The Greens
This page introduces the Greens and how they can be used to talk about groups of objects.
Forming and using sets
Greens assert the existence of sets and can donate and receive variables on all sides. Unlike Reds and Blues, the word inside the Green is not a predicate, but the name of the variable itself.
It's a bit cumbersome to always assert that S is a set, so from now on whenever we assert the existence of something using a capital letter (like "S"), we'll just assume it is a set instead of writing out "set(S)" all the time.
When a Green receives a variable, it asserts that the variable it received is a subset of its own variable.
In other words, the region of spacetime the donated variable covers is contained within the region of spacetime of the Green's variable.
- Idiomatic translation
- There is a set of a cat and a dog.
- Literal translation
- There exists a thing x such that x is a dog, and there exists a thing y such that y is a cat, and there exists a set S such that x and y are subsets of S.
- Formal semantics
- ∃x dog(x) & ∃y cat(y) & ∃S x, y ⊆ S
When Greens donate its variable to a Blue, you can talk about something that applies to the entire set as a whole.
- Idiomatic translation
- The the cat and the dog are playing.
- Literal translation
-
There exists a thing x such that x is a dog,
and there exists a thing y such that y is a cat,
and there exists a set S such that x and y are subsets of S,
and e is an event of S playing. - Formal semantics
- ∃x dog(x) & ∃y cat(y) & ∃S x, y ⊆ S & ∃e play(e, S)
Note that in this sentence we are asserting the existence of a single event e, which both the cat and the dog are partaking in. If we want to assert that the cat and dog are both playing separately, we would need two Blues with the predicate "play" attached to the cat and dog Reds respectively.
Indexing
Since the word inside the Green is the name of the Green's variable and not a predicate, you can use a Green with the same word elsewhere in the sentence and still be talking about the same set.
This section is missing an example!
Expansion
Since Greens donate and receive its variable on every side, they can expand just like Reds without changing their meaning.