Anselm's Ontological Argument
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 frequently called the ontological argument. An ontological argument is one that is based on the study of existence (ontology) - it argues that God's existence is proven for God by definition is existence itself.
His critic Gaunilo argued that if you imagine the best possible island that does not mean it exists. Anselm replied that the island was different and that the island would never be that than which a greater cannot be thought. Gaunilo would have agreed with Anselm's critics who accused Anselm of thinking his mind was good enough to conceive God and to imagine him into existence! God would be too great to be understandable by the human mind. If that was Anselm's aim then he was making a God in his head and worshipping an idol.
The Maximally Great Being
In his Proslogion, Anselm stated, “God is that than which a greater cannot be thought." So there is nothing greater or better than God who is perfection itself. But is God really perfect? He lets evil happen and sometimes even commands it for the sake of a greater good. But the fact remains there is nothing perfect about any of that. Anselm's point indicates that no being can be God. Anselm didn't mean to infer that! He denied the inference in order to make a new case for God based on how God is that than which a greater cannot be thought.
You would need to deal with evil before you could say God is the greatest. He didn't do that. It is very wrong to try and prove God's existence unless you look at evil first. People come before faith and people come before your belief in God.
Playing with words
That than which a greater cannot be thought would actually be a being that cannot be conceived. In other words, it is too strange and incomprehensible to be conceived. All believers claim to know that God is there but they deny that they can understand God. In truth, we cannot understand the smallest atom. So Anselm's argument fails simply because it is about words and it does not know what it is talking about. It's simple logic. If God is nothing like what we can imagine then we cannot prove him the way Anselm may have tried to for we don't even know what we mean.
If God is that than which a greater cannot be thought then no being is God. An illogical God who is perfect and able to reproduce himself infinitely would be better. And our idea of what is greater is imperfect. We would need to be as wise as God to know what that than which a greater cannot be thought means and is. Anselm just led to people thinking God into existence - ie inventing him for themselves.
It is replied by believers that an illogical God who does only good is not better than a logical God who only does good. The illogical God can make it good to put innocent people in Hell for no reason. But what if he could but does not? What if this illogical God does all the things a logical God would do?
In the Proslogion, Anselm says, "God is that than which a greater cannot be thought God could not be this if he did not exist so God exists. We have the idea that God would be that so it must be the same in reality as well if he is that than which a greater cannot be thought.” There is little agreement about what this means. It is taken for an ontological argument but even that is not certain. An ontological argument is about being - it is about showing a being exists.
It is debated if Anselm really gave an ontological argument.
It is debated that the argument is meant to be a proof such as would convince unbelievers.
It is debated if the argument is philosophical or theological. Perhaps Anselm is not giving an argument for God for others but merely speaking from his own experience that tells him that God must exist for his faith is so strong.

The argument says that God is that than which a greater cannot be thought. It is said that if this is a definition of God then the argument is an ontological argument. Those who deny that the argument is ontological say that the assertion is not a definition but merely an attempt to make us see how beyond all our ideas of greatness God must be. Gaunilo mistook the argument to be saying that God is the greatest possible being but that would be a definition. But rather than a definition of God the argument says that God is mysterious and undefinable.
Is God Logically Necessary?
Anselm may have argued that once you understand what God is you will see that God must exist just like when you know what 1 is and what 2 is you will know that 1+1 are 2. In other words, it would be logically necessary for God to exist just as it would be logically necessary for 1+1 to be 2. The idea of God is full of paradoxes meaning you don’t know if it is coherent unless you have logical proofs that he exists which would show that it must hold together. Therefore the proof would be no good unless there were other proofs for God’s existence. You have to prove God exists to be sure that you understand what he is before Anselm's argument can work. No such proof exists and all that are offered as proof are just superstition. It cannot stand alone as a proof - it is only a proof if God is proved other ways first.
Some say, and Anselm might have meant, that if it is logically possible that God exists he must exist. The argument fails because it assumes that we know all about what is logically possible and logically impossible. We do not. Perhaps if we think it is logically possible for there to be a God there is some unknown reason why we are wrong. It is logically possible to our minds that there might never have been a God so if this means that there is no God then it means there is no God. If the argument works one way, it works the other. To accept the argument would really to be make yourself out to be a better God than God and become a know-all.
Imagine there is nothing not even God. The thought makes sense. It could have happened. So God’s non-existence is a logical possibility – it could have happened.
The critics have said that versions of the argument that say it is about God being a logically necessary being fail for something could be logically necessary without us being aware of it (page 42, Reason and Religion). But if God can be logically done without in our minds then he should be dropped for the sake of simplicity and simplicity is inseparable from rationality. This should be done even if we are wrong for we don’t know and have to do our best. And if there were a God we would know for he would raise our intelligence to perceive that he exists. They say it would destroy our freedom to believe but belief is not faith which is belief mixed with commitment so who cares? When we can reason about spirits and about causality and necessity and still cannot see how God has to exist like 1 has to be 1 then it follows that he is NOT logically necessary.

