Right:

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

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

All are "gradually getting more like ___" and they are 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:

Let's say "meta" means the whole imitates its parts, and "doubly-meta" means 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 another way of putting it:

Let's say a "pattern" is something like "star-shaped" and a "pattern-parametrized pattern" is something like "all but one are [pattern]". An object can match a pattern. A collection of objects, with respect to a particular pattern, can match a pattern-parametrized pattern.

A drawing on the right shows a collection of collections. Each collection matches the same pattern-parametrized pattern (with respect to its own pattern); furthermore the collection of collections matches that same pattern-parametrized pattern (also with respect to some pattern, a pattern all the collections satisfy).

Likewise a drawing on the left shows a collection of collections, and there 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 any pattern).

Another solution to the BP with the above examples is "not all groups share some obvious property vs. all do." It is hard to come up with examples foiling this alternative solution because the pattern-dependent-pattern has to do with not all objects in the collection fitting a pattern.

Shown sorted ambiguously above are some examples that would fit left only by particular interpretation: EX8220 "all are 'all are ___' " and EX8222 "palindrome with respect to being a palindrome with respect to ___" (where every 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 ___"and all but one are black.

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

All are "gradually getting more like ___" and they are 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: let's say "meta" means the whole imitates its parts, and "doubly-meta" means 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 another way of putting it: let's say a "pattern" is something like "star-shaped" and a "pattern-parametrized pattern" is something like "all but one are [pattern]". An object can match a pattern. A collection of objects, with respect to a particular pattern, can match a pattern-parametrized pattern.

A drawing on the right shows a collection of collections. Each collection matches the same pattern-parametrized pattern (with respect to its own pattern); furthermore the collection of collections matches that same pattern-parametrized pattern (also with respect to some pattern, a pattern all the collections satisfy).

Likewise a drawing on the left shows a collection of collections, and there 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 any pattern).

Another solution to the BP with the above examples is "not all groups share some obvious property vs. all do." It is hard to come up with examples foiling this alternative solution because the pattern-dependent-pattern has to do with not all objects in the collection fitting a pattern.

Shown sorted ambiguously above are some examples that would fit left only by particular interpretation: EX8220 "all are 'all are ___' " and EX8222 "palindrome with respect to being a palindrome with respect to ___" (where every 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 ___"and all but one are black.

All are "every other is ___" and every other is filled-in polygons.

All are "gradually getting more like ___" and they are 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: let's say "meta" means the whole imitates its parts, and "doubly-meta" means the whole imitates its parts with respect to the way it imitates its parts. Left are doubly-meta, while right are just meta.

Each example showcases some property that depends on other properties: "X with respect to __[property]__".

Currently, an alternative solution is "not all groups share some obvious property vs. all do." It is hard to come up with examples foiling this alternative solution because the pattern groups share usually has to do with not all objects in them fitting a pattern.

Shown sorted ambiguously above are some examples that would fit left only by particular interpretation: EX8220 "all are 'all are ___' " and EX8222 "palindrome with respect to being a palindrome with respect to ___" (where every 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 ___"and all but one are black.

All are "every other is ___" and every other is filled-in polygons.

All are "gradually getting more like ___" and they are 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: let's say "meta" means the whole imitates its parts, and "doubly-meta" means the whole imitates its parts with respect to the way it imitates its parts. Left are doubly-meta, while right are just meta.

Each example showcases some property that depends on other properties: "X with respect to __[property]__".

Currently, an alternative solution is "not all groups share some obvious property vs. all do." It is hard to come up with examples foiling this alternative solution because the pattern groups share usually has to do with not all objects in them fitting a pattern.

Shown sorted ambiguously above are some examples that would fit left only by particular interpretation: EX8220 "all are 'all are ___' " and EX8222 "palindrome with respect to being a palindrome with respect to ___" (where every 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 ___"and all but one are black.

All are "every other is ___" and every other is filled-in polygons.

All are "gradually getting more like ___" and they are 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: let's say "meta" means the whole imitates its parts, and "doubly-meta" means the whole imitates its parts with respect to the way it imitates its parts. Left are doubly-meta, while right are just meta.

Each example showcases some property that depends on other properties: "X with respect to __[property]__".

Currently, in none of the uploaded left examples do all the groups shown follow the same pattern, so an alternative solution is "not all groups share some obvious property vs. all do." The relevant group-property usually has to do with not all objects in it satisfying a certain property.

Shown sorted ambiguously above are some examples that would fit left interpreted as follows: EX8220 "all are 'all are ___' " and EX8222 "palindrome with respect to being a palindrome with respect to ___", where every example is a palindrome with respect to some property. These are hard to parse.

