Simple example: how switching identification procedures swaps patients

Here is a concrete example.   We want to count gannets.

1. There is one gannet above the water.
2. There are two gannets under the water.
3. There are two pigeons above the water and pigeons don’t swim.
4. At any given time, the gannets under the water cannot be the gannets above the water.
5. And by genetic definition the gannets cannot be the pigeons.
6. Thus, we are confronted with two genetically defined species and two circumstances.
7. Forensic Procedure: If I select and define my population of “gannets” by way of DNA identification, I identify the one gannet which was above the water and the two gannets that were under the water. The pigeons are not a genetic match, and so I eliminate them from the count. What underlies my claim of “three gannets” are all gannets.
8. Circumstantial Procedure: Later, I select and define my population of “gannets” by the circumstance where gannets spend a lot of time — flying above the sea. My conclusion is human but untenable, “Therefore, what flies above the sea is a gannet.” If I find three birds above the water, I simply check them off on my clipboard, calling them “three gannets” … because they fit the circumstantial definition imposed upon them by my chosen identification procedure. I have one gannet, it is true, but I also have two pigeons which are simply renamed, “gannets,” because they happened to be flying above the water too.
9. If I use the DNA examination (7) to prove to a purchaser how many gannets there are but then use the circumstantial definition (8) when actually selling them, I swap out the submerged gannets used in the advertisement and swap in the pigeons for the sale, employing a bait-and-switch scheme.

“Above” and “Below” the water is above and below a circumstantial cutoff point. Given that DNA testing put us closer to the original aim and established a statistical fact, opting later for a circumstantial judgment effectively de-identifies the underwater gannets and the flying pigeons, swapping them when switching identification procedures. The transfer is the same when the FH were first identified in genetic terms when claiming prevalence and underdiagnosis, but then later identified circumstantially when sold treatments.