Negative God
We cannot know what God is, but rather what He is not.
(Saint) Thomas Aquinas, Summa Theologica, Of The Simplicity of God
We know things only by comparison to other things – nothing exists except if something which is not-it also exists. For example, you identify your friend Bob by contrasting all of your friends who are not Bob. In fact, you go further: you contrast your friends from those people you know but who are not your friends. And, people you know from people you don't know. This goes on and on; it is one of the fundamental activities of a human brain.
We have names for those things which exist in our form of life: water, cups, friends, strangers. Now consider this: what is left when you eliminate everything for which we have a name?
This is the essence of what is called Apophatic theology – this is, if you can name an attribute of God, you're not talking about God. So, in a manner of speaking, God is whatever is left when you eliminate everything with a name.
Now, if you take that to be the definition of God (a so-called negative definition), then by definition God must exist. This might not be the old bearded man in the clouds version you grew up hearing about, but face it, you didn't really believe in that anyway, did you?