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 ___'"and all but one are black.

All are "every other is ___" and every other is filled-in polygons.

All are "gradually getting more like ___" and they are 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: let's say "meta" means the whole imitates its parts, and "doubly-meta" means the whole imitates its parts with respect to the way it imitates its parts. Left are doubly-meta, while right are just meta.

Each example showcases some property that depends on other properties: "X with respect to __[property]__".

Currently, in none of the uploaded left examples do all the groups shown follow the same pattern, so an alternative solution is "not all groups share some obvious property vs. all do." The relevant group-property usually has to do with not all objects in it satisfying a certain property.

Shown sorted ambiguously above are some examples that would fit left interpreted as follows: EX8220 "all are 'all are ___' " and EX8222 "palindrome with respect to being a palindrome with respect to ___", where every example is a palindrome with respect to some property. These are hard to parse.

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

"Exhaustive list of all exhaustive lists of all ____."

X "X Y" vs. all are "X Y" and X Z.

X "X Y" vs. all are "X Y" and X Z. (See description.)

Right:

All are "all but one are ___'"and all but one are black.

All are "every other is ___" and every other is filled-in polygons.

All are "gradually getting more like ___" and they are 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: let's say "meta" means the whole imitates its parts, and "doubly-meta" means the whole imitates its parts with respect to the way it imitates its parts. Left are doubly-meta, while right are just meta.

Each example showcases some property that depends on other properties: "X with respect to __[property]__".

Currently, in none of the uploaded left examples do all the groups shown follow the same pattern, so an alternative solution is "not all groups share some obvious property vs. all do." The relevant group-property usually has to do with not all objects in it satisfying a certain property.

Shown sorted ambiguously above are some examples that would fit left interpreted as follows: EX8220 "all are 'all are ___' " and EX8222 "palindrome with respect to being a palindrome with respect to ___", where every example is a palindrome with respect to some property. These are hard to parse.

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 ___'"and all but one are black.

All are "every other is ___" and every other is filled-in polygons.

All are "gradually getting more like ___" and they are 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 ___".

Another way of putting it: let's say "meta" means the whole imitates its parts, and "doubly-meta" means the whole imitates its parts with respect to the way it imitates its parts. Left are doubly-meta, while right are just meta.

Each example showcases some property that depends on other properties: "X with respect to __[property]__".

Currently, in none of the uploaded left examples do all the groups shown follow the same pattern, so an alternative solution is "not all groups share some obvious property vs. all do." The relevant group-property usually has to do with not all objects in it satisfying a certain property.

Shown sorted ambiguously above are some examples that would fit left interpreted as follows: EX8220 "all are 'all are ___' " and EX8222 "palindrome with respect to being a palindrome with respect to ___", where every example is a palindrome with respect to some property. These are hard to parse.

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 ___'"and all but one of these groups are black.

All are "every other is ___" and every other is filled-in polygons.

All are "gradually getting more like ___" and they are 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 ___".

Another way of putting it: let's say "meta" means the whole imitates its parts, and "doubly-meta" means the whole imitates its parts with respect to the way it imitates its parts. Left are doubly-meta, while right are just meta.

Each example showcases some property that depends on other properties: "X with respect to __[property]__".

Currently, in none of the uploaded left examples do all the groups shown follow the same pattern, so an alternative solution is "not all groups share some obvious property vs. all do." The relevant group-property usually has to do with not all objects in it satisfying a certain property.

Shown sorted ambiguously above are some examples that would fit left interpreted as follows: EX8220 "all are 'all are ___' " and EX8222 "palindrome with respect to being a palindrome with respect to ___", where every example is a palindrome with respect to some property. These are hard to parse.

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

"Exhaustive list of all exhaustive lists of all ____."

Left example: Out of the groups shown, all but one are "all but one are ___".

Right example: All are "all but one are ___" and all but one of these groups are black.

More examples fitting left: "every other is 'every other is ___' " and "gradually getting more like 'gradually getting more like ___' ".

Another way of putting it: let's say "meta" means the whole imitates its parts, and "doubly-meta" means the whole imitates its parts with respect to the way it imitates its parts. Left are doubly-meta, while right are just meta.

Each example showcases some property that depends on other properties: "X with respect to __[property]__".

Currently, in none of the uploaded left examples do all the groups shown follow the same pattern, so an alternative solution is "not all groups share some obvious property vs. all do." The relevant group-property usually has to do with not all objects in it satisfying a certain property.

