Wish they'd taught philosophy at my school. Never mind.
I suspect if I read all the posts above in detail I'd find much of it has already been said but my take on it:
1. God is a being of which nothing greater can be conceived.
This is one possible definition of a Deity. We may run with it. I'm unsure "greater" is well defined though, and may cause issues.
2. I can conceive of such a being
Can you ? Are you conceiving this being in detail, which would take an infinite mind, or are you simply accepting the concept, which is not quite the same thing ? Folk can accept all manner of things without looking into the detail of whether they can exist in reality or even in detail in the imagination. But again let's run with this vague, "I can sort of describe it so that's good enough" conception.
3. It is greater to exist in reality than merely in the imagination
That use of the word "greater" again. What is "greater" about existing in reality rather than the imagination ? I reject that completely. At best it needs clarification.
4. Therefore the being of which I conceive must exist in reality
And that follows, I believe, from the muddled/missing definitions used earlier. And is why there is not an infinite number of Gods as I can imagine a new one each time I try. This is only a good argument for God if you ignore the weaknesses as it goes along.
By the way I don't accept we should state old philosophers talk a load of nonsense. That is just insulting to them. One needs to put things forward to discuss or one gets nowhere. It is with different generations/different mindsets we spot things they appeared not to at the time. For sure much of what is suggested will be found to be flawed but good for them for bringing it up for examination.
Going back to Jim's clarifications. I do not see this surprisingly compelling bit.
Bad enough we reach a point where the answer is that we don't know, so have to investigate both possibilities. Worse that one path immediately shows it would disprove a Deity by reason of the path assumption being that a prefect being can not exist. Possible existence surely can not equate to definite existence. It is surely that question we are exploring in the first place.
I think the Gödel page has assumptions that seem irrelevant at the start but prove to be relevant. I'm unsure I want to give myself a headache struggling through the symbolism stuff but:
The issue of fictional characters not believing in themselves ought not arise as they don't exist, so any belief in their beliefs are mere imagination. In any case there are mental conditions out there in the real world where some folk are convinced they are dead. Why not a fictional character who is convince they do not exist ? And the definition of God, that it encompasses all rationality but not all irrationality too, and one is simply going to dismiss a God who has both as it should ?
If one chooses a poor basis upon which to argue then the conclusions are suspect at best. Good for a classroom discussion, but creates no revelation.
If I can imagine something perfect then it must be real. Since, existence is a necessary condition for perfection. Why would anyone decide perfection needs existence ? Existing perfection requires existence, imagined perfection does not, I'm not even sure it needs thought, but that's a different discussion whether things not thought of can be considered to exist in the set of unthought thoughts.
And I apologise in advance for all the millions of typos that will suddenly appear as I push the Submit button.i