I am quite aware that nowadays men laugh at those who reason on
definitions; the laughers deserve to be laughed at. There is no theory
more fertile in universal and important results; it is the root by which
the whole tree of human science grows and lives. For to define things is
to mark out their nature. To introduce a new idea of definition is to
introduce a new idea of the nature of things; it is to tell us what
beings are, of what they are composed, into what elements they are
capable of being resolved. In this lies the merit of these dry
speculations; the philosopher seems occupied with arranging mere
formulas; the fact is, that in them he encloses the universe.
Take, say logicians, an animal, a plant, a feeling, a geometrical
figure, an object or group of objects of any kind. Doubtless the object
has its properties, but it has also its essence. It is manifested to the
outer world by an indefinite number of effects and qualities; but all
these modes of being are the results or products of its inner nature.
There is within it a certain hidden substratum which alone is primitive
and important, without which it can neither exist nor be conceived, and
which constitutes its being and our notion of it.[402] They call the
propositions which denote this essence definitions, and assert that the
best part of our knowledge consists of such propositions.
On the other hand, Mill says that these kinds of propositions teach us
nothing; they show the mere sense of a word, and are purely verbal.[403]
What do I learn by being told that man is a rational animal, or that a
triangle is a space contained by three lines? The first part of such a
phrase expresses, by an abbreviative word, what the second part
expresses in a developed phrase. You tell me the same thing twice over;
you put the same fact into two different expressions; you do not add one
fact to another, but you go from one fact to its equivalent. Your
proposition is not instructive. You might collect a million such, my
mind would remain entirely void; I should have read a dictionary, but
not have acquired a single piece of knowledge. Instead of saying that
essential propositions are important, and those relating to qualities
merely accessory, you ought to say that the first are accessory, and the
second important. I learn nothing by being told that a circle is a
figure formed by the revolution of a straight line about one of its
points as centre; I do learn something when told that the chords which
subtend equal arcs in the circle are themselves equal, or that three
given points determine the circumference. What we call the nature of a
being is the connected system of facts which constitutes that being. The
nature of a carnivorous mammal consists in the fact that the property of
giving milk, and all its implied peculiarities of structure, are
combined with the possession of sharp teeth, instincts of prey, and the
corresponding faculties. Such are the elements which compose its nature.
They are facts linked together as mesh to mesh in a net. We perceive a
few of them; and we know that beyond our present knowledge and our
future experience, the network extends to infinity its interwoven and
manifold threads. The essence or nature of a being is the indefinite sum
of its properties. Mill says:
"The definition, they say, unfolds the nature of the thing: but no
definition can unfold its whole nature; and every proposition in which
any quality whatever is predicated of the thing, unfolds some part of
its nature. The true state of the case we take to be this: All
definitions are of names, and of names only; but in some definitions it
is clearly apparent, that nothing is intended except to explain the
meaning of the word; while in others, besides explaining the meaning of
the word, it is intended to be implied that there exists a thing,
corresponding to the word."[404]
Abandon, then, the vain hope of eliminating from properties some
primitive and mysterious being, the source and abstract of the whole;
leave entities to Duns Scotus; do not fancy that, by probing your ideas
in the German fashion, by classifying objects according to genera and
species like the schoolmen, by reviving the nominalism of the Middle
Ages or the riddles of Hegelian metaphysics, you will ever supply the
want of experience. There are no definitions of things; if there are
definitions, they only define names. No phrase can tell me what a horse
is; but there are phrases which will inform me what is meant by these
five letters. No phrase can exhaust the inexhaustible sum of qualities
which make up a being; but several phrases may point out the facts
corresponding to a word. In this case definition is possible, because we
can always make an analysis, which will enable us to pass from the
abstract and summary term to the attributes which it represents, and
from these attributes to the inner or concrete feelings which constitute
their foundation. From the term "dog" it enables us to rise to the
attributes "mammiferous, carnivorous," and others which it represents;
and from these attributes to the sensations of sight, of touch, of the
dissecting knife, on which they are founded. It reduces the compound to
the simple, the derived to the primitive. It brings back our knowledge
to its origin. It transforms words into facts. If some definitions, such
as those of geometry, seem capable of giving rise to long sequences of
new truths,[405] it is because, in addition to the explanation of a
word, they contain the affirmation of a thing. In the definition of a
triangle there are two distinct propositions--the one stating that
"there may exist a figure bounded by three straight lines"; the other,
that "such a figure may be termed a triangle." The first is a postulate,
the second a definition. The first is hidden, the second evident; the
first may be true or false, the second can be neither. The first is the
source of all possible theorems as to triangles, the second only resumes
in a word the facts contained in the other. The first is a truth, the
second is a convention; the first is a part of science, the second an
expedient of language. The first expresses a possible relation between
three straight lines, the second gives a name to this relation. The
first alone is fruitful, because it alone conforms to the nature of
every fruitful proposition, and connects two facts. Let us, then,
understand exactly the nature of our knowledge: it relates either to
words or to things, or to both at once. If it is a matter of words, as
in the definition of names, it attempts to refer words to our primitive
feelings: that is to say, to the facts which form their elements. If it
relates to beings, as in propositions about things, its whole effort is
to link fact to fact, in order to connect the finite number of known
properties with the infinite number to be known. If both are involved,
as in the definitions of names which conceal a proposition relating to
things, it attempts to do both. Everywhere its operation is the same.
The whole matter, in any case, is to understand each other--that is, to
revert to facts, or to learn--that is, to add facts to facts.