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For if Agamemnon could not count his feet (and without number how

could he?) he must have been a pretty sort of general indeed. No

man should be a soldier who cannot count, and indeed he is hardly

to be called a man. But I am not speaking of these practical

applications of arithmetic, for number, in my view, is rather to

be regarded as a conductor to thought and being. I will explain

what I mean by the last expression:-Things sensible are of two

kinds; the one class invite or stimulate the mind, while in the

other the mind acquiesces. Now the stimulating class are the

things which suggest contrast and relation. For example, suppose

that I hold up to the eyes three fingers-a fore finger, a middle

finger, a little finger-the sight equally recognizes all three

fingers, but without number cannot further distinguish them. Or

again, suppose two objects to be relatively great and small,

these ideas of greatness and smallness are supplied not by the

sense, but by the mind.