It might seem odd to list “existence” as an attribute of God, but that’s not actually the point here. Of course believers think that their god exists — what is at issue is how God exists. According to philosophical theism, God exists in a very special and unique way: God’s existence is necessary rather than contingent.
This is a particular philosophical differentiation which most people are probably unfamiliar with and certainly never have occasion to use in their daily lives. Nevertheless, it does play an important role in a variety of philosophical discussions, including theological debates.
Most things are regarded as existing contingently, which means that it is possible for them not to exist. Your computer is “contingent” in that its existence relies upon the prior existence of other objects and other processes. It is possible that none of them, however, would have given rise to your computer — thus, it is possible for your computer to never have existed.
Everything in the universe is regarded as “contingent.” God, however, is regarded as a being who exists in a radically different way. God doesn’t depend upon anything to exist. There are no prior objects, no prior beings, and no prior processes which gave rise to the existence of God. Being completely independent of everything, God isn’t contingent on anything. Thus, God does not exist contingently.
This means that God exists necessarily (this idea is sometimes expressed by saying that God is self-existent or by the Latin term aseity). The idea that God does not depend upon anything else for existence is not the only way to understand the idea of “necessary,” however. It is also possible for something to be logically necessary. A logically necessary proposition is one which must be true and cannot be false. The idea that God necessarily exists has been extended to incorporate the idea that God is logically necessary as well.
Therefore, it is argued by many theologians it isn’t possible for God not to have existed. We can conceive of the non-existence of computers and tables and planets, but not of God — indeed, the very idea of God not existing is conceived as being logically contradictory. The premise that if God does exist then God must exist plays an important role in the development of the Ontological Argument for the existence of God, first proposed by Anselm of Canterbury.
Being logically necessary does not seem to follow, logically or empirically, from the attribute of existing necessarily. Just because a being is not dependent upon anything for its existence does not appear to allow us to conclude that, therefore, any statement that it does not exist is a logical contradiction. Perhaps because of this many philosophers inclined to accept the first sense of God being necessary have not also accepted the arguments that God is logically necessary.
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