“what we know” is inextricable from “how we know it”.
If we know something, but we don’t know how we know it, then how can it be verified/disproven?
If don’t know something, but we know how to know it (the color of the sky is found by looking at the sky), then that can be fixed (look at the sky). (Although that starts to get into “what is the sky”—the way you define it effects answers to questions like “what color is it”.)
E.g. say there is a test T for cancer C, for which n% of positives track to real cancer, and the cancer has a d% 5-year risk of death. However the test preferentially picks up on deadlier forms of the cancer, so given a positive result, your risk of death is higher than n*d/100.
If I say “you have cancer C”, you’ll assume you have a 5 year risk of death of d.
If I say “You have an n% chance of having cancer C”, you’ll assume you have an n*d/100 5 year risk of death.
If I say “You tested positive on test T”, you can discover your actual chance of death over 5 years. So knowing the test result rather than the summary, even the detailed summary, is more informative.
OTOH, your estimates in scenario 3 will be heavily dependent on who gets tested. If the governing body changes the testing recommendations, your chance of death given a positive result on T will change. So knowing “you have n% chance of cancer” is in some ways a more robust result.
If we know something, but we don’t know how we know it, then how can it be verified/disproven?
If don’t know something, but we know how to know it (the color of the sky is found by looking at the sky), then that can be fixed (look at the sky). (Although that starts to get into “what is the sky”—the way you define it effects answers to questions like “what color is it”.)
This feels like some of what I was getting at.
E.g. say there is a test T for cancer C, for which n% of positives track to real cancer, and the cancer has a d% 5-year risk of death. However the test preferentially picks up on deadlier forms of the cancer, so given a positive result, your risk of death is higher than n*d/100.
If I say “you have cancer C”, you’ll assume you have a 5 year risk of death of d.
If I say “You have an n% chance of having cancer C”, you’ll assume you have an n*d/100 5 year risk of death.
If I say “You tested positive on test T”, you can discover your actual chance of death over 5 years. So knowing the test result rather than the summary, even the detailed summary, is more informative.
OTOH, your estimates in scenario 3 will be heavily dependent on who gets tested. If the governing body changes the testing recommendations, your chance of death given a positive result on T will change. So knowing “you have n% chance of cancer” is in some ways a more robust result.