Every relation that is transitive and irreflexive is asymmetrical. |
But it is not irreflexive either, since 1 is related to itself. |
The argument is that without distinct individuals that are metaphysically prior to the relations, there is nothing to stand in the irreflexive relations that are supposed to confer individuality on the relata. |
Every asymmetrical relation is irreflexive. |
A relation on a set is irreflexive provided that no element is related to itself. |