republic (books 6 - 10)
I will try, I said; and I wish you would share the inquiry
with me, and say "yes" or "no" when I attempt to distinguish
in my own mind what branches of knowledge have this attract-
ing power, in order that we may have clearer proof that arith-
metic 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 un-
trustworthy that further inquiry 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 illus-
tration will make my meaning clearer: here are three fingers--
a little finger, a second finger, and a middle finger.
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.
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 differ-
ence made by the circumstance that one of the fingers is in the
middle and the other at the extremity? And in like manner
does the touch adequately perceive the qualities of thickness or
thinness, of 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.