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being essentially a man is to be the same as either being
essentially a not-man or essentially not being a man, then its essence
will be something else. Therefore our opponents must say that there
cannot be such a definition of anything, but that all attributes are
accidental; for this is the distinction between substance and
accident-'white' is accidental to man, because though he is white,
whiteness is not his essence. But if all statements are accidental,
there will be nothing primary about which they are made, if the
accidental always implies predication about a subject. The
predication, then, must go on ad infinitum. But this is impossible;
for not even more than two terms can be combined in accidental
predication. For (1) an accident is not an accident of an accident,
unless it be because both are accidents of the same subject. I mean,
for instance, that the white is musical and the latter is white,
only because both are accidental to man. But (2) Socrates is
musical, not in this sense, that both terms are accidental to
something else. Since then some predicates are accidental in this
and some in that sense, (a) those which are accidental in the latter
sense, in which white is accidental to Socrates, cannot form an
infinite series in the upward direction; e.g. Socrates the white has
not yet another accident; for no unity can be got out of such a sum.
Nor again (b) will 'white' have another term accidental to it, e.g.
'musical'. For this is no more accidental to that than that is to
this; and at the same time we have drawn the distinction, that while
some predicates are accidental in this sense, others are so in the
sense in which 'musical' is accidental to Socrates; and the accident
is an accident of an accident not in cases of the latter kind, but
only in cases of the other kind, so that not all terms will be
accidental. There must, then, even so be something which denotes
substance. And if this is so, it has been shown that contradictories
cannot be predicated at the same time.
Again, if all contradictory statements are true of the same
subject at the same time, evidently all things will be one. For the
same thing will be a trireme, a wall, and a man, if of everything it
is possible either to affirm or to deny anything (and this premiss
must be accepted by those who share the views of Protagoras). For if
any one thinks that the man is not a trireme, evidently he is not a
trireme; so that he also is a trireme, if, as they say,
contradictory statements are both true. And we thus get the doctrine
of Anaxagoras, that all things are mixed together; so that nothing
really exists. They seem, then, to be speaking of the indeterminate,
and, while fancying themselves to be speaking of being, they are
speaking about non-being; for it is that which exists potentially
and not in complete reality that is indeterminate. But they must
predicate of every subject the affirmation or the negation of every
attribute. For it is absurd if of each subject its own negation is
to be predicable, while the negation of something else which cannot be
predicated of it is not to be predicable of it; for instance, if it is
true to say of a man that he is not a man, evidently it is also true
to say that he is either a trireme or not a trireme. If, then, the
affirmative can be predicated, the negative must be predicable too;
and if the affirmative is not predicable, the negative, at least, will
be more predicable than the negative of the subject itself. If,
then, even the latter negative is predicable, the negative of
'trireme' will be also predicable; and, if this is predicable, the
affirmative will be so too.
Those, then, who maintain this view are driven to this conclusion,
and to the further conclusion that it is not necessary either to
assert or to deny. For if it is true that a thing is a man and a
not-man, evidently also it will be neither a man nor a not-man. For to
the two assertions there answer two negations, and if the former is
treated as a single proposition compounded out of two, the latter also
is a single proposition opposite to the former.
Again, either the theory is true in all cases, and a thing is both

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