An ontological argument, then, has to do with existence in some way. It argues that something about existence--about the nature of existence--leads to God.
The most famous version is St. Anselm's from the Prosologion:
"God, by definition, is that for which no greater can be conceived. God exists in the understanding. If God exists in the understanding, we could imagine him to be greater by existing in reality. Therefore God must exist."Let's break that down:
1. God is that for which no greater can be conceived.
By definition, God is the greatest being that can be imagined. We cannot imagine anyone, real or not, greater than God. This is a definition, or a starting point, for the argument. This is the kind of God we're discussing and, if successful, proving to exist.
2. God exists in the understanding.
Simply, we can imagine God. All of us, believers and unbelievers, can understand what is meant by the name "God" and hold the idea in our minds. This seems non-controversial.
3. If God exists in the understanding, we could imagine him to be greater by existing in reality.
Is it "greater" to exist or not exist? It seems reasonable that existence is better than non-existence. You cannot do anything or be anything without existence. Everything we experience requires existence.
4. Therefore, God must exist.
Here is the logical leap, and not everyone is comfortable making it. God is the greatest possible being. It is greater to exist than not exist, therefore an existing God is greater than a non-existing God.
Which God do we have? Let's assume it's imaginary-God. In that case, there is something greater: namely, real-God. Real-God is greater than imaginary-God. So, by definition (God is that which nothing is greater), imaginary-God can't be our God. That leaves the other option: real-God.
Others have followed on with their own forms of the ontological argument. I'm a New Jerseyan, so I feel obliged to mention Kurt Gödel's ontological proof. It can be a difficult read, especially if you're not familiar with modal logic.
Catholic apologist Dave Armstrong analyzed several versions in his post on The Ontological Argument for God's Existence: A concept greater than which first meets the eye.
Dr. William Lane Craig defends the ontological argument against several criticisms in a video on The Ontological Argument and Objective Morality. He briefly describes a version of the argument based on possible worlds (created, I believe, by Dr. Alvin Plantinga) in What is the Ontological Argument?
What does this have to do with my life? We'll get into the Christian life eventually--step-by-step--but for now consider what the YouCat says in response to the question of being free to pursue evil:
"Man is freest when he is always able to say yes to the good; when no addiction, no compulsion, no habit prevents him from choosing and doing what is right and good. A decision in favor of the good is always a decision leading toward God." (YouCat Q. 287)If God is the greatest possible good--the maximal good--then any movement toward good must be a movement toward God. Any movement, however small, toward any good, however small, is a movement toward God. That gives us such hope! The fallen-away Christian who still seeks a good, perhaps by caring for his family or by seeking truth academically or by serving a charity, is still turning in some way toward God. The atheist who authentically seeks to know and do good is, unknowingly, seeking God. And God has promised us that all who seek find. (Mt 7:7)