There are some who, as we said, both themselves assert that it
is possible for the same thing to be and not to be, and say that
people can judge this to be the case. And among others many writers
about nature use this language. But we have now posited that it is
impossible for anything at the same time to be and not to be, and by
this means have shown that this is the most indisputable of all
principles.-Some indeed demand that even this shall be demonstrated,
but this they do through want of education, for not to know of what
things one should demand demonstration, and of what one should not,
argues want of education. For it is impossible that there should be
demonstration of absolutely everything (there would be an infinite
regress, so that there would still be no demonstration); but if
there are things of which one should not demand demonstration, these
persons could not say what principle they maintain to be more
self-evident than the present one.
    We can, however, demonstrate negatively even that this view is
impossible, if our opponent will only say something; and if he says
nothing, it is absurd to seek to give an account of our views to one
who cannot give an account of anything, in so far as he cannot do
so. For such a man, as such, is from the start no better than a
vegetable. Now negative demonstration I distinguish from demonstration
proper, because in a demonstration one might be thought to be
begging the question, but if another person is responsible for the
assumption we shall have negative proof, not demonstration. The
starting-point for all such arguments is not the demand that our
opponent shall say that something either is or is not (for this one
might perhaps take to be a begging of the question), but that he shall
say something which is significant both for himself and for another;
for this is necessary, if he really is to say anything. For, if he
means nothing, such a man will not be capable of reasoning, either
with himself or with another. But if any one grants this,
demonstration will be possible; for we shall already have something
definite. The person responsible for the proof, however, is not he who
demonstrates but he who listens; for while disowning reason he listens
to reason. And again he who admits this has admitted that something is
true apart from demonstration (so that not everything will be 'so
and not so').
    First then this at least is obviously true, that the word 'be'
or 'not be' has a definite meaning, so that not everything will be 'so
and not so'. Again, if 'man' has one meaning, let this be
'two-footed animal'; by having one meaning I understand this:-if 'man'
means 'X', then if A is a man 'X' will be what 'being a man' means for
him. (It makes no difference even if one were to say a word has
several meanings, if only they are limited in number; for to each
definition there might be assigned a different word. For instance,
we might say that 'man' has not one meaning but several, one of
which would have one definition, viz. 'two-footed animal', while there
might be also several other definitions if only they were limited in
number; for a peculiar name might be assigned to each of the
definitions. If, however, they were not limited but one were to say
that the word has an infinite number of meanings, obviously
reasoning would be impossible; for not to have one meaning is to
have no meaning, and if words have no meaning our reasoning with one
another, and indeed with ourselves, has been annihilated; for it is
impossible to think of anything if we do not think of one thing; but
if this is possible, one name might be assigned to this thing.)
    Let it be assumed then, as was said at the beginning, that the
name has a meaning and has one meaning; it is impossible, then, that
'being a man' should mean precisely 'not being a man', if 'man' not
only signifies something about one subject but also has one
significance (for we do not identify 'having one significance' with
'signifying something about one subject', since on that assumption
even 'musical' and 'white' and 'man' would have had one
significance, so that all things would have been one; for they would
all have had the same significance).
    And it will not be possible to be and not to be the same thing,
except in virtue of an ambiguity, just as if one whom we call 'man',
others were to call 'not-man'; but the point in question is not
this, whether the same thing can at the same time be and not be a
man in name, but whether it can in fact. Now if 'man' and 'not-man'
mean nothing different, obviously 'not being a man' will mean
nothing different from 'being a man'; so that 'being a man' will be
'not being a man'; for they will be one. For being one means
this-being related as 'raiment' and 'dress' are, if their definition
is one. And if 'being a man' and 'being a not-man' are to be one, they
must mean one thing. But it was shown earlier' that they mean
different things.-Therefore, if it is true to say of anything that
it is a man, it must be a two-footed animal (for this was what 'man'
meant); and if this is necessary, it is impossible that the same thing
should not at that time be a two-footed animal; for this is what
'being necessary' means-that it is impossible for the thing not to be.
It is, then, impossible that it should be at the same time true to say
the same thing is a man and is not a man.