5.1 Informal definition

Definition

Informally speaking, a type is a label (or, more simply, name) which we give to a group of entities with similar traits.

The entities with similar traits can be, e.g.:

  • Individuals (as in the types "Person", "Cat", "Bus", etc.),
  • Properties (as in the types "Beautiful", "Intelligent", "Mortal", "Blue", "Red", etc.),
  • Actions (as in the types "Kiss", "Blink", "Go", "Live", etc.)
  • Abstract entities (as in the types "NaturalNumber", "DecimalNumber", "Set", etc.).

Thus, when we say "groups of entities with similar traits", we are not only referring to groups of individuals (e.g., "Peter", "Paul", "Mary"), but precisely to groups of entities. An "entity" can be anything at all, even properties and abstract entities.

Types only exist in the abstract

Types always only exist in the abstract. For example, "John" is not a type but a name for a particular individual. (Which individual we are referring to by this name is dependent on context). But types always only exist in the abstract. Since a type is a name given to a group of entities, it can only exist in the abstract.

However, the converse does not hold, that everything that is abstract is a type. For example, "2" is an abstract entity: You cannot point to a concrete thing and say "This is the thing called '2'". But even though "2" is abstract, it is not a type. Rather, it is an instance of the type "NaturalNumber".

Example and counterexample of a type

Let us give some more examples. For example, "Animal" is a type. The group of entities which are given the label "Animal" includes inviduals such as the neighbor's dog and the bird in the tree outside the window.

However, "Fido" is not a type, but a name we give to an instance of the type "Dog".


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