Posterior Analytics   

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 to
C, i.e. that the angle in a semicircle is a right angle. Moreover, B
is identical with (b) the defining form of A, since it is what A's
definition signifies. Moreover, the formal cause has already been
shown to be the middle. (c) 'Why did the Athenians become involved
in the Persian war?' means 'What cause originated the waging of war
against the Athenians?' and the answer is, 'Because they raided Sardis
with the Eretrians', since this originated the war. Let A be war, B
unprovoked raiding, C the Athenians. Then B, unprovoked raiding, is
true of C, the Athenians, and A is true of B, since men make war on
the unjust aggressor. So A, having war waged upon them, is true of
B, the initial aggressors, and B is true of C, the Athenians, who were
the aggressors. Hence here too the cause-in this case the efficient
cause-is the middle term. (d) This is no less true where the cause
is the final cause. E.g. why does one take a walk after supper? For
the sake of one's health. Why does a house exist? For the preservation
of one's goods. The end in view is in the one case health, in the
other preservation. To ask the reason why one must walk after supper
is precisely to ask to what end one must do it. Let C be walking after
supper, B the non-regurgitation of food, A health. Then let walking
after supper possess the property of preventing food from rising to
the orifice of the stomach, and let this condition be healthy; since
it seems that B, the non-regurgitation of food, is attributable to
C, taking a walk, and that A, health, is attributable to B. What,
then, is the cause through which A, the final cause, inheres in C?
It is B, the non-regurgitation of food; but B is a kind of
definition of A, for A will be explained by it. Why is B the cause
of A's belonging to C? Because to be in a condition such as B is to be
in health. The definitions must be transposed, and then the detail
will become clearer. Incidentally, here the order of coming to be is
the reverse of what it is in proof through the efficient cause: in the
efficient order the middle term must come to be first, whereas in