Why we confuse
types and instances
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Contents
Ambiguity
in natural language propositions
The
word “a” and the phrase “is a”
Different
domain-specific vocabularies
A
description can be a type and an instance
Propositional statements are rich in examples of sets, types and instances.
Forgive me for using examples that play with the language used to make the propositions.
· The ten words in this sentence instantiate the type "word".
· The words "word", "sentence" and "type" instantiate the word type "noun".
· Word types (article, noun, pronoun, adjective, verb, adverb, conjunction, preposition, and interjection) are instances in the set of word types.
· Those word types are also subtypes of “part of speech” - a class to which a word is assigned in accordance with its syntactic functions.
Natural language is not formal logic; it is just what evolved to help humans survive.
People do not formulate propositions carefully, and almost everybody struggles with logical analysis.
For evidence that people find formal logic extremely difficult to cope with, find Wason, 1968.
The ambiguity of natural language undermines ontological exactitude (if indeed such an ideal could ever be reached).
And confusion between types and instances is widespread.
|
Proposition |
Alternative type and instance
readings |
|
The trees in my garden drop their leaves |
All types of tree in my garden drop their leaves? All the individual trees in my garden drop their leaves? |
|
John and Mary drive the same car |
John and Mary drive the same particular car? John and Mary drive the same type of car? |
|
The bicycle needs attention |
A particular bicycle needs attention – perhaps repair? The bicycle, as a type, needs attention - perhaps redesign? |
|
Red, white and blue are kinds of colour |
Red, white and blue are types of colour? Red, white and blue are instances in the set of colours? |
|
I have finished the process |
I have finished drawing a flowchart to define the process type? I have finished performing an instance of a process? |
|
Every employee has a telephone |
The employee type has an attribute type called telephone? Every employee instance has been given a telephone? |
|
Events affect the entity |
Event types affect the entity (type or instance) Event instances effect the entity instance (One implies the other. It might not matter which meaning is taken.) |
The indefinite article (“a”) is important; it changes the meaning of sentences.
The placement of the word “type” in a sentence can also change its meaning.
Mistakes are easily made, and the grammar of a sentence may not make it meaning clear.
|
Proposition about a type |
Proposition about an
individual thing |
|
Bicycle is a type of vehicle. |
A bicycle is an instance of “vehicle”. |
|
Shirt is an instance of product type |
My shirt is an instance of the product type “shirt”. |
|
Colour is a type of sensory perception. |
A colour (such as yellow) is an instance of the type called “colour”. |
The difficult of writing such examples makes me doubt my ability to write without error or ambiguity.
Many definition examples above take the form: “a thing is a thing”.
The “is a” phrase is ambiguous – sometimes “is a kind of”, sometimes “is an instance of”.
The term class is often used to mean a set or collection of members, where each member conforms to one or more types.
Does class = type = set? It depends on the domain you work in.
Maths
This paper was mostly written without reference to set theory.
In mathematics, sets/classes/collections are pretty much the same thing (there are some subtle differences but they aren’t relevant here).
In this context, a set is static, contains a fixed collection of members.
Social sciences
In modelling social and business systems, the focus is on dynamic sets rather than static sets.
Humanity, as a class, is a collection of people, where each person conforms to the type mammal, and to the type animal with a bloodstream.
A dynamic set is the ever-changing collection of objects that currently manifest the features of a type.
OO programming
Object-oriented software vocabulary is especially confusing. For example in Java:
· primitive types are called "types"
· complex (concrete) types are called "classes"
· abstract classes are called "types"
· and, if that wasn’t bad enough, there are "class types".
Java draws a distinction between a primitive type and a class type (on the web).
Note this telling comment from the web on OO programming.
"You might be confused by all the different terminology used.”
Philosophy
Encyclopaedia Britannica says:
“When philosophers want to talk about words (or sentences or books) that are located in specific places for specific periods of time, they use the term tokens of the word (or sentence or book); can appear in different places and times, they use the term types of word (or sentence or book).
In the terminology introduced above, one can say that word tokens are concrete and word types are abstract.”
Poetry
The famous sentence "Rose is a rose is a rose is a rose." was written by Gertrude Stein as part of the 1913 poem Sacred Emily.
Later, Stein said
she meant that using the name of a thing (a rose) invokes the
idea of it.
Rose
is a word token (there are 10 word tokens in the sentence) and a word type
(there are 3 word types in the sentence) and a rose has the features of the
universal rose type.
The type of a rose
is an idea, or combination of ideas, that is describable by spelling out one or
more features shared by all roses.
Set and type may have the same name
A set is a collection; a type is a description; but we may use the same word to label both.
“Genus” is a noun with three meanings: 1) birth or origin 2) a kind or type 3) a set or group of individuals with common attributes.
All subtypes are instances in a set of
subtypes
Subtypes are members of a set – the set that is the subtypes of a type.
Unicycle and bicycle are subtypes of “cycle”; and also instances of cycle type.
Red, white and blue are subtypes of “colour”, and also instances in the set of colours.
Someone recently wrote to me saying that an instance inherits the features of its type. Well, it does in a loose conversational way.
But “inheritance” is used by OO programmers to mean extending a type’s features to form a subtype, not to mean instantiating a type with values.
As soon as you abstract a description from a physical reality, the description becomes a physical reality.
It may be recorded on paper, or recorded in the mysterious bio-electro-chemistry of a brain.
And once recorded, it can be described as an instance of a paper record, or brain memory.
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