Introduction

Abstract

In the realm of choice it is much simpler to reject error than to establish truth. This stringent proposition runs consistently through all thought and action which in any way present alternatives; the nature of the phenomenon is the infinity of possibilities and the belief that one combination of factors is superior to all others. To establish this kind of truth the physical sciences sometimes resort to a canvas and test of all alternatives rendering the selection of the best a matter of comparison with the desired criteria. Experience of one kind or another frequently intercedes to limit the spectrum of possible solutions and therefore to reduce the dimensions of the problem. To test a new mathematical proposition one has simply to demonstrate its derivation from the known in terms of procedural conventions internal to the system. This is a pure logic that limits procedural choice but nevertheless confronts the mathematician with a sometimes prodigious selection. In the area of physical work when a tool fails for a new purpose a new tool must be developed. The problem controls the tool and the inventor but he, the inventor, must select among all the materials and forms possible plus their combinations. The final test is the work itself. Yet the question of whether the new tool is the best of all possible tools cannot be definitely answered in nature, or in work, as it can in the case of a logical system such as mathematics. The data of mathematics are thought, the data of nature, action. Often they reflect each other but just as often they do not. Ultimately they appear to rest on experience which is the memory of nature and its reduction to thought.