ne thing,
and then another, and so on _ad infinitum_, I form the idea of "All;"
so, by denying one thing and then other things, finally by denying All,
I arrive at the idea of Nothing.--But it is just this assimilation which
is arbitrary. We fail to see that while affirmation is a complete act of
the mind, which can succeed in building up an idea, negation is but the
half of an intellectual act, of which the other half is understood, or
rather put off to an indefinite future. We fail to see that while
affirmation is a purely intellectual act, there enters into negation an
element which is not intellectual, and that it is precisely to the
intrusion of this foreign element that negation owes its specific
character.

To begin with the second point, let us note that to deny always consists
in setting aside a possible affirmation.[98] Negation is only an
attitude taken by the mind toward an eventual affirmation. When I say,
"This table is black," I am speaking of the table; I have seen it
black, and my judgment expresses what I have seen. But if I say, "This
table is not white," I surely do not express something I have perceived,
for I have seen black, and not an absence of white. It is therefore, at
bottom, not on the table itself that I bring this judgment to bear, but
rather on the judgment that would declare the table white. I judge a
judgment and not the table. The proposition, "This table is not white,"
implies that you might believe it white, that you did believe it such,
or that I was going to believe it such. I warn you or myself that this
judgment is to be replaced by another (which, it is true, I leave
undetermined). Thus, while affirmation bears directly on the thing,
negation aims at the thing only indirectly, through an interposed
affirmation. An affirmative proposition expresses a judgment on an
object; a negative proposition expresses a judgment on a judgment.
_Negation, therefore, differs from affirmation properly so called in
that it is an affirmation of the second degree: it affirms something of
an affirmation which itself affirms something of an object._

But it follows at once from this that negation is not the work of pure
mind, I should say of a mind placed before objects and concerned with
them alone. When we deny, we give a lesson to others, or it may be to
ourselves. We take to task an interlocutor, real or possible, whom we
find mistaken and whom we put on his guard. He was affirming something:
w