Quantifier (definition)

Note

The definition is a work in progress!

General Definition

Quantifiers are elements of quantity that are used to define the selection (essentially, all or some) of tokens within the set of the target object type (e.g., a noun such as 'rock').
For instance, quantifiers allow the referent of a certain type of object (e.g., table, turtle, rock) to point to all tokens of that type (e.g., "all rocks") or some tokens of that type (e.g., "some rocks").

Kinds of Quantifiers

Given some object x:
1. Universal Quantifier (interpreted as: "for all x..." "all x..." "any x...")
2. Existential Quantifier (interpreted as: "for some x..." "some x..." "there exists (at least one) x...")

Example

One can make a proposition such as "turtles are green." Now, this certainly can be true given that certain conditions are met. What are these conditions? One type of condition is that of quantity; quantifiers allow for defining this condition. For instance, "turtles are green" can be divided into symbolic representations as follows:
Given some object x:
T = "turtles"
G(x) = "x is/are green"
G(T) = "turtles are green"
Now, this does not express what we may really intend when making this proposition. What we may really be stating is "the property of being green can be attributed to all turtles" or "with respect to all turtles, it is the case that the property of being green is attributed to turtles." Quantifiers are used to express this perhaps non-overt statement using symbols:
A(T)[G(T)]