The solution of the difficulty that is raised about the
motion-whether it is in the movable-is plain. It is the fulfilment
of this potentiality, and by the action of that which has the power of
causing motion; and the actuality of that which has the power of
causing motion is not other than the actuality of the movable, for
it must be the fulfilment of both. A thing is capable of causing
motion because it can do this, it is a mover because it actually
does it. But it is on the movable that it is capable of acting.
Hence there is a single actuality of both alike, just as one to two
and two to one are the same interval, and the steep ascent and the
steep descent are one-for these are one and the same, although they
can be described in different ways. So it is with the mover and the
moved.

    This view has a dialectical difficulty. Perhaps it is necessary that
the actuality of the agent and that of the patient should not be the
same. The one is "agency" and the other "patiency"; and the outcome
and completion of the one is an "action", that of the other a
"passion". Since then they are both motions, we may ask: in what are
they, if they are different? Either (a) both are in what is acted on
and moved, or (b) the agency is in the agent and the patiency in the
patient. (If we ought to call the latter also "agency", the word would
be used in two senses.)

    Now, in alternative (b), the motion will be in the mover, for the
same statement will hold of "mover" and "moved". Hence either every
mover will be moved, or, though having motion, it will not be moved.

    If on the other hand (a) both are in what is moved and acted on-both
the agency and the patiency (e.g. both teaching and learning, though
they are two, in the learner), then, first, the actuality of each will
not be present in each, and, a second absurdity, a thing will have two
motions at the same time. How will there be two alterations of quality
in one subject towards one definite quality? The thing is
impossible: the actualization will be one.

    But (some one will say) it is contrary to reason to suppose that
there should be one identical actualization of two things which are
different in kind. Yet there will be, if teaching and learning are the
same, and agency and patiency. To teach will be the same as to
learn, and to act the same as to be acted on-the teacher will
necessarily be learning everything that he teaches, and the agent will
be acted on. One may reply:

    (1) It is not absurd that the actualization of one thing should be
in another. Teaching is the activity of a person who can teach, yet
the operation is performed on some patient-it is not cut adrift from a
subject, but is of A on B.

    (2) There is nothing to prevent two things having one and the same
actualization, provided the actualizations are not described in the
same way, but are related as what can act to what is acting.

    (3) Nor is it necessary that the teacher should learn, even if to
act and to be acted on are one and the same, provided they are not the
same in definition (as "raiment" and "dress"), but are the same merely
in the sense in which the road from Thebes to Athens and the road from
Athens to Thebes are the same, as has been explained above. For it
is not things which are in a way the same that have all their
attributes the same, but only such as have the same definition. But
indeed it by no means follows from the fact that teaching is the
same as learning, that to learn is the same as to teach, any more than
it follows from the fact that there is one distance between two things
which are at a distance from each other, that the two vectors AB and
BA, are one and the same. To generalize, teaching is not the same as
learning, or agency as patiency, in the full sense, though they belong
to the same subject, the motion; for the "actualization of X in Y" and
the "actualization of Y through the action of X" differ in definition.

    What then Motion is, has been stated both generally and
particularly. It is not difficult to see how each of its types will be
defined-alteration is the fulfillment of the alterable qua alterable
(or, more scientifically, the fulfilment of what can act and what
can be acted on, as such)-generally and again in each particular case,
building, healing, &c. A similar definition will apply to each of
the other kinds of motion.