Topic: definition

topics > Group: naming


command language
definition languages
dictionary for natural language
function definition
macro syntax definition
meaning of words
referential transparency
replacement as defining a variable
using a description as a name
words defined by words


A definition defines the meaning of a term. A definition in mathematics is different than a definition in a dictionary or natural language. A definition has a context, a headword, and the definition itself. It may define a synonym or a new concept.

A mathematical definition is a name that stands for an expression. It does not expand the theory or system. It may be preceded by an existence theorem that proves the existence of the definiendum. (cbb 12/00)

Subtopic: role of definition up

Quote: a definition is a transition between one technique into another, e.g., from mathematics to logic; not an abbreviation [»wittL_1939]
Quote: any definition can be misinterpreted
Quote: definition arises from stating what we mean; i.e., the statement of which the word is a sign becomes a definition [»aris_322a]

Subtopic: definition and identity up

Quote: things are one when they share the same definition; e.g., despite size differences [»aris_322a]
Quote: define by genus together with successive differentia; e.g., animal that is biped that is featherless [»aris_322a]

Subtopic: definition as abbreviation up

Quote: definitions add brevity and convenience to an otherwise universal, primitive notation
Quote: a definition may faithfully paraphrase a term in a narrower notation, or explicate a term, or create a new notation [»quinWV1_1951]
Quote: combine primitive and concise notations by rules of translation which define primitive equivalents for concise terms [»quinWV1_1951]
Quote: a definition in math and logic should be nominal; i.e., does not expand the theory or system, for comprehension only [»postSW7_1978]

Subtopic: definition is not abbreviation up

Quote: any definition is divisible
Quote: is p|q an abbreviation for ~p.~q or is it vice versa; i.e., definition is not abbreviation

Subtopic: prior relations up

Quote: except when defining new terms, definition hinges on prior relations of synonymy [»quinWV1_1951]
QuoteRef: cbb_1973 ;;4/22/74 definition-- to fix or mark the limits of

Subtopic: programming as definition up

Quote: as we write code, we stop frequently to define new terms

Subtopic: mathematical definition up

Quote: in math, a definition is preceded by an existence theorem, or an axiom/hypothesis that postulates its existence [»postSW7_1978]
Quote: a definition consists of a context, a definiendum, and its definiens in terms of known concepts [»postSW7_1978]
Quote: can always affix "by definition" to a mathematical proposition; this refers to a picture, e.g., "12*12=144", in a standards archive

Related Topics up

Group: philosophy   (60 topics, 2323 quotes)

Topic: command language (23 items)
Topic: definition languages (3 items)
Topic: dictionary for natural language (41 items)
Topic: function definition (25 items)
Topic: macro syntax definition (10 items)
Topic: meaning of words (21 items)
Topic: referential transparency (26 items)
Topic: replacement as defining a variable (8 items)
Topic: using a description as a name (21 items)
Topic: words defined by words
(25 items)

Updated barberCB 4/04
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