To expand further. The principle that agreement between multiple detectors can increase our epistemic confidence in what each of them are claiming is not just a theoretical proposal. I argue that we’ve seen a nice demonstration of this principle in action in the case of the proton radius puzzle, which started around 2010 when the value of the the proton radius measured by a new method (muonic hydrogen) disagreed starkly with previous values.
A flurry of further precise measurements on the proton radius using different methods were then pursued over the next decade, with a greater level of precision and care than attempted before. The majority of them agreed with the new value. Finally, in 2019 the results of a very different method (electron-scattering) also agreed with the new value. At this point people started saying that the puzzle had been solved.
Now, if we only valued predictions and not postdictions, then all of the results after 2010 would be epistemically meaningless, even if pursued with very different methods. After all, they already knew the new value that they “wanted”, and was biased towards it.
But that’s a simplistic take. In reality, many careful practices are put into place to reduce the effect of personal bias. For example, many precision measurement groups blind the absolute value of the quantity they are measuring and only reveal it at the very end, after all of the analysis is finished. This prevents tweaking with the parameters of the data analysis until they agree with what one “thinks” is the right answer. This practice is also carried out in LIGO in the form of “false injections”, where a separate team has the job of secretly sending in fake signals into the apparatus and testing to see if those pass the analysis routine.
These careful, bias-reducing practices further justify why we don’t seem to care so much about the temporal order of results. What matters is whether a measurement is precise, rigorous, carefully studied, and well-understood, regardless of the time when it was performed. A more precise measurement that comes more recently is always going to be valued over an older measurement that is cruder.