Yes, those are valid arguments! Maybe I should have reformulated it to "a real god is better than an imaginary god" directy, then that does not work anymore. But I am no expert either ;)
The real way to break it down is by attacking (1). One common answer is that this does not prove the existence of the "biblical god" at all. Nothing about an omniscient creator God in heaven. It just proves there is a "best" thing. For all we know it could be a potato.
Another way is to say that by accepting (1), we basically already assume a God exists. So, nothing new was concluded by proving he does. This logical flaw is called "begging the question". Although not everyone agrees if that is the case here.
Let's separate it up, with this argument, people often do follow the logic, but do not accept the premises.
Premise 1: God is defined as the greatest thing that we can possibly concieve ("that for which no greater can be conceived")
Premise 2: real things are better than imaginary things
We can imagine God (he exists in understanding). A real God is better than an imaginary God (2).
Then, if God does not exist, we can concieve a greater thing (a real God) this leads to a contradiction with respect to (1). Therefore by proof of contradiction, God must exist
The real way to break it down is by attacking (1). One common answer is that this does not prove the existence of the "biblical god" at all. Nothing about an omniscient creator God in heaven. It just proves there is a "best" thing. For all we know it could be a potato.
Another way is to say that by accepting (1), we basically already assume a God exists. So, nothing new was concluded by proving he does. This logical flaw is called "begging the question". Although not everyone agrees if that is the case here.