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'the diagonal of a square is commensurate with the side'), on the
other hand the theory that everything is true. These views are
practically the same as that of Heraclitus; for he who says that all
things are true and all are false also makes each of these
statements separately, so that since they are impossible, the double
statement must be impossible too.-Again, there are obviously
contradictories which cannot be at the same time true-nor on the other
hand can all statements be false; yet this would seem more possible in
the light of what has been said.-But against all such views we must
postulate, as we said above,' not that something is or is not, but
that something has a meaning, so that we must argue from a definition,
viz. by assuming what falsity or truth means. If that which it is true
to affirm is nothing other than that which it is false to deny, it
is impossible that all statements should be false; for one side of the
contradiction must be true. Again, if it is necessary with regard to
everything either to assert or to deny it, it is impossible that
both should be false; for it is one side of the contradiction that
is false.-Therefore all such views are also exposed to the often
expressed objection, that they destroy themselves. For he who says
that everything is true makes even the statement contrary to his own
true, and therefore his own not true (for the contrary statement
denies that it is true), while he who says everything is false makes
himself also false.-And if the former person excepts the contrary
statement, saying it alone is not true, while the latter excepts his
own as being not false, none the less they are driven to postulate the
truth or falsity of an infinite number of statements; for that which
says the true statement is true is true, and this process will go on
to infinity.
Evidently, again, those who say all things are at rest are not
right, nor are those who say all things are in movement. For if all
things are at rest, the same statements will always be true and the
same always false,-but this obviously changes; for he who makes a
statement, himself at one time was not and again will not be. And if
all things are in motion, nothing will be true; everything therefore
will be false. But it has been shown that this is impossible. Again,
it must be that which is that changes; for change is from something to
something. But again it is not the case that all things are at rest or
in motion sometimes, and nothing for ever; for there is something
which always moves the things that are in motion, and the first
mover is itself unmoved.
Book V
1

'BEGINNING' means (1) that part of a thing from which one would
start first, e.g a line or a road has a beginning in either of the
contrary directions. (2) That from which each thing would best be
originated, e.g. even in learning we must sometimes begin not from the
first point and the beginning of the subject, but from the point
from which we should learn most easily. (4) That from which, as an
immanent part, a thing first comes to be, e,g, as the keel of a ship
and the foundation of a house, while in animals some suppose the
heart, others the brain, others some other part, to be of this nature.
(4) That from which, not as an immanent part, a thing first comes to
be, and from which the movement or the change naturally first
begins, as a child comes from its father and its mother, and a fight
from abusive language. (5) That at whose will that which is moved is
moved and that which changes changes, e.g. the magistracies in cities,
and oligarchies and monarchies and tyrannies, are called arhchai,
and so are the arts, and of these especially the architectonic arts.
(6) That from which a thing can first be known,-this also is called
the beginning of the thing, e.g. the hypotheses are the beginnings
of demonstrations. (Causes are spoken of in an equal number of senses;
for all causes are beginnings.) It is common, then, to all
beginnings to be the first point from which a thing either is or comes

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