Was thinking today about the modal ontological argument specifically as it relates to our multiple conceptions of God across civilizational history - wanted to formalize it.

Essentially the fundamental argument here is that, by necessity, either the S5 argument used in the modal ontological argument leads to a multiplicity of possible deities that, by the ontological argument itself, must exist.

Let me know if anyone finds any counterarguments/issues in the logic here - there are certainly axiomatic counterarguments, but I've workshopped a few of them and they seem weak?

Definition 1: Property P is positive iff it contributes to greatness.
Definition 2: X is God-like iff X has all positive properties.
Definition 3: X necessarily exists iff X exists in all possible worlds.

Axiom 1: If P is positive and P entails Q, then Q is positive.
Axiom 2: Either P is positive or ¬P is positive, not both.
Axiom 3: God-likeness is positive.
Axiom 4: Necessary existence is positive.

Definition 4: A divine conception is a set of attributes that could coherently belong to a greatest possible being.

Lemma 1 (Conception Multiplicity): Multiple coherent divine conceptions exist.
Proof:

Empirically observable across religious traditions (personal/impersonal, trinity/unity).
These conceptions differ substantively yet each maintains internal coherence.
Each can be articulated without logical contradiction.

Challenge 1: "But seemingly contradictory attributes (justice vs. mercy) must reconcile in a unique maximal being!"
Response:

Reconciliation attempts typically employ one of three strategies:
a) Definitional gerrymandering (redefining justice until it's compatible with mercy).
b) Mysterious transcendence ("They're reconciled beyond human understanding").
c) Hierarchical subordination (one attribute trumps the other).
Each strategy fails:
a) Creates vacuous concepts that lose normative force.
b) Renders the conception unfalsifiable and meaningless.
c) Admits multiple possible hierarchies → multiple conceptions.

Definition 5: A conception parameter φ is any attribute dimension admitting multiple coherent values.

Lemma 2 (Parameter Space): Divine conception space contains multiple independent parameters.
Proof:

Consider attributes: consciousness type, moral character, relation to time, aesthetics.
These vary independently (personal timeless being ≠ impersonal timeless being).
Each parameter admits mul

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