Is God a necessary being?

This question falls into an area of modal logic ie modal logic describes the relationship between what is necessary and what is contingent or possible and what is impossible. Or what has to exist necessarily or self existent or what exist contingently ie is possible but not necessarily so.

One way to do this logically is to imagine multiple possible worlds ie you have the actual world/universe and then what the universe could have possibly been given different circumstances.

A thing or being or truth that exists necessarily is something that exists in all possible worlds including the actual world. It requires no further explanation because there is no logical/coherent way of imagining it as anything else. For example the equation 2 + 2 =4 is something we would not attempt to explain further because it is more plausible to assume it could not possibly be something else. That is, it is true in all possible worlds.

A thing or being that exists contingently may possible exist or not exist in some possible world ie my friend John exists in this world, but does not exist in all possible worlds ie I can imagine a possible world whereby given different circumstances John would not exist. I can therefore reasonably ask "where did John come from?" or "How is John here?"

So we could formulate an argument with a starting proposition

"If John exist, he exists as a necessary being."

To pull down the premise I would simply have to provide a logically coherent example of a possible world where John does not exist. I could say for example, "If John's parents had never met then John would not exist. Therefore John is not a necessary being because he does not exist in all possible worlds.

Or I could start with the proposition

"If 2 + 2 = 4 is true then it is necessarily true (ie true in all possible worlds).

To pull down the argument I might say, perhaps there is a possible world where the laws of mathematics are different ie if the starting conditions at the big bang messed up the maths somehow.

The one making the premise could then logically ask you, "then why is 2 + 2 = 4 true in the actual world?" And if a plausible coherent explanation could not be provided, then it would stand as true that 2 + 2 = 4 is more plausibly understood as a necessary truth ie true in all possible worlds.

So we then apply that to the question about how God is possible and I will put forward the proposition

"If God exist, He exists as a necessary being."

It would be up to you then to describe coherently a possible world where God did not exist. If you succeeded you could then logically ask yourself question ie "how could God exist?" If not then the answer would be the same as for the question how is 2 + 2 = 4. Because it is necessarily - ie there is no logically coherent alternative.

Because God by definition is a necessary being the atheist cannot simply deny God's existence on the basis of lack of evidence. To deny God and remain logically coherent he must demonstrate why God cannot exist in ANY possible world(to do so only requires he can imagine one possible world where God does not exist).

Otherwise it stands as more plausible that God exists rather than not.