Shown sorted ambiguously above are some examples that would fit left interpreted as follows: EX8220 "all are 'all are ___' " and EX8222 "palindrome with respect to being a palindrome with respect to ___", where every example is a palindrome with respect to some property. These are hard to parse.

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 quite fit left in this Problem, although it does seem doubly-meta in some sense. Still, there is no odd one out with respect to the property of having an odd one out. Instead of having the form "X 'X __' ", this is more like "X [the _appearing in 'X_'] ". Similarly, consider "gradual transition with respect to what the gradual transition is between", etc. These examples could make for a different Bongard Problem.

Left example: Out of the groups shown, all but one are "all but one are ___".

Right example: All are "all but one are ___" and all but one of these groups are black.

More examples fitting left: "every other is 'every other is ___' " and "gradually getting more like 'gradually getting more like ___' ".

Another way of putting it: let's say "meta" means the whole imitates its parts, and "doubly-meta" means the whole imitates its parts with respect to the way it imitates its parts. Left are doubly-meta, while right are just meta.

Each example showcases some property that depends on other properties: "X with respect to __[property]__".

Currently, in none of the uploaded left examples do all the groups shown follow the same pattern, so an alternative solution is "not all groups share some obvious property vs. all do." The relevant group-property usually has to do with not all objects in it satisfying a certain property.

Shown sorted ambiguously above are some examples that would fit left interpreted as follows: EX8220 "all are 'all are ___' " and EX8222 "palindrome with respect to being a palindrome with respect to ___", where every example is a palindrome with respect to some property. These are hard to parse.

EX8231, "palindromic with respect to the property the group is palindromic in" does not quite fit left in this Problem, although it does seem doubly-meta in some sense. Still, it is not palindromic with respect to the property of being palindromic. Instead of having the form "X 'X Y' ", this is more like "X [the Y appearing in 'X Y'] ". Similarly, consider "gradual transition with respect to what the gradual transition is between", "odd one out with respect to what property is the odd one out", etc. This idea could make for another Bongard Problem.

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

"Exhaustive list of all exhaustive lists of all ____."

Left example: Out of the groups shown, all but one are "all but one are ___".

Right example: All are "all but one are ___" and all but one of these groups are black.

Let's say "meta" means the whole imitates its parts, and "doubly-meta" means the whole imitates its parts with respect to the way it imitates its parts. Left are doubly-meta, while right are just meta.

Each example showcases some property that depends on other properties: "X with respect to __[property]__".

Currently, in none of the uploaded left examples do all the groups shown follow the same pattern, so a valid alternative solution is "not all groups share some obvious property vs. all do." This is because the relevant group-property usually has to do with not all objects in it satisfying a certain property, and thus not all groups can satisfy that group-property. Some group-properties would allow the whole group to be the same, but these tend to be hard to parse. Indeed, shown sorted ambiguously above are some examples that would fit left interpreted as follows: EX8220 "all are 'all are ___' " and EX8222 "palindrome with respect to being a palindrome with respect to ___", where every example is a palindrome with respect to some property. It may confuse the message to include any examples like these on the left side.

Clarification: EX8231, "palindromic with respect to the property the group is palindromic in" does not quite fit left in this Problem, although it does seem doubly-meta in some sense. Still, it is not palindromic with respect to the property of being palindromic. Instead of having the form "X 'X __' ", this is more like "X [the __appearing in 'X__'] ". Analogously, consider "gradual transition with respect to what the gradual transition is", "odd one out with respect to what property is the odd one out", etc. This idea could make for another Bongard Problem.

Below is a list of left example ideas that would be impossible to make. Please add and sign any more ideas you have.

"Exhaustive list of all exhaustive lists of all ____". - Aaron David Fairbanks, Nov 23 2020

More examples fitting left: "every other is 'every other is ___' " and "gradually getting more like 'gradually getting more like ___' ".

Left example: Out of the groups shown, all but one are "all but one are ___".

Right example: All are "all but one are ___" and all but one of these groups are black.

Let's say "meta" means the whole imitates its parts, and "doubly-meta" means the whole imitates its parts with respect to the way it imitates its parts. Left are doubly-meta, while right are just meta.

More left examples: "every other is 'every other is ___' " and "gradually getting more like 'gradually getting more like ___' ".

Each example showcases some property that depends on other properties: "X with respect to __[property]__".