Modal version 
This version of Anselm’s argument is the modal version and is spelled out in the Handbook of Christian Apologetics (page 71). It presupposes that God is a consistent concept for if God were not it would not be logically possible for him to exist. But you have to deal with the problem of evil and with many others for example the creation problem before you can say that and these people all put these things down as inscrutable mysteries! The possible world version says that it is possible that there is a world where that than which a greater and better and more powerful cannot be thought exists and if it exists in that world it exists in all possible worlds and in this one. It too relies on God being a consistent idea. This version has been used and defended by Plantinga.
The Christian belief is that God is like a thought - you cannot detect him but he is there had he is not a material being and has no parts. In other words he is spirit. But we don't know if spirit is a coherent concept. It is not true that thoughts are like spirits. We know they are caused by powers in the brain so they are not like ghosts.


Is Anselm's argument really about God?


Surprisingly the argument is more about the existence of spirit than of God as such!  If spirit cannot exist or if for some reason an infinite spirit cannot exist then clearly there is nothing more to be said.  There cannot be a God.  Spirit being possible does not mean there is a God.  But spirit being impossible means there cannot be a God!


The believers in God always use an ontological argument without realising it when they say an entity can exist and have no components.  Believers imagine it is possible for something to exist and have no parts or material composition.  But they only imagine.  There is no way of learning anything about spirit or if it is possible.  You cannot sense it.  And as a material being nobody could expect you to.  You cannot expect a being who only sees black and white to understand what pink is.  The believers are guilty of thinking, "I can imagine such an entity therefore it exists."  That is even worse than arguing that if God makes sense he exists.  Behind all ontological arguments or arguments for God based on Anselm is the dreadful and arrogant attempt to imagine God into existence!  If that is what you have to do to believe in God then the argument leads to you doing evil in order to believe and no seriously good God would accept worship from you!  No unbeliever could be expected to respect your belief in God for the belief does not respect God either!  Belief in God would be against science too for science knows that nothing can be imagined into existence!
Other views

Others think that Anselm was not giving a philosophical proof for God but was merely saying that when you see that if God exists he has to be that than which a greater cannot be thought you will see evidence of this in your own spiritual life and you will sense it and you will understand this in your mind and see that God must exist in reality and not just in your mind or thinking.

Another interpretation of Anselm also holds that he was not trying to prove God at all. It says he was only wondering how it could be true that God exists if God exists. In other words, he wants to know how God can make himself exist and concludes that it is because he is so great that he causes himself to exist. Since he is the greatest in the mind being that than which a greater cannot be thought he is the greatest in reality.

Descartes taught that when you have the concept of God as that than which a greater cannot be thought this thought must have been made by a being as great for thoughts are real things and what is a great thought can only be created by a greater and better being. This argument is defended in the Handbook of Christian Apologetics (page 68). So the idea of God proves that God exists by virtue of the design argument. He is assuming that good things can only be made by equally good or better things which is wrong. If nothing, not even God existed, there would be some good in that so good has to exist the same way as 2+2 have to be 4 and does not require a creator or anything to exist to be true.


Also, we cannot really imagine what God is like with any accuracy. Can you imagine what it is like to be a being without parts? You cannot. So, how can you imagine God? The thought of God does not prove that he exists for we cannot think of what God is like but only what our experience says he might be like. We only think of symbols of God and not God.

MY VIEW - Anselm was not using a logical argument for God.  It's an argument for being swept away in awe and finding God in that awe.

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