# Definition

A definition is a statement that explains the meaning of a term.

For example, the statement "A triangle is a polygon that has three sides" or a grammar.

Some terms, called `primitive notions`_ cannot be defined.

Semantically, a definition might be viewed as recognition procedure. For example, "An x is a square iff x has four equal sides", which defines a set. => A definition is a representation of a set?

# 1   Function

A definition binds a symbol to an expression.

Definitions are the foundation of reason.

If you can't define it, what you think it exists?

Studying things that cannot be defined: Ask what would happen if they were not present. (e.g, Camus's absurd without Death)

# 2   Matter

A definition consists of three parts:

1. A definiedum, a term to be defined
2. A copula
3. A definiens, an expression that gives the meaning of a term.

For example, in "A triangle is a polygon that has three sides", the definiedum is "a triangle", the definiens is "a polygon that has three sides", and the copula is "is".

Note: A concept may have multiple definiedum (aliases). Note: A definiedum may have multiple definiens.

Typically, an item is defined in terms of its form rather than its function, which leads artists to explore the idea of dysfunctional objects. For example a teapot, whose spout is above the handle. This is what the debate about form following function loosely refers to.

# 3   Properties

A definition is circular if it is recursive, but with no base case.

# 4   Classification

Definitions can be divided into: intensional & extensional definitions, stipulative definitions, and lexical definitions.

## 4.1   Intensional Definition

An intensional definition is a definition that gives the meaning of a term by specifying its intension.

Example:
An intensional definition of a game, such as chess, would be the rules of the game. Necessary: Any game properly called a game of chess must have been played by those rules. Sufficient: Every game played by the rules of chess must be a game of chess.
Example:
An intensional definition of bachelor is 'unmarried man'. Necessary: Any bachelor must be an unmarried man. Sufficient: Every unmarried man is a bachelor.

### 4.1.1   Genus-differentia definition

A genus-differentia definition is an intensional definition that defines its subject by first stating the broad category it belongs to and then distinguished by specific properties.

Example: "A triangle is a plane figure that has three straight bounding sides."

A genus-differentia definition has two parts:

1. A genus
2. A differentia

The genus is an existing definition that serves as a portion of the new definition; all definitions with the same genus are considered members of that genus.

The differentia is the portion of the new definition that is not provided by the genera.

Example: In "A triangle is a plane figure that has three straight bounding sides.", the genus is "plane figure" and the differential is "has three straight bounding sides".

Genus-differentia definitions are used to avoid repeatedly specifying properties.

Note: Genus-differentia definitions are used in Linnaean taxonomy to categorize living things.

> A 'genus' is what is predicated in the category of essence of a number of things exhibiting differences in kind.

In other words, a superclass.

### 4.1.2   Recursive Definition (Inductive definition)

A recursive definition is an intensional definition that defines a term in terms of itself.

Example: "A number, n, is a natural number, iff n is 0 or pred(n) is a natural number." Example: "A number, n, is an even number iff n is 0 or n // 2 is an even number."

### 4.1.3   Purpose

An intensional definition gives a way to generate all members of a set and only these (necessary and sufficient conditions).

Intensional definitions are necessary for defining infinite collections_, since enumerating them is impossible.

## 4.2   Extensional Definition

An extensional definition is a definition that formulates its meaning by specifying its extension.

Example: The nations of the world are Afghanistan, Albania, Algeria, ..., Zimbabwe. Example: The elements are Hydrogen, Helium, ...

### 4.2.1   Enumerative Definition

An enumerative definition is an extensional definition that gives an explicit and exhaustive listing of all the objects that fall under the concept or term in question.

Example: A suit in a deck of playing cards is either a club, a diamond, a heart, or a spade. Example: A boolean type is either true or false

### 4.2.2   Ostensive Definition

An ostensive definition ("definition by pointing") is an extensional definition that conveys the meaning of a term by pointing out some examples and counterexamples.

To function, an ostensive definition needs to choose objects in such a way that the intersection of essences (the only properties they have in common) is the essence of the term.

For example, an ostensive definition of "red" might be "Apples, stop signs, and roses are red."

An ostensive definition is useful when a term is difficult to define verbally, either because the words will not be understood (as with children and new speakers of a language) or because of the nature of the term (such as colors or sensations).

## 4.3   Other

### 4.3.1   Stipulative Definition

A stipulative definition is a type of definition in which a new or currently-existing term is given a specific meaning for the purposes of argument or discussion in a given context.

### 4.3.2   Theoretical definitions

A theoretical (or conceptual) definition gives the meaning of a word in terms of the theories of a specific discipline.

### 4.3.3   Persuasive Definition

A persuasive definition is a form of definition which purports to describe the 'true' or 'commonly accepted' meaning of a term, while in reality stipulating an uncommon or altered use, usually to support an argument for some view, or to create or alter rights, duties or crimes.

The terms thus defined will often involve emotionally charged but imprecise notions, such as "freedom", "terrorism", "democracy", etc. In argumentation the use of a stipulative definition is an example of the definist fallacy

The term "persuasive definition" was introduced by philosopher C.L. Stevenson as part of his emotive theory of meaning

This "loaded language" is often used in rhetoric.

Euphemism is an attempt to avoid undesirable connotations.

### 4.3.4   Lexical Definition

The canonical definition.

### 4.3.5   Precising Definition

A precising definition is a definition that extends the lexical definition of a term for a specific purpose by including additional criteria that narrow down the set of things meeting the definition.

Precising definitions are generally used in contexts where vagueness is unacceptable; many legal definitions are precising definitions, as are company policies. This type of definition is useful in preventing disputes that arise from the involved parties using different definitions of the term in question.

This is similar to a stipulative definition, but differs in that a stipulative definition may contradict the lexical definition, while a precising definition does not.

# 5   Production

Definitions can be produced by gathering examples of things that we recognize as belonging to it, and then that we recognize as not, and then contrasting them to find which features strictly belong to goal objects. For example, it cannot be that men are defined by having arms, since we could a man missing his arms a man.

## 6.1   Avoid the passive voice

Consider these typical definitions:

Coffee is a drink that is produced by brewing roasted coffee beans.

Python is a general-purpose language that was created by Guido van Rossum in 1991.

The author should rewrite the dependent clauses in the active voice both to ensure the subject is named and for brevity:

Coffee is a drink that people produce by brewing roasted coffee beans.

Python is a general-purpose language that Guido van Rossum created in 1991.

# 7   Duality

Some things are actually multiple things:

• Matter and energy
• Wave particle duality
• The Holy Trinity
• Brain and mind (arguable)