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In other words, the fact that the criterion we happen to use has a fine ancestry of highbrow statistical theorems does not justify its use. Such justification must come from empirical evidence that it works.
--
Shewhart, Walter A. (1931). Economic control of quality of manufactured product. D. Van Nostrand Company. p. 18. 

 

Walter A. Shewhart

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[On Empiricism] It is evident, on the basis of our considerations, that this appearance of success cannot in the least be regarded as a sign of truth and correspondence with nature. Quite the contrary, suspicion arises that the absence of major difficulties is a result of the decrease of empirical content brought about by the elimination of alternatives, and of facts that can be discovered with their help. In other words, the suspicion arises that this alleged success is due to the fact that the theory, when extended beyond its starting point, was turned into rigid ideology. Such Ideology is "successful" not because it agrees so well with the facts; it is successful because no facts have been specified that could constitute a test, and because some such facts have been removed. Its "success" is entirely man-made. It was decided to stick to some ideas, come what may, and the result was, quite naturally, the survival of these ideas. If now the initial decision is forgotten, or made only implicitly, for example, if it becomes common law in physics, then the survival itself will seem to constitute independent support., it will reinforce the decision, or turn it into an explicate one, and in this way close the circle. This is how empirical "evidence" may be created by a procedure which quotes as its justification the very same evidence it has Produced.

 

Paul Karl Feyerabend

 

Any theory based on experience is necessarily statistical; that is to say, it formulates an ideal average which abolishes all exceptions at either end of the scale and replaces them by an abstract mean. This mean is quite valid though it need not necessarily occur in reality. Despite this it figures in the theory as an unassailable fundamental fact. ... If, for instance, I determine the weight of each stone in a bed of pebbles and get an average weight of 145 grams, this tells me very little about the real nature of the pebbles. Anyone who thought, on the basis of these findings, that he could pick up a pebbles of 145 grams at the first try would be in for a serious disappointment. Indeed, it might well happen that however long he searched he would not find a single pebble weighing exactly 145 grams. The statistical method shows the facts in the light of the ideal average but does not give us a picture of their empirical reality. While reflecting an indisputable aspect of reality, it can falsify the actual truth in a most misleading way.

 

Carl Jung

 

To pass freely through open doors, it is necessary to respect the fact that they have solid frames. This principle, by which the old professor had always lived is simply a requisite of the sense of reality. But if there is a sense of reality, and no one will doubt that it has its justification for existing, then there must also be something we can call a sense of possibility. Whoever has it does not say, for instance: Here this or that has happened, will happen, must happen; but he invents: Here this or that might, could, or ought to happen. If he is told that something is the way it is, he will think: Well, it could probably just as well be otherwise. So the sense of possibility could be defined outright as the ability to conceive of everything there might be just as well, and to attach no more importance to what is than to what is not.

 

Robert Musil

 

What attracted me so strongly and exclusively to mathematics, apart from the actual content, was particularly the specific nature of the mental processes by which mathematical concepts are handled. This way of deducing and discovering new truths from old ones, and the extraordinary clarity and self-evidence of the theorems, the ingeniousness of the ideas... had an irresistible fascination for me. Beginning from the individual theorems, I grew accustomed to delve more deeply into their relationships and to grasp whole theories as a single entity. That is how I conceived the idea of mathematical beauty...

 

Ferdinand Eisenstein

 

To call out for the hand of the enemy is a rather extreme measure, yet a better one, I think, than to remain in continual fever over an accident that has no remedy. But since all the precautions that a man can take are full of uneasiness and uncertainty, it is better to prepare with fine assurance for the worst that can happen, and derive some consolation from the fact that we are not sure that it will happen.

 

Michel de Montaigne