I instantly disliked your terminology of true vs fake. If I understand it correctly, you are making a distinction between widely agreed upon quantification procedures (like measuring weight) and those which are are either not well defined or contentious (cheeseburger surplus). You do not seem to stipulate that the output of these procedures be useful in any way, but maybe it is implied? Anyway, I would call these “metrics”, not “numbers”.
If I were to try to quantify the “trueness” of these “numbers”, I would look into repeatability of the quantification procedures and their robustness to small deviations (an equivalent of well-posedness in mathematics) and, separately, their acceptance level, i.e. the fraction of the experts in the area who use the same procedure. This gives you at least two separate dimensions, and I am sure there are others I overlooked. Additionally, only useful metrics are worth putting an effort in, though I am not sure how to quantify usefulness in a repeatable, acceptable and useful way (trying to be reflectively consistent here).
In summary, I would first identify which metrics would be useful, then figure out several robust ways to design them, then work on the acceptance level.
Measuring weight is not a single procedure, it’s many procedures that agree, because they’re measuring something that “exists” in some sense. So I’d go the other way round, and first try to figure out which quantities “exist”, regardless of usefulness. That’s how electricity was discovered, it was pretty useless at first.
Also this text by Lawrence Kesteloot might be relevant.
Measuring weight is not a single procedure, it’s many procedures that agree, because they’re measuring something that “exists” in some sense.
I suspect that your definition of “exists” is circular. How can we tell if something exists other than by having “procedures that agree”?
That’s how electricity was discovered
What was discovered is “many procedures that agree”, like rubbing some materials resulting in sparks, similar sparks between objects during a thunderstorm, etc. These were eventually abstracted into the concept of electricity, which ended up being very useful in its predictive power and practical applications.
So I’d go the other way round, and first try to figure out which quantities “exist”, regardless of usefulness.
...And you do that by finding the “procedures that agree”.
Oh, and I find the content of your link rather presumptuous due to its failure of imagination. I can easily imagine that “their” equivalent of math, physics or comp sci has nothing in common with ours.
I instantly disliked your terminology of true vs fake. If I understand it correctly, you are making a distinction between widely agreed upon quantification procedures (like measuring weight) and those which are are either not well defined or contentious (cheeseburger surplus). You do not seem to stipulate that the output of these procedures be useful in any way, but maybe it is implied? Anyway, I would call these “metrics”, not “numbers”.
If I were to try to quantify the “trueness” of these “numbers”, I would look into repeatability of the quantification procedures and their robustness to small deviations (an equivalent of well-posedness in mathematics) and, separately, their acceptance level, i.e. the fraction of the experts in the area who use the same procedure. This gives you at least two separate dimensions, and I am sure there are others I overlooked. Additionally, only useful metrics are worth putting an effort in, though I am not sure how to quantify usefulness in a repeatable, acceptable and useful way (trying to be reflectively consistent here).
In summary, I would first identify which metrics would be useful, then figure out several robust ways to design them, then work on the acceptance level.
Measuring weight is not a single procedure, it’s many procedures that agree, because they’re measuring something that “exists” in some sense. So I’d go the other way round, and first try to figure out which quantities “exist”, regardless of usefulness. That’s how electricity was discovered, it was pretty useless at first.
Also this text by Lawrence Kesteloot might be relevant.
I suspect that your definition of “exists” is circular. How can we tell if something exists other than by having “procedures that agree”?
What was discovered is “many procedures that agree”, like rubbing some materials resulting in sparks, similar sparks between objects during a thunderstorm, etc. These were eventually abstracted into the concept of electricity, which ended up being very useful in its predictive power and practical applications.
...And you do that by finding the “procedures that agree”.
Oh, and I find the content of your link rather presumptuous due to its failure of imagination. I can easily imagine that “their” equivalent of math, physics or comp sci has nothing in common with ours.
Yeah, now I agree with your point.