Definition
A definition is a statement of the meaning of a term (a word, phrase, or other set of symbols).
"); and precising definitions, which reduce the vagueness of a word, typically in some special sense ("'Large', among female Asian elephants, is any individual weighing over 5,500 pounds.").
[3] Thus, the "seven deadly sins" can be defined intensionally as those singled out by Pope Gregory I as particularly destructive of the life of grace and charity within a person, thus creating the threat of eternal damnation.
An extensional definition, on the other hand, would be the list of wrath, greed, sloth, pride, lust, envy, and gluttony.
By contrast, the name "man" denotes real things (men) that have a certain quid rei.
[14] More recently Kripke's formalisation of possible world semantics in modal logic led to a new approach to essentialism.
A homonym is, in the strict sense, one of a group of words that share the same spelling and pronunciation but have different meanings.
A distinction is sometimes made between "true" homonyms, which are unrelated in origin, such as skate (glide on ice) and skate (the fish), and polysemous homonyms, or polysemes, which have a shared origin, such as mouth (of a river) and mouth (of an animal).
Frequently, a definition uses a phrase built with common English words, which has no meaning outside mathematics, such as primitive group or irreducible variety.
On the other hand, lambda-calculi are a kind of logic where the definitions are included as the feature of the formal system itself.
Authors have used different terms to classify definitions used in formal languages like mathematics.
Norman Swartz classifies a definition as "stipulative" if it is intended to guide a specific discussion.
[20] In contrast, a "descriptive" definition can be shown to be "right" or "wrong" with reference to general usage.
Stevenson has identified persuasive definition as a form of stipulative definition which purports to state the "true" or "commonly accepted" meaning of a term, while in reality stipulating an altered use (perhaps as an argument for some specific belief).
Stevenson has also noted that some definitions are "legal" or "coercive" – their object is to create or alter rights, duties, or crimes.
Normally this consists of three steps: For instance, we could define a natural number as follows (after Peano): So "0" will have exactly one successor, which for convenience can be called "1".
[24][25][26][27] Given that a natural language such as English contains, at any given time, a finite number of words, any comprehensive list of definitions must either be circular or rely upon primitive notions.
The scholastic philosophers claimed that the highest genera (called the ten generalissima) cannot be defined, since a higher genus cannot be assigned under which they may fall.
[25] Locke supposes in An Essay Concerning Human Understanding[33] that the names of simple concepts do not admit of any definition.
More recently Bertrand Russell sought to develop a formal language based on logical atoms.
Saul Kripke pointed to difficulties with this approach, especially in relation to modality, in his book Naming and Necessity.
