The Ontological argument (non-modal)

P1. There does not exist a being such that none greater can be conceived [assumption for reductio]
P2. For all beings whose existence can be negated, that being is not as great as a being whose existence is not negatable.
P3. That none greater can be conceived's is not as great as a being whose existence is not negatable
P4. There cannot be a being who is both that which none greater can be conceived and not as great as others.
C. There exists a being such that none greater can be conceived.
Potential objections.

Thomistic: see pic

Response: Anyone who accepts the first premise does so in hopes of denying it, thus the atheist and the theist both accept the essence must signify the same thing. The rest follows by reductio and avoids issues of circularity.
Kantian: Existence isn't a predicate.

Response: At no premise was existence predicated to God, rather, it was treated as a connective in the first premise, and addressing the nature of the premise in the 2 and 3rd premises.
Gaunilo: This logic would not apply to an Island whose existence is none greater.

Response: Particulars like Islands, Pizzas, etc, are by the necessity of the reductio instances of finite beings, whose existence is limited by their essences. God is not necessarily a particular.
Humian objection: A priori terms are definitional, God only definitionally exists.

Response: The premise "All A priori terms are definitional" is a definitional statement or an empirical one. If the former, it's self-refuting, if not, it's not universal as no inductive claim is.
Gasking's objection: A non-existent God creating the universe is a greater God, therefore God doesn't exist.

Response: Non-existent entities cannot stand in causal relationships, as the negation of existence is the negation of causal powers.
Russel's objection: The essence of an entity can be described and their existence still remains in question.

Response: No essence was described in the positive, but only in the negative. Namely, he is not an entity whom any other is greater.
Subjective objection: Greatness is not an objective property.

Response: This is false, in areas like math and logic, there are criteria for better or worse systems. Simplicity is one example of this. Since science is committed to the existence of these metrics, so are we.
Ahmed's objection: a non-negatable existence is not a great-making property.

Response: All negatable existences are contingent on a contingent factor, and thus their greatness is limited.
Law's objection: Does an evil God necessarily exist as well?

Response: A being such that none evil can exist is a self-harming being, and would thus be a self-limiting and self-hindering being. If not, then there could hypothetically be a worse being.
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