Further, the understanding either affirms or denies
every object of understanding or thought (as is clear from the
）whenever it is right or wrong. When, in asserting or denying, it
combines the predicates in one way, it is right; when in the other, it
Again, unless it is maintained
merely for argument's sake, the intermediate must exist beside all
contrary terms; so that one will say what is neither true nor false.
And it will exist beside what is and what is not; so that there will
be a form of change beside generation and destruction.
Again, there will also be an intermediate in all classes in which
the negation of a term implies the contrary assertion; e.g., among
numbers there will be a number which is neither odd nor not-odd. But
this is impossible, as is clear from the definition.2
Again, there will be an infinite progression, and
existing things will be not only half as many again, but even
more.For again it
will be possible to deny the intermediate in reference both to its
assertion and to its negation, and the result will be something3
for its essence is something distinct.
Again, when a man is asked whether a thing is white and says "no,"
he has denied nothing except that it is <white>, and its
not-being <white> is a negation.
this view has occurred to certain people in just the same way as other
paradoxes have also occurred; for when they cannot find a way out from
eristic arguments, they submit to the argument and admit that the
conclusion is true.
then, hold the theory for this kind of reason, and others because they
require an explanation for everything. In dealing with all such
persons the starting-point is from definition;and definition results from the
necessity of their meaning something; because the formula, which their
term implies, will be a definition.4
The doctrine of Heraclitus, which says that
everything is and is not,5
make all things true; and that of Anaxagoras6
seems to imply an intermediate in contradiction,
so that all things are false; for when things are mixed, the mixture
is neither good nor not-good; and so no statement is true.
It is obvious from this analysis that the one-sided and sweeping
statements which some people make cannot be substantially
true—some maintaining that nothing is true (for they say
that there is no reason why the same rule should not apply to
everything as applies to the commensurability of the diagonal of a
), and some that
everything is true.These
theories are almost the same as that of Heraclitus. For the theory
which says that all things are true and all false also makes each of
these statements separately;