CHAPTER I - ON THE NATURE OF A CALCULUS

Summary

Signs. Words, spoken or written, and the symbols of Mathematics are alike signs. Signs have been analysed into (α) suggestive signs, (β) expressive signs, (γ) substitutive signs.

A suggestive sign is the most rudimentary possible, and need not be dwelt upon here. An obvious example of one is a knot tied in a handkerchief to remind the owner of some duty to be performed.

In the use of expressive signs the attention is not fixed on the sign itself but on what it expresses; that is to say, it is fixed on the meaning conveyed by the sign. Ordinary language consists of groups of expressive signs, its primary object being to draw attention to the meaning of the words employed. Language, no doubt, in its secondary uses has some of the characteristics of a system of substitutive signs. It remedies the inability of the imagination to bring readily before the mind the whole extent of complex ideas by associating these ideas with familiar sounds or marks; and it is not always necessary for the attention to dwell on the complete meaning while using these symbols. But with all this allowance it remains true that language when challenged by criticism refers us to the meaning and not to the natural or conventional properties of its symbols for an explanation of its processes.