Our discussion of the nature of physical concepts has shown that a main reason for formulating concepts is to use them in connection with mathematically stated laws. It is tempting to go one step further and to demand that practicing scientists deal only with ideas corresponding to strict measurables, that they formulate only concepts reducible to the least ambiguous of all data: numbers and measurements. The history of science would indeed furnish examples to show the great advances that followed from the formation of strictly quantitative concepts. (Holton and Brush 2001, 170)
(….) The nineteenth-century physicist Lord Kelvin commended this attitude in the famous statement:
I often say that when you can measure what you are speaking about and express it in numbers you know something about it; but when you cannot measure it, when you cannot express it in numbers, your knowledge is of meagre and unsatisfactory kind: it may be the beginning of knowledge, but you have scarcely, in your thoughts, advanced to the stage of Science, whatever the matter may be. (“Electrical Units of Measurement”)
Useful though this trend is within its limits, there is an entirely different aspect to scientific concepts: indeed it is probable that science would stop if every scientist were to avoid anything other than strictly quantitative concepts. We shall find that a position like Lord Kelvin’s (which is similar to that held at present by some thinkers in the social sciences) does justice neither to the complexity and fertility of the human mind nor to the needs of contemporary physical science itself—not to scientists nor to science. Quite apart from the practical impossibility of demanding of one’s mind that at all times it identify such concepts as electron only with the measurable aspects of that construct, there are specifically two main objections: First, this position misunderstands how scientists as individuals do their work, and second, it misunderstands how science as a system grows out of the contribution of individuals. (Holton and Brush 2001, 170-171)
(….) While a scientist struggles with a problem, there can be little conscious limitation on his free and at times audacious constructions. Depending on his field, his problem, his training, and his temperament, he may allow himself to be guided by a logical sequence based on more or less provisional hypotheses, or equally likely by “feelings for things,” by likely analogy, by some promising guess, or he may follow a judicious trial-and-error procedure.
The well-planned experiment is, of course, by far the most frequent one in modern science and generally has the best chance of success; but some men and women in science have often not even mapped out a tentative plan of attack on the problems, but have instead let their enthusiasms, their hunches, and their sheer joy of discovery suggest the line of work. Sometimes, therefore, the discovery of a new effect or tool or technique is followed by a period of trying out one or the other applications in a manner that superficially almost seems playful. Even the philosophical orientation of scientists is far less rigidly prescribed than might be supposed. (Holton and Brush 2001, 170-171)