Er, no, I was just mistaken. (And forgot to retract the great-grandparent—done now.) For a pair of sets who do carve reality at (one of) its joints but still is like that, try A = {(10, 0), (30, 0), (50, 0), (70, 0)} and B = {(40, 1), (40, 1), (40, 1), (40, 1)}.
(What I was thinking were cases were A = {10, 20, 30, 40} and B = {11, 21, 31, 41}, where it is the case that “two random members of A are more alike than a random member of A and a random member of B”, and my point was that “Two random men are more alike than a random man and a random woman” doesn’t rule out {men} and {women} being like that.)
Er, no, I was just mistaken. (And forgot to retract the great-grandparent—done now.) For a pair of sets who do carve reality at (one of) its joints but still is like that, try A = {(10, 0), (30, 0), (50, 0), (70, 0)} and B = {(40, 1), (40, 1), (40, 1), (40, 1)}.
(What I was thinking were cases were A = {10, 20, 30, 40} and B = {11, 21, 31, 41}, where it is the case that “two random members of A are more alike than a random member of A and a random member of B”, and my point was that “Two random men are more alike than a random man and a random woman” doesn’t rule out {men} and {women} being like that.)
Ah, okay then. That makes sense.