Unconventional Religion

[Angrboda]

Leibniz's Law is a bi-conditional that claims the following: Necessarily, for anything, x, and anything, y, x is identical to y if and only if for any property x has, y has, and for any property y has, x has. Because this is a bi-conditional, it is comprised of two conditional statements (i) and (ii):

• (i) If x is identical to y, then for any property x has, y has and for any property y has, x has.
  
• (ii) If for any property x has, y has, and for any property y has, x has, then x is identical to y.
  

[note 1]

The Indiscernibility of Identicals

(i) is called the Indiscernibility of Identicals because it claims that self-identical object(s) must be indiscernible from themselves. It is a fairly uncontroversial thesis. I say "fairly" because there are philosophers who deny this claim. ... Almost everyone else, however, will grant that if something, x, is identical with something, y, then x and y have all of the same properties; x and y are just one thing, after all, merely called by two different names "x" and "y." If Superman is identical to Clark Kent, then Superman wears glasses and Clark Kent has x-ray vision (because Clark Kent wears glasses and Superman has x-ray vision). Since Superman is identical to Clark Kent, there is no property that Superman has that Clark Kent does not have, and there is no property that Clark Kent has that Superman doesn't; "they" are just one guy, after all, not two.

— Leibniz's Law, the Indiscernibility of Identicals, and the Identity of Indiscernibles

Fully human and fully divine?

According to Liebniz' law, which rests on classical logic and traditional ontologies, in order for two hypothetical things to be the same thing, they must share all the same properties. I am fully human. There are many properties of the divine which I lack. However, to be fully divine, I would have to possess all these properties. If a thing is any part divine in a non-human way, then they are not fully human. If they possess human characteristics which the divine do not possess, then they are not fully divine. The only way you can be fully divine and fully human and still be consistent with Liebniz' law is for the properties that make something divine to be the same as the properties that make something human. This is bad news for the Trinity. There are potential outs, however. You can give up traditional ontology (I think I might be able to get there using Stoic ontological principles). Most Christians would not be willing to do this, and giving up the ontological assumptions behind Liebniz' law leads to all sorts of unforeseen consequences; you can't just change ontologies without having everything else change as a result. Liebniz' law also rests on classical logic, and there are non-classical logics that you could appeal to in order to resolve the dilemma. Like changing ontologies, changing logics has consequences which most Christians would not be willing to accept. So the only remaining solution is to say that classical logic and ontology applies everywhere else, but it does not apply to Jesus and God. However, since you're still accepting classical logic in general, this is a case of special pleading, and it is therefore not logically valid and cannot be presumed to be true as a consequence of this logical error.

So, realistically, Trinitarian Christians have to accept one of three options: give up traditional ontology and Liebniz' law, give up classical logic, or accept that you can't get there from here. [note 2]


I leave it up to Trinitarian Christians which part of their worldview they want to give up.




[note 1] There are varying interpretations of what Liebniz' law is and how it should be stated; I've stated here an interpretation which is convenient to the structure of my argument, but which I believe is essentially non-controversial.

[note 2] And the logic you replace classical logic with has to satisfy certain criteria; without doing too much thinking about it, the law of non-contradiction would likely have to go in its classical form. I believe the class of logics described by such maneuvers is generally termed paraconsistent logics.