Currently, in none of the uploaded left examples do all the groups shown follow the same pattern, so a valid alternative solution is "not all groups share some obvious property vs. all do." This is because the relevant group-property usually has to do with not all objects in it satisfying a certain property, and thus not all groups can satisfy that group-property. Some group-properties would allow the whole group to be the same, but these tend to be hard to parse. Indeed, shown sorted ambiguously above are some examples that would fit left interpreted as follows: EX8220 "all are 'all are ___' " and EX8222 "palindrome with respect to being a palindrome with respect to ___", where every example is a palindrome with respect to some property. It may confuse the message to include any examples like these on the left side.

Clarification: EX8231, "palindromic with respect to the property the group is palindromic in" does not quite fit left in this Problem, although it does seem doubly-meta in some sense. Still, it is not palindromic with respect to the property of being palindromic. Instead of having the form "X 'X __' ", this is more like "X [the __appearing in 'X__'] ". Analogously, consider "gradual transition with respect to what the gradual transition is", "odd one out with respect to what property is the odd one out", etc. This idea could make for another Bongard Problem.

Below is a list of left example ideas that would be impossible to make. Please add and sign any more ideas you have.

"Exhaustive list of all exhaustive lists of all ____". - Aaron David Fairbanks, Nov 23 2020

Let's say "meta" means the whole imitates its parts, and "doubly-meta" means the whole imitates its parts with respect to the way it imitates its parts. Left are doubly-meta, while right are just meta.

In one left example, out of the groups shown, all but one are "all but one are ___". In the corresponding right example, all are "all but one are ___" and all but one of these groups are black.

More left examples: "every other is 'every other is ___' " and "gradually getting more like 'gradually getting more like ___' ".

Each example showcases some property that depends on other properties: "X with respect to __[property]__".

Currently, in none of the uploaded left examples do all the groups shown follow the same pattern, so a valid alternative solution is "not all groups share some obvious property vs. all do." This is because the relevant group-property usually has to do with not all objects in it satisfying a certain property, and thus not all groups can satisfy that group-property. Some group-properties would allow the whole group to be the same, but these tend to be hard to parse. Indeed, shown sorted ambiguously above are some examples that would fit left interpreted as follows: EX8220 "all are 'all are ___' " and EX8222 "palindrome with respect to being a palindrome with respect to ___", where every example is a palindrome with respect to some property. It may confuse the message to include any examples like these on the left side.

Clarification: EX8231, "palindromic with respect to the property the group is palindromic in" does not quite fit left in this Problem, although it does seem doubly-meta in some sense. Still, it is not palindromic with respect to the property of being palindromic. Instead of having the form "X 'X __' ", this is more like "X [the __appearing in 'X__'] ". Analogously, consider "gradual transition with respect to what the gradual transition is", "odd one out with respect to what property is the odd one out", etc. This idea could make for another Bongard Problem.

Below is a list of left example ideas that would be impossible to make. Please add and sign any more ideas you have.

"Exhaustive list of all exhaustive lists of all ____". - Aaron David Fairbanks, Nov 23 2020

X "X Y" vs. all are "X Y" and X Z.

Let's say "meta" means the whole imitates its parts; "doubly-meta" means the whole imitates its parts with respect to the way it imitates its parts. Left are doubly-meta, while right are just meta.

In one left example, out of the groups shown, all but one are "all but one are ___". In the corresponding right example, all are "all but one are ___" and all but one of these groups are black.

More left examples: "every other is 'every other is ___' " and "gradually getting more like 'gradually getting more like ___' ".

Each example showcases some property that depends on other properties: "X with respect to __[property]__".

Currently, in none of the uploaded left examples do all the groups shown follow the same pattern, so a valid alternative solution is "not all groups share some obvious property vs. all do." This is because the relevant group-property usually has to do with not all objects in it satisfying a certain property, and thus not all groups can satisfy that group-property. Some group-properties would allow the whole group to be the same, but these tend to be hard to parse. Indeed, shown sorted ambiguously above are some examples that would fit left interpreted as follows: EX8220 "all are 'all are ___' " and EX8222 "palindrome with respect to being a palindrome with respect to ___", where every example is a palindrome with respect to some property. It may confuse the message to include any examples like these on the left side.

Clarification: EX8231, "palindromic with respect to the property the group is palindromic in" does not quite fit left in this Problem, although it does seem doubly-meta in some sense. Still, it is not palindromic with respect to the property of being palindromic. Instead of having the form "X 'X __' ", this is more like "X [the __appearing in 'X__'] ". Analogously, consider "gradual transition with respect to what the gradual transition is", "odd one out with respect to what property is the odd one out", etc. This idea could make for another Bongard Problem.

Below is a list of left example ideas that would be impossible to make. Please add and sign any more ideas you have.

"Exhaustive list of all exhaustive lists of all ____". - Aaron David Fairbanks, Nov 23 2020