Chapter 4, Partial Solutions and the Provisional Elimination of Elements of Complexity, part 1

Suppose that we never find out for certain whether x is unity or zero or something else, we then begin to experiment in a different direction. We try to find out which of the hypothetical values of x throw most light on other questions, and if we find that some particular value of x—for instance, unity—makes it easier than does any other value to understand things about y and z, we have to be very careful not to slip into asserting that x is unity. But the teacher would be quite right in saying to the class, “For the present we will leave alone thinking about what would happen if x were something different from unity, and attend only to such questions as can be solved on the supposition that x is unity.” This is what is called in Algebra “provisional elimination of some elements of complexity.” It might happen that one of the older pupils, specially clever at mathematics, but not very well disciplined, should start some point connected with the supposition that x is something different than unity. It would be the teacher's business to remind her: “At present we are dealing with the supposition that x is unity. When we have exhausted that subject we will investigate your question. But, till then, please do not distract the attention of the class by talking about what is not the business on hand at present.” If the girl forgot, the teacher might say: “I should very much like you to try your own suggestion in private, but please do not talk about it in class till I give you leave.”