I think you meant to say something different with this paragraph, or I am confused:
Diagnostic dilution is always structurally invalid, but it misleads us specifically when the conclusion hinges on forgetting X . “Bob is a practising doctor, so Bob can prescribe medications, so Bob can probably prescribe Ozempic” is a fine inference because it goes through without forgetting that Bob is a doctor. But consider the same chain starting with “Bob is a vet”: now the inference does not go through unless we forget Bob’s job, and indeed the conclusion is false.
This does not seem to be an example of “diagnostic dilution”
X: Bob is a doctor (vet)
Y: Bob can prescribe medicine
A: Bob can prescribe Ozempic
“Bob is a doctor so Bob can prescribe medicine. Bob can prescribe medicine so Bob can probably prescribe Ozempic.” (Unsound, but turns out to be fine bc conclusion is about the same as “Bob is a doctor who can prescribe medicine, so Bob can probably prescribe Ozempic”, which is the sound version of the argument.)
“Bob is a vet so Bob can prescribe medicine. Bob can prescribe medicine so Bob can probably prescribe Ozempic.” Now we see why the argument is unsound—it can go wrong given a different premise.
I think you meant to say something different with this paragraph, or I am confused:
This does not seem to be an example of “diagnostic dilution”
X: Bob is a doctor (vet) Y: Bob can prescribe medicine A: Bob can prescribe Ozempic
“Bob is a doctor so Bob can prescribe medicine. Bob can prescribe medicine so Bob can probably prescribe Ozempic.” (Unsound, but turns out to be fine bc conclusion is about the same as “Bob is a doctor who can prescribe medicine, so Bob can probably prescribe Ozempic”, which is the sound version of the argument.)
“Bob is a vet so Bob can prescribe medicine. Bob can prescribe medicine so Bob can probably prescribe Ozempic.” Now we see why the argument is unsound—it can go wrong given a different premise.
Ok it does seem like an example then. Thank you for spelling it out.