The special issue of definition

The issue of definition is not only extremely important, but also multifaceted; therefore, it is devoted its own page.

"Definition"

What is a 'definition'?—The 'definition' of an expression is a clarification of its semantics. The expression being defined is called the 'definiendum'; the phrase defining the term is called the 'definiens'.

Meaning (intension) and reference (extension)

The semantics of an expression can have two dimensions:

(1) its meaning, an "intension". For example, the meaning of "kleine Häuser" is 'small houses', and the meaning of "Morgenstern" is 'morning star'. 

(2) its reference, an "extension". For example, "kleine Häuser" refers to small houses, and the reference of "Morgenstern" is the planet Venus.

Natural vs. artificial terms

Expressions defined can either be expressions of common language ("natural" expression), or artificial expressions ("technical terms").

Analysis vs. stipulation

A definition can either represent the semantics which a given expression already has--this is an "analytic" definition, or "analysis"--, or attach meaning and/or reference to an expression--this is called "stipulative" definition.

(1) An analytic definition would be: "'Bachelor' means 'unmarried man'."

(2) A stipulative definition would be: "'Asens' shall mean 'without meaning'". There are different kinds of notation, including, e.g.: "'Asens' := 'without meaning'"

Since Carnap, there is the idea of a middle course, "explication": The semantics of an expression which already has meaning and/or reference is precisified.

(3) An explication would be: "In the following, 'big' will refer to a size of at least 100 cm."