Change the range not the language on confidence intervals

There was a debate about naming the interval between Sander and Andrew in the British Medical Journal in 2019 where they each debated “compatibility interval” versus “uncertainty interval“. After reflecting on the argument between Fisher and Neyman-Pearson I believe that rather than compatibility, the purpose of the “realized interval” is uncertainty - i.e. uncertainty in the test hypotheses supported by the data. Can we say compatibility of the test hypotheses with the study data - we could perhaps but then is that really the core purpose of the interval? Sander stated that “ Nonetheless, all values in a conventional 95% interval can be described ashighly compatible with data under the background statistical assumptions, in the very narrow sense of having P>0.05 under those assumptions.“ These “values” are means of sampling probability models and therefore I could restate this as “ Nonetheless, all values in a conventional 95% interval can be described asthe range of test hypotheses supported by the data under the background statistical assumptions, in the very narrow sense of being less divergent from the data under those assumptions.“ That implies uncertainty (my view) rather than compatibility though I agree there may be a case for Sander’s compatibility. Terminology matters, and as Sander has stated, we should not co-opt words from English language whose everyday meanings are far from the statistical meaning - compatibility may be more so than uncertainty.