Definition: Statement to the effect
that in certain conditions C a term A may be replaced by a term B and
conversely. This seems the clearest basic definition of
"definition". Two normal reasons to justify this are that, in those
conditions C, the meaning of A and the meaning of B are the same, or A
is just a conventional abbreviation for B, with the same import. The
reason this is then a formally valid
inference is that terms with the
same meaning have the same denotations, and hence statements P and Q
that are all the same except that P has at one or more place a
definition for A instead of A must have the same
truthvalue in the same
conditions.
It should also be clear that the phrase "in
certain conditions C" covers a lot, and not too clearly. One
reason for this fact is that as soon as we have
propositional attitudes,
one person may know that a certain term A is defined by B and another
may not, and so the substituting of defining for defined terms does
not unproblematically produce statements of the same truthvalues for
all persons.
In any case it makes sense to regard definitions as explicit
assumptions in arguments until one has proved that the definition can be
proved as an equivalence or an identity.
1. Descriptive vs. stipulative definitions
There are two basic kinds of definitions: descriptive definitions,
that attempt to describe in what sense a certain term is used in a
certain society, and stipulative definitions, that propose a
sense for a certain term, possibly regardless of the sense(s) the term
has in any given society.
Quite often it is not clear for a given definition to what extent it
is descriptive or stipulative, in as much as even most honest rendering
of the various usages and meanings of a term in a society will contain
some stipulative elements, and in as much even clearly stipulative
definitions will normally follow some of the received meanings of a
term.
In this Philosophical Dictionary it makes by far the most sense to
consider each and every definition a stipulative definition, even
if it is quite close to some received usage or definition of the same
term.
2. Creative vs. uncreative definitions
The distinction in the previous section is related to the distinction
between creative vs. uncreative definitions. Formally speaking, which
means here especially: with reference to some presupposed formal system
of reasoning, an uncreative definition in such a system corresponds to
an equivalence that is instantiated: There is  according to the
assumptions of the system  something that is defined in terms of the
equivalence, and that is consistent with the rest of the system.
Accordingly, an uncreative definition corresponds to a piece of
terminology that circumscribes what the term stands for, but that can be
wholly removed or avoided in as much as the defined term can be replaced
by its equivalent defining expression.
By contrast, creative definitions embody some assumption, usually to
the effect that there is something that corresponds to the defined term.
Without a fully formalized system it is often not easy to prove or see
whether a definition used in the system is creative or not. And the
reason for the term "creative" is that a creative definitions entails
statements that are provable in the system, but that are not provable if
the definition is removed, which is to say, in other words, that the
used equivalence in the definition is not provable in the system.
A proper axiomatic system
is generally supposed to be free from creative definitions, since a
proper axiomatic system lists all its
assumptions explicitly as
axioms (and doesn't  consciously or not 
smuggle them inside by what seem to be mere terminological conventions).
