“Isness” definitely doesn’t need to be transitive.
It can be used to give properties to a subject. An apple is crisp, red, and 100g. Crisp isn’t red, red isn’t 100g, and 100g isn’t crisp.
It can also be used to specify a general case. Honeycrisp is an apple. Golden Delicious is an apple. Fuji is an apple. All three of Honeycrisp, Fuji and Golden Delicious are distinct.
An apple is crisp, red, and 100g. Crisp isn’t red, red isn’t 100g, and 100g isn’t crisp.
True, but then crisp isn’t apple, red isn’t apple, and 100g isn’t apple: All your examples have the property that if x is y, then y isn’t x, which means it’s an asymmetric relation, while in the trinity there’s symmetry: The father is god, god is the father.
Honeycrisp is an apple. Golden Delicious is an apple. Fuji is an apple
We can go further and say that apples are fruit, and that Honeycrisp are fruit. That is transitive.
What you’re describing is a strict partial order, which is not an equivalence, but the whole thing being some sort of equivalence is kinda important if Trinitarians want to be monotheists. Equivalences need to be reflexive, symmetric and transitive, at least if you ask mathematicians.
