I. LEXICAL DEFINITIONS
rough approximation of the meaning of a word; they elucidate the
preexistent meaning of a word.
II. STIPULATIVE DEFINITIONS
do not report any preexistent meaning of a word; rather, they
stipulate (create) the convenient new abbreviations.
Example: Let ‘it is drizzmog' mean ‘it is drizzling, humid and foggy'.
III. ANALYTIC DEFINITIONS
Precise accounts of what concepts (words) mean; they display in
clear and precise terms the exact meaning of some expression or
word.
The correct analytical definition must be (A) immune from counterexamples (it must represent a necessary equivalence between two expressions) and it also must be (B) enlightening (i.e., it must use only clear terms, and cannot be circular).
A. Immunity from counterexamples
(DB1) X is a bachelor =def. X is an unmarried man.
(A problem with this definition is that it counts widowers and divorces as bachelors.)(DB2) X is a bachelor =def. X is an unmarried man who has never been married.
(This is a better definition, but it still has a problem, namely it counts small children and the Pope as bachelors.)(DB3) X is a bachelor =def. X is an unmarried man who has never been married and is eligible to be married.
B. The definition also must be enlightening (informative).
(DT) X is a table =def. X is a very tableish piece of furniture.
(This definition does not help us to understand what tables are.)
CONCEPTS
I. SHARP (PRECISE) CONCEPTS
Concepts that can be defined in an extremely precise way:
(DC) X is a circle =def. X is a closed plane curve, equidistant at all points from a given point.
II. VAGUE CONCEPTS
Concepts that cannot be defined with the same precision as the
sharp concept; still, in the paradigm cases the objects share the
same characteristics. Examples: a river, a table. It's very hard to
distinguish precisely a river from a stream, or table (e.g., a
laboratory table) from a desk. However, all paradigm (typical,
exemplary) rivers will have some common elements -- banks, a
bed, some water constrained in its flow by banks and a bed, etc.
III. OPEN CONCEPTS
Concepts which are very vague; it is impossible to give both
sufficient and necessary conditions for any open concept. Even
paradigm cases share only some but not all characteristics.
Nevertheless, there is a family resemblance between games -- not all games are the same, but each game is like some other games.