branches of knowledge have this attracting power, in order that we may
have clearer proof that arithmetic is, as I suspect, one of them.

Explain, he said.

I mean to say that objects of sense are of two kinds; some of them do
not invite thought because the sense is an adequate judge of them;
while in the case of other objects sense is so untrustworthy that
further enquiry is imperatively demanded.

You are clearly referring, he said, to the manner in which the senses
are imposed upon by distance, and by painting in light and shade.

No, I said, that is not at all my meaning.

Then what is your meaning?

When speaking of uninviting objects, I mean those which do not pass
from one sensation to the opposite; inviting objects are those which
do; in this latter case the sense coming upon the object, whether at a
distance or near, gives no more vivid idea of anything in particular
than of its opposite. An illustration will make my meaning
clearer:--here are three fingers--a little finger, a second finger, and
a middle finger.

Very good.

You may suppose that they are seen quite close: And here comes the
point.

What is it?

Each of them equally appears a finger, whether seen in the middle or at
the extremity, whether white or black, or thick or thin--it makes no
difference; a finger is a finger all the same. In these cases a man is
not compelled to ask of thought the question, what is a finger? for the
sight never intimates to the mind that a finger is other than a finger.

True.

And therefore, I said, as we might expect, there is nothing here which
invites or excites intelligence.

There is not, he said.

But is this equally true of the greatness and smallness of the fingers?
Can sight adequately perceive them? and is no difference made by the
circumstance that one of the fingers is in the middle and another at
the extremity? And in like manner does the touch adequately perceive
the qualities of thickness or thinness, or softness or hardness? And
so of the other senses; do they give perfect intimations of such
matters? Is not their mode of operation on this wise--the sense which
is concerned with the quality of hardness is necessarily concerned also
with the quality of softness, and only intimates to the soul that the
same thing is felt to be both hard and soft?

You are quite right, he said.

And must not the soul be perplexed at this intimation which the sense
gives of a hard which is also