St Anselm of Canterbury stated that God is that than which a greater or better cannot be conceived or thought of. Since God is greater than can be imagined he must exist for he wouldn't be the greatest unless he existed.  This is called the ontological argument. 
Infinity of numbers argument
Some teach the following. We are able to think of the infinity of numbers so we could think of the idea of there being infinite good. God is identified with infinite good.

The Handbook of Christian Apologetics declares that we cannot think of anything at all being limited unless we know that infinity and unlimitedness is possible (page 69). It says that infinity is there even if we do not realise it and that it must have come from God. But we see so many different things around us and the things we judge as limited are seen as less than that. A child can see things as limited without realising that we are in infinite space and that numbers have no end.
But even if there were nothing at all, countlessness would still exist. 1 and 1 would still be 2 though there is nothing.
Infinity does not exist in one sense but in another it is real. This has nothing to do with God.

Existence is not a predicate or power
Believers hold that God is existence or God is being – because he causes existence he must be existence. Some say that there must be a that than which a greater cannot be thought for existence is a quality and so it would not be that than which a greater cannot be thought if it did not exist. But existence is not a quality or a power. There is such a thing as nothing. Nothing exists and you don’t say that a power or quality called existence causes it!
If there was nothing at all, 1 and 1 is still 2. This truth is not a power which is why it exists even if no God or anything exists.

When seen as a pointer to God rather than a proof
The New Catholic Encyclopaedia argues that the Anselm argument was not an ontological argument; ontological has to do with being and the nature of it. In other words, it is not scientifically or rationally proving that there is a being. What it is doing is saying is that one must believe in God as that than which a greater cannot be thought and since the understanding develops our insight to what this means we will see it validate and verify itself. In other words, we believe on faith and cannot understand God and the more we understand the more we see that God is that than which a greater cannot be thought and must exist. It is like believing that Napoleon lost everything at Waterloo and the more you understand it the more sure you are that it happened. It is only an argument that works for believers. It is not for unbelievers. Gaunilo, Anselm’s critic, said that it was mad for Anselm to define God arbitrarily and then claim to prove that definition and he argued that to imagine an island greater than which cannot be thought does not mean that island exists. Anselm replied that it was not arbitrary for God would have to be above human understanding and that his argument applies only to God and not to anything like an island that is greater than anything that can be conceived for the island might be beyond our understanding but it is not something that is as great as God who is infinitely great and perfect. I would reply that it makes no difference. What has quantity have to do with it if it is something than which a greater we cannot think of?

A priori
Some think they can tell by the argument that it is intended to be a priori. That is it does not argue from any existing thing that there is a God. If they are right then it argues that there is a God like one would argue that 1=1 which is an a priori truth. They declare that the premise that the supreme being is that than which a greater cannot be thought and the other premise that God must exist in reality when he is that than which a greater cannot be thought are both a priori meaning that the conclusion must be (page 23, Taking Leave of God). But we do not see their truth in the way we see 1=1 as true so they are not a priori and the argument fails.

What God?
The argument assumes that the personal three in one God of Christianity is that than which a greater cannot be thought. But why should it be this version of God, this idea? There are other ideas. If logic or theology need God to be a loving relationship between three "persons" then why three? With an infinite God you expect it to be countless persons.

If God is that than which a greater cannot be thought then how does the trinity come into all that?  The trinity doctrine says that God is only three persons. There are three persons in God. The attraction of the doctrine is the idea that these persons are united by love. So God is a community. But what if God is that than which a greater cannot be thought? An infinite community of persons would be greater than three.  A trinitarian God cannot be that than which a greater cannot be thought.
Kant and Hume
Kant and David Hume held that Anselm made a logical error. Anselm assumed that existence is a predicate - this is the notion that existence adds something to a definition (page 221, Philosophy of Religion for A Level, OCR Edition, Anne Jordan, Neil Lockyer and Edwin Tate, Nelson Thornes Ltd, 1999). In other words, existence is like a skin colour it is something an entity has or hasn't got. But to speak of an entity lacking existence is contradictory. An entity is what exists. So Anselm thought that existence is a property and God by definition cannot lack this property so if you understand what God means you must understand that he exists.

God creating the understanding of God?

Some think that the idea of God is so perfect that only God could help you think of him so the idea of God implies there is a God.  But man can never imagine God in reality.  Man can only think he can.  The argument then is an argument for imagining God into existence.  Even if there is a God you are not interested in him but in the one you imagine.

Prime Number

There is no greatest prime number but the ontological argument would seem to prove there is.  If the argument proves a maximally great God it proves a maximally great prime number as well.  There is a prime number than which a greater cannot be thought.  The number must exist in the mind.  It exists in reality as well for it cannot exist in the mind unless it really is a true number.  If the ontological argument works then it works if God is not a being but a number!!
Laying it to rest
There are other matters that are more important even than God and therefore have more right to be considered to be a power that which no greater or better can be thought. The that than which a greater cannot be thought isn't so great if it has unnecessary components. It should be basic. Why not say that intelligence is that than which a greater cannot be thought? Why not say that consciousness is that than which a greater cannot be thought? It makes more sense to say one of these things. Intelligence is better than love for love is dangerous and impotent without it. Consciousness is better than love for only conscious beings can love. The Bible describes God as love. It seems it would go for the idea that love, God, is that than which a better or greater cannot be thought. But then love is no use without intelligence. The Christian God is too complicated to be that than which a greater cannot be thought.
If you have a choice, do you want people to love or to serve God? It is better for people to love each other than for them to care about God. Efforts to prove or give evidence for God are disgraceful. The end result is always an idol!

St Anselm left the world nothing that should perturb atheists. Christians have little to do when they ponder over the pathetic argument he left. And that is why their nonsense has to be challenged.
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