The Complete Aristotle (eng.)

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.
<
    div id="section22" class="section" title="4">
4
    The science of nature is concerned with spatial magnitudes and
motion and time, and each of these at least is necessarily infinite
or finite, even if some things dealt with by the science are not,
e.g. a quality or a point-it is not necessary perhaps that such
things should be put under either head. Hence it is incumbent on
the person who specializes in physics to discuss the infinite and
to inquire whether there is such a thing or not, and, if there is,
what it is.
    The appropriateness to the science of this problem is clearly
indicated. All who have touched on this kind of science in a way
worth considering have formulated views about the infinite, and
indeed, to a man, make it a principle of things.
    (1) Some, as the Pythagoreans and Plato, make the infinite a
principle in the sense of a self-subsistent substance, and not as a
mere attribute of some other thing. Only the Pythagoreans place the
infinite among the objects of sense (they do not regard number as
separable from these), and assert that what is outside the heaven
is infinite. Plato, on the other hand, holds that there is no body
outside (the Forms are not outside because they are nowhere),yet
that the infinite is present not only in the objects of sense but
in the Forms also.
    Further, the Pythagoreans identify the infinite with the even.
For this, they say, when it is cut off and shut in by the odd,
provides things with the element of infinity. An indication of this
is what happens with numbers. If the gnomons are placed round the
one, and without the one, in the one construction the figure that
results is always different, in the other it is always the same.
But Plato has two infinites, the Great and the Small.
    The physicists, on the other hand, all of them, always regard
the infinite as an attribute of a substance which is different from
it and belongs to the class of the so-called elements-water or air
or what is intermediate between them. Those who make them limited
in number never make them infinite in amount. But those who make
the