The Complete Aristotle (eng.)

essential nature is
exhibited. So we conclude that neither can the essential nature of
anything which has a cause distinct from itself be known without
demonstration, nor can it be demonstrated; and this is what we
contended in our preliminary discussions.
9
    Now while some things have a cause distinct from themselves,
others have not. Hence it is evident that there are essential
natures which are immediate, that is are basic premisses; and of
these not only that they are but also what they are must be assumed
or revealed in some other way. This too is the actual procedure of
the arithmetician, who assumes both the nature and the existence of
unit. On the other hand, it is possible (in the manner explained)
to exhibit through demonstration the essential nature of things
which have a ‘middle’, i.e. a cause of their substantial being
other than that being itself; but we do not thereby demonstrate
it.
10
    Since definition is said to be the statement of a thing’s
nature, obviously one kind of definition will be a statement of the
meaning of the name, or of an equivalent nominal formula. A
definition in this sense tells you, e.g. the meaning of the phrase
‘triangular character’. When we are aware that triangle exists, we
inquire the reason why it exists. But it is difficult thus to learn
the definition of things the existence of which we do not genuinely
know-the cause of this difficulty being, as we said before, that we
only know accidentally whether or not the thing exists. Moreover, a
statement may be a unity in either of two ways, by conjunction,
like the Iliad, or because it exhibits a single predicate as
inhering not accidentally in a single subject.
    That then is one way of defining definition. Another kind of
definition is a formula exhibiting the cause of a thing’s
existence. Thus the former signifies without proving, but the
latter will clearly be a quasi-demonstration of essential nature,
differing from demonstration in the arrangement of its terms. For
there is a difference between stating why it thunders, and stating
what is the essential nature of thunder; since the first statement
will be ‘Because fire is quenched in the clouds’, while the
statement of what the nature of thunder is will be ‘The noise of
fire being quenched in the clouds’. Thus the same statement takes a
different form: in one form it is continuous demonstration, in the
other definition. Again, thunder can be defined as noise in the
clouds, which is the conclusion of the demonstration embodying
essential nature. On the other hand the definition of immediates is
an indemonstrable positing of essential nature.
    We conclude then that definition is (a) an indemonstrable
statement of essential nature, or (b) a syllogism of essential
nature differing from demonstration in grammatical form, or (c) the
conclusion of a demonstration giving essential nature.
    Our discussion has therefore made plain (1) in what sense and of
what things the essential nature is demonstrable, and in what sense
and of what things it is not; (2) what are the various meanings of
the term definition, and in what sense and of what things it proves
the essential nature, and in what sense and of what things it does
not; (3) what is the relation of definition to demonstration, and
how far the same thing is both definable and demonstrable and how
far it is not.
11
    We think we have scientific knowledge when we know the cause,
and there are four causes: (1) the definable form, (2) an
antecedent which necessitates a consequent, (3) the efficient
cause, (4) the final cause. Hence each of these can be the middle
term of a proof, for (a) though the inference from antecedent to
necessary consequent does not hold if only one premiss is
assumed-two is the minimum-still when there are two it holds on
condition that they have a single common middle term. So it is from
the assumption of this single middle term that the conclusion
follows necessarily. The following example will also show this. Why
is the angle in a semicircle a right angle?-or from what assumption
does it follow that it is a right angle? Thus, let A be right
angle, B the half of two right angles, C the angle in a semicircle.
Then B is the cause in virtue of which A, right angle, is
attributable to C, the angle in a semicircle, since B=A and the
other, viz. C,=B, for C is half of two right angles. Therefore it
is the assumption of B, the half of two right angles, from which it
follows that A is attributable