come up with examples foiling this alternative solution because (what was above called) the pattern-parametrized pattern usually has to do with not all objects in the collection fitting the pattern. (See BP568, which is about BP ideas that are always overridden by a simpler solution.)

Sorted ambiguously are examples that would fit left by wishful interpretation: EX8220 "all are 'all are ___' " and EX8222 "palindrome with respect to being a palindrome with respect to ___" (every shown collection is a palindrome with respect to some property, and all things in a list being the same is a palindrome).

Here is a list of left example ideas that would be impossible to make:

- Exhaustive list of all exhaustive lists of all ____.

Right:

All are "all but one are ___"; all but one are black.

All are "every other is ___"; every other is solid polygons.

All are "gradually getting more like ___"; is gradually getting more like black triangles.

Left:

All but one are "all but one are ___".

Every other is "every other is ___".

Gradually getting more like "gradually getting more like ___".

Here is another way of putting it:

Call it "meta" when the whole imitates its parts, and call it "doubly-meta" when the whole imitates its parts with respect to the way it imitates its parts. Left are doubly-meta, while right are just meta.

Here is a more specific way of putting it:

Call something like "star-shaped" a "pattern". An object can match a pattern.

Call something like "all but one are [pattern]" a "pattern-parametrized pattern". A collection of objects, with respect to a particular pattern, can match a pattern-parametrized pattern.

A drawing on the right shows many collections. Every collection matches the same pattern-parametrized pattern (with respect to various patterns); furthermore the collection of collections matches that same pattern-parametrized pattern (with respect to some pattern that collections can match).

Likewise a drawing on the left shows a collection of collections, with some noticeable recurring pattern-parametrized pattern. The collection of collections must match that pattern-parametrized pattern with respect to the pattern of matching that pattern-parametrized pattern (with respect to various patterns).

An unintended solution to this BP is "not all groups share some obvious property vs. all do." It is hard to come up with examples foiling this alternative solution because (what was above called) the pattern-parametrized pattern usually has to do with not all objects in the collection fitting the pattern. (See BP568, which is about BP ideas that are always overridden by a simpler solution.)

Sorted ambiguously are examples that would fit left by wishful interpretation: EX8220 "all are 'all are ___' " and EX8222 "palindrome with respect to being a palindrome with respect to ___" (every shown collection is a palindrome with respect to some property, and all things in a list being the same is a palindrome).

Here is a list of left example ideas that would be impossible to make:

- Exhaustive list of all exhaustive lists of all ____.

Right:

All are "all but one are ___"; all but one are black.

All are "every other is ___"; every other is solid polygons.

All are "gradually getting more like ___"; is gradually getting more like black triangles.

Left:

All but one are "all but one are ___".

Every other is "every other is ___".

Gradually getting more like "gradually getting more like ___".

Here is another way of putting it:

Call it "meta" when the whole imitates its parts, and call it "doubly-meta" when the whole imitates its parts with respect to the way it imitates its parts. Left are doubly-meta, while right are just meta.

Here is a more specific way of putting it:

Call something like "star-shaped" a "pattern". An object can match a pattern.

Call something like "all but one are [pattern]" a "pattern-parametrized pattern". A collection of objects, with respect to a particular pattern, can match a pattern-parametrized pattern.

A drawing on the right shows many collections. Every collection matches the same pattern-parametrized pattern (with respect to various patterns); furthermore the collection of collections matches that same pattern-parametrized pattern (with respect to some pattern that collections can match).

Likewise a drawing on the left shows a collection of collections, with some noticeable recurring pattern-parametrized pattern. The collection of collections must match that pattern-parametrized pattern with respect to the pattern of matching that pattern-parametrized pattern (with respect to various patterns).

An unintended solution to this BP is "not all groups share some obvious property vs. all do." It is hard to come up with examples foiling this alternative solution because (what was above called) the pattern-parametrized pattern usually has to do with not all objects in the collection fitting the pattern. (See BP568, which is about BP ideas that are always overridden by a simpler solution.)

Sorted ambiguously are examples that would fit left only by a stretched interpretation: EX8220 "all are 'all are ___' " and EX8222 "palindrome with respect to being a palindrome with respect to ___" (every shown collection is a palindrome with respect to some property).

Here is a list of left example ideas that would be impossible to make:

- Exhaustive list of all exhaustive lists of all ____.

Right:

All are "all but one are ___"; all but one are black.

All are "every other is ___"; every other is solid polygons.

All are "gradually getting more like ___"; is gradually getting more like black triangles.

Left:

All but one are "all but one are ___".

Every other is "every other is ___".

Gradually getting more like "gradually getting more like ___".

Here is another way of putting it:

Call when the whole imitates its parts "meta", and call when the whole imitates its parts with respect to the way it imitates its parts "doubly-meta". Left are doubly-meta, while right are just meta.

Here is a more specific way of putting it:

Call something like "star-shaped" a "pattern". An object can match a pattern.

Call something like "all but one are [pattern]" a "pattern-parametrized pattern". A collection of objects, with respect to a particular pattern, can match a pattern-parametrized pattern.

A drawing on the right shows many collections. Every collection matches the same pattern-parametrized pattern (with respect to various patterns); furthermore the collection of collections matches that same pattern-parametrized pattern (with respect to some pattern that collections can match).

Likewise a drawing on the left shows a collection of collections, with some noticeable recurring pattern-parametrized pattern. The collection of collections must match that pattern-parametrized pattern with respect to the pattern of matching that pattern-parametrized pattern (with respect to various patterns).

An unintended solution to this BP is "not all groups share some obvious property vs. all do." It is hard to come up with examples foiling this alternative solution because (what was above called) the pattern-parametrized pattern usually has to do with not all objects in the collection fitting the pattern. (See BP568, which is about BP ideas that are always overridden by a simpler solution.)

Sorted ambiguously are examples that would fit left only by a stretched interpretation: EX8220 "all are 'all are ___' " and EX8222 "palindrome with respect to being a palindrome with respect to ___" (every shown collection is a palindrome with respect to some property).

Here is a list of left example ideas that would be impossible to make:

- Exhaustive list of all exhaustive lists of all ____.