The Australian philosopher, Douglas Gasking (in an essay, "Mathematics and the World", included in The World of Mathematics (19xx), V. III, Ed. James R. Newman) tells us that mathematics and logic are incorrigible, whereas physics is corrigible.A given declaration ("pattern"!) of logico-mathematics is incorrigibly what it's said to be. You don't change it for not applying or seeming useful. Rather, you leave it unchanged and replace it by another declaration ("pattern").
But, when a declaration ("pattern") of current physics fails, we change the pattern itself.
We can use incorrigible patterns as figures (Figure&Ground) to expose corrigible patterns as grounds.
Example: In the kitchen fill a vessel with 2 cups of water; then 2 more cups of water; stirring. You'll fil this measures out to 2 cups of water. (So what?) Now do the same with 2 cups of alcohol, and 2 more cups of alcohol; result: measured out 4 cops of alcohol. (Patience!) Now mix 2 cups of water and two cups of alcohol. You''ll find that they don't quite measure out to 4 cups of liquid. Why? Molecules of water and alcohol differ in size. The result here is comparable to mixing 2 barrels of tennis balls with 2 barrels of ping-pong balls, wherein ping-pong balls fit in the interstices that tennis balls cannot fill. THIS IS A FAILURE OF APPLICATION OF ARITHMETIC TO CHEMICAL PHYSICS, RESULTING IN BETTER UNDERSTANDING OF MOLECULAR CHEMISTRY.
And this F&G strategy induces WIN-WIN hypotheses. If the hypothesis is confirmed, you WIN. If not, its Figure-of-failure vs. its Ground-of-disagreement may expose something you'd never know or think of investigating! So, you WIN, after all!
I formulate a homology to explain the value of INCORRIGIBILITY to CORRIGIBLE science. firmground: load:: mathematics: science. If you had to push a load, such as an automobile, which ground would you rather stand on for the pushing: concrete? or an ice sheet? If the latter, you'd move youself rather than the load. If a CORRIGIBLE basis were used to assist in evaluating science, and if "failure" occurred, you might not be sure that the "failure" was due to the science or the "ground" used. By remaining INCORRIBIBLE, the "failure" can be recognized in science.(This doesn't work for Alternative Science, which doesn't risk formulating hypotheses-subject- to-tests.)