ion may be turned into an essential definition by
a change of the connotation (not the denotation) of the name; and, in
fact, thus are manufactured almost all scientific definitions, which,
being landmarks of classification, and not meant to declare the meaning
of the name (though, in fact, they do declare it in its new use), are
ever being modified (as is the definition of a science itself) with the
advance of knowledge. Thus, a technical definition helps to expound the
artificial classification from which it grows; but ordinary definition
cannot expound, as the Aristotelians fancied it could, the natural
classification of things, i.e. explain their division into _kinds_, and
the relations among the _kinds_: for the properties of every _kind_ are
innumerable, and all that definition can do is to state the connotation
of the name.

Both these two modes, viz. the essential but incomplete Definition, and
the accidental, or Description, are imperfect; but the Realists'
distinction between definition of names and of things is quite
erroneous. Their doctrine is now exploded; but many propositions
consistent with it alone (e.g. that the science of geometry is deduced
from definitions) have been retained by Nominalists, such as Hobbes.
Really a definition, as such, cannot explain a thing's nature, being
merely an identical proposition explaining the meaning of a word. But
definitions of names _known to be names of really existing objects_, as
in geometry, include two propositions, one a definition and another a
postulate. The latter affirms the existence of a thing answering to the
name. The science is based on the postulates (whether they rest on
intuition or proof), for the demonstration appeals to them alone, and
not on the definitions, which indeed might, though at some cost of
brevity, be dispensed with entirely. It has been argued that, at any
rate, definitions are premisses of science, _provided_ they give such
meanings to terms as suit existing things: but even so, the inference
would obviously be from the existence, not of the name which means, but
of the thing which has the properties.

One reason for the belief that demonstrative truths follow from the
definitions, not from the postulates, was because the postulates are
never quite true (though in reality so much of them is true as is true
of the conclusions). Philosophers, therefore, searching for something
more accurately true, surmised that definitions must be s