Signs are of three kinds,
1st, the icon, which represents its object by virtue of a character which it would equally possess did the object and the interpreting mind not exist;
2nd, the index, which represents its object by virtue of a character which it could not possess did the object not exist, but which it would equally possess did the interpreting mind not operate;
3rd, the symbol, which represents its object by virtue of a character which is conferred upon it by an operation of the mind.
An icon represents its object insofar as it resembles that object. It conveys no information, nor does it put the mind into a position to acquire information. Yet the utility of icons is evidenced by the diagrams of the mathematician, whether they involve continuity, like geometrical figures, or are arrays of discrete objects like a body of algebraical formulae, all of which are icons. Icons have to be used in all thinking.