To say that God is a necessary being means to accept that He exists (with His attributes intact) in every possible world. It is not enough to say that He exists only in our world: this kind of claim will render Him contingent (present in some worlds - possibly in none! - and absent in others).

We cannot conceive of the World without numbers, relations, and properties, for instance. These are necessary entities because without them the World as we known and perceive it would not exist. Is this equally true when we contemplate God? Can we conceive of a God-less World?

Moreover: numbers, relations, and properties are abstracts. Yet, God is often thought of as a concrete being. Can a concrete being, regardless of the properties imputed to it, ever be necessary? Is there a single concrete being - God - without which the Universe would have perished, or not existed in the first place? If so, what makes God a privileged concrete entity?

Additionally, numbers, relations, and properties depend for their existence (and utility) on other beings, entities, and quantities. Relations subsist between objects; properties are attributes of things; numbers are invariably either preceded by other numbers or followed by them.

Does God depend for His existence on other beings, entities, quantities, properties, or on the World as a whole? If He is a dependent entity, is He also a derivative one? If He is dependent and derivative, in which sense is He necessary?

Many philosophers confuse the issue of existence with that of necessity. Kant and, to some extent, Frege, argued that existence is not even a logical predicate (or at least not a first-order logical predicate). But, far more crucially, that something exists does not make it a necessary being. Thus, contingent beings exist, but they are not necessary (hence their "contingency").

At best, ontological arguments deal with the question: does God necessarily exist? They fail to negotiate the more tricky: can God exist only as a Necessary Being (in all possible worlds)?

Modal ontological arguments even postulate as a premise that God is a necessary being and use that very assumption as a building block in proving that He exists! Even a rigorous logician like Gödel fell in this trap when he attempted to prove God's necessity. In his posthumous ontological argument, he adopted several dubious definitions and axioms:

(1) God's essential properties are all positive (Definition 1); (2) God necessarily exists if and only if every essence of His is necessarily exemplified (Definition 3); (3) The property of being God is positive (Axiom 3); (4) Necessary existence is positive (Axiom 5).

These led to highly-debatable outcomes:

(1) For God, the property of being God is essential (Theorem 2); (2) The property of being God is necessarily exemplified.

Gödel assumed that there is one universal closed set of essential positive properties, of which necessary existence is a member. He was wrong, of course. There may be many such sets (or none whatsoever) and necessary existence may not be a (positive) property (or a member of some of the sets) after all.

Worst of all, Gödel's "proof" falls apart if God does not exist (Axiom 3's veracity depends on the existence of a God-like creature). Plantinga has committed the very same error a decade earlier (1974). His ontological argument incredibly relies on the premise: "There is a possible world in which there is God!"

Veering away from these tautological forays, we can attempt to capture God's alleged necessity by formulating this Axiom Number 1:

"God is necessary (i.e. necessarily exists in every possible world) if there are objects or entities that would not have existed in any possible world in His absence."

We should complement Axiom 1 with Axiom Number 2:

"God is necessary (i.e. necessarily exists in every possible world) even if there are objects or entities that do not exist in any possible world (despite His existence)."

The reverse sentences would be:

Axiom Number 3: "God is not necessary (i.e. does not necessarily exist in every possible world) if there are objects or entities that exist in any possible world in His absence."

Axiom Number 4: "God is not necessary (i.e. does not necessarily exist in every possible world) if there are no objects or entities that exist in any possible world (despite His existence)."

Now consider this sentence:

Axiom Number 5: "Objects and entities are necessary (i.e. necessarily exist in every possible world) if they exist in every possible world even in God's absence."

Consider abstracta, such as numbers. Does their existence depend on God's? Not if we insist on the language above. Clearly, numbers are not dependent on the existence of God, let alone on His necessity.

Yet, because God is all-encompassing, surely it must incorporate all possible worlds as well as all impossible ones! What if we were to modify the language and recast the axioms thus:

Axiom Number 1:

"God is necessary (i.e. necessarily exists in every possible and impossible world) if there are objects or entities that would not have existed in any possible world in His absence."

We should complement Axiom 1 with Axiom Number 2:

"God is necessary (i.e. necessarily exists in every possible and impossible world) even if there are objects or entities that do not exist in any possible world (despite His existence)."

The reverse sentences would be:

Axiom Number 3: "God is not necessary (i.e. does not necessarily exist in every possible and impossible world) if there are objects or entities that exist in any possible world in His absence."

Axiom Number 4: "God is not necessary (i.e. does not necessarily exist in every possible and impossible world) if there are no objects or entities that exist in any possible world (despite His existence)."

Now consider this sentence:

Axiom Number 5: "Objects and entities are necessary (i.e. necessarily exist in every possible and impossible world) if they exist in every possible world even in God's absence."

According to the Vander Laan modification (2004) of the Lewis counterfactuals semantics, impossible worlds are worlds in which the number of propositions is maximal. Inevitably, in such worlds, propositions contradict each other (are inconsistent with each other). In impossible worlds, some counterpossibles (counterfactuals with a necessarily false antecedent) are true or non-trivially true . Put simply: with certain counterpossibles, even when the premise (the antecedent) is patently false, one can agree that the conditional is true because of the (true , formally correct) relationship between the antecedent and the consequent.

Thus, if we adopt an expansive view of God - one that covers all possibilities and impossibilities - we can argue that God's existence is necessary.