Group:
philosophy
Topic:
command language
Topic:
definition languages
Topic:
dictionary for natural language
Topic:
function definition
Topic:
macro syntax definition
Topic:
meaning of words
Topic:
referential transparency
Topic:
replacement as defining a variable
Topic:
using a description as a name
Topic:
words defined by words
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Summary
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 
| 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]
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Subtopic: definition and identity
| 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]
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Subtopic: definition as abbreviation
| 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]
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Subtopic: definition is not abbreviation
| 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
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Subtopic: prior relations
| 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
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Subtopic: programming as definition
| Quote: as we write code, we stop frequently to define new terms
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Subtopic: mathematical definition
| 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
[»wittL_1939]
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Related Topics
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)
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