“Doctors make the worst patients, but some believe the converse may also be true − that patients make the best doctors.”
Is the second statement really the converse of the first if it switches “worst” to “best”?
Nope. It’s not really a good fit for that sort of analysis; if we state p: X is a good doctor, and q: X is a good patient, then we can say “if p, then not q”; the closest we can come to the second proposition is “if q, then p,” which doesn’t bear much relationship at all to the first.
Premise: “If you have East Asian genes, your eyes exhibit the epicanthic fold.” (For purposes of this post, never mind whether it is a valid premise, a stereotype, or what.)
Converse: “If your eyes have the epicanthic fold, you have East Asian genes.”
Inverse: “If you do not have East Asian genes, your eyes do not have epicanthic folds.”
Contrapositive: “If you do not have the epicanthic fold, then you do not have East Asian genes.”
A premise and its contrapositive are logically related – if one is true, the other is true as well. Its inverse and converse are also logically related in the same way – each is the contrapositive of the other – and are not logically related to the original premise.
Strictly speaking, the converse would be “Non-doctors are not the worst patients.”
So, to call “Patients make the best doctors” the converse is to assume tacitly that
[ol]
[li] to be a non-doctor is equivalent to being a patient, and[/li][li] to be a non-worst-patient is equivalent to being a best-doctor.[/li][/ol]
Another vote for: It’s not the converse, and the concept of “converse” doesn’t even really apply to that kind of statement.
The converse of a conditional statement “If P then Q” would be “If Q then P.” So, you could say that the converse of “If a person is a doctor, they’re a bad patient” would be “If a person is a bad patient, they’re a doctor.” (I hope it’s obvious that the converse is not logically equivalent: just because a conditional statement is true doesn’t make its converse true.)
The inverse of “If P then Q” would be “If not P then not Q.” So, you could say that the converse of “If a person is a doctor, they’re a bad patient” would be “If a person is not a doctor then they’re not a bad patient.” (This is not logically equivalent to the original statement, but it is logically equivalent to its converse.)
Oops. What I gave isn’t strictly speaking the converse. My statement just means the same thing as the converse. Thudlow Boink gave the actual converse.
In the early 1980s, I went to New Orleans. I guess it was the peak of the Urban Cowboy fad, and there were country & western beer halls with mechanical bulls in them. One was selling a bumper sticker, “If you ain’t a cowboy, you ain’t sh__” At the time, I thought the converse might prove it, that is, “If you are a cowboy, you are sh__.”
Years later, I got to know some cowboys, and I know they aren’t.
Now, would microbiologists make the best, or the worst sauerkraut?
The first claim has the form p ==> ¬q. Its converse is ¬q ==> p, which is equivalent to ¬p ==> q. The second claim is that q ==> p. So it is nothing like the converse. Maybe vice versa would describe it better…