I don’t see where I assumed that the groups were disjoint. My point was that “Two random men are more alike than a random man and a random woman”, while technically true, isn’t particularly informative about men and women.
Ah, my mistake. I thought you were saying that given your proposition is (asserted to be true), the idea that two random men are more alike than a random man and woman must be meaningfully true.
I don’t see where I assumed that the groups were disjoint. My point was that “Two random men are more alike than a random man and a random woman”, while technically true, isn’t particularly informative about men and women.
Ah, my mistake. I thought you were saying that given your proposition is (asserted to be true), the idea that two random men are more alike than a random man and woman must be meaningfully true.