Edge case: A population of one. This one person is in charge of the whole population and of themself. If the only group is the whole population, this person is a leader.

The premise states that "someone is in charge of the set of no people". This someone does not belong to the set of no people, so this someone is the "ruler" of this empty set.

In a population of one, that one person would have to take on this charge.

But is it meaningful to say that someone is the "ruler of no people"? Is "ruler" to be considered as a purely mathematical concept, empty of any sociological meaning? Or does it imply that there should be at least one person who should follow the ruler's rules?

If the conditions required for a mathematical statement to be true also require that the words used to make that statement lose all meaning, is that mathematical statement valid?

Edge case: A population of one. This one person is in charge of the whole population and of themself. If the only group is the whole population, this person is a leader.

The premise states that "someone is in charge of the set of no people". This someone does not belong to the set of no people, so this someone is the "ruler" of this empty set.

In a population of one, that one person would also have to take on this charge and be a ruler.

But is it meaningful to say that someone is the "ruler of no people"? Is "ruler" to be considered as a purely mathematical concept, empty of any sociological meaning? Or does it imply that there should be at least one person who should follow the ruler's rules?

If the conditions required for a mathematical statement to be true also require that the words used to make that statement lose all meaning, is that mathematical statement valid?