with me, and say “yes” or “no” when I attempt to distinguish in my own mind what 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 obects sense is so untrustworthy 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 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 the other at the extremity? And in like manner does the touch adequately perceive the qualities of thickness or
