try the doctrine upon a complex whole,
short of infinite, such as the number 695,788. Sir W. Hamilton would not,
I suppose, have maintained that this number is inconceivable. How long
did he think it would take to go over every separate unit of this whole,
so as to obtain a perfect knowledge of the exact sum, as different from
all other sums, either greater or less?"

[AZ] In reference to this last paradox, Mr. Mill quotes from
_Essays by a Barrister_: "There is a world in which,
whenever two pairs of things are either placed in
proximity or are contemplated together, a fifth thing is
immediately created and brought within the contemplation
of the mind engaged in putting two and two together....
In such a world surely two and two would make five. That
is, the result to the mind of contemplating two twos
would be to count five." The answer to this reasoning
has been already given by Archdeacon Lee in his Essay on
Miracles. The "five" in this case is not the sum of two
and two, but of two and two _plus_ the new creature,
_i.e._, of two and two _plus_ one.

[BA] The sense in which Sir W. Hamilton himself uses the word
_conception_ is explained in a note to _Reid's Works_,
p. 377--namely, the combination of two or more
attributes in a _unity of representation_. The second
sense which Mr. Mill imagines is simply a mistake of his
own. When Hamilton speaks of being "unable to conceive
as possible," he does not mean, as Mr. Mill supposes,
physically possible under the law of gravitation or some
other law of matter, but mentally possible as a
representation or image; and thus the supposed second
sense is identical with the first. The third sense may
also be reduced to the first; for to conceive two
attributes as combined in one representation is to form
a notion subordinate to those of each attribute
separately. We do not say that Sir W. Hamilton has been
uniformly accurate in his application of the test of
conceivability; but we say that his inaccuracies, such
as they are, do not affect the theory of the
conditioned, and that in all the long extracts which Mr.
Mill quotes, with footnotes, indicating "first sense,"
"second sense," "third sense," the author's meaning may
be more accurately expl