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In the ontological argument, Anselm assumes that "A being that exists as an idea in the mind and in reality is, other things being equal, greater than a being that exists only as an idea in the mind". Isn't this a very big assumption? He hasn't even defined properly what greatness is. He should 1st define what greatness is and then logically prove that assumption from his definition. If someone claims that "A being that exists as an idea in the mind and in reality, other things being equal, has the same greatness as a being that exists only as an idea in the mind", how will the defenders of ontological argument argue against it?

I haven't read about Gödel's ontological proof and other more rigorous ontological arguments. Do they have similar axioms/assumptions which are not reasonable?

Even if we assume the ontological argument; does it say anything about God except the fact that it is maximally great? Can ontological arguments tell anything about the number of maximally great beings?

For example, I can claim that the universe and laws of physics are the maximally great beings and the universe and laws of physics are gods and therefore they necessarily exist.

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A being that exists as an idea in the mind and in reality is, other things being equal, greater than a being that exists only as an idea in the mind

The idea of greater than here seems reasonable enough. We could represent it by saying that if a and b are assumed greater than zero, then a + b is greater than a, which is true enough.

There is a problem, though, of course, so it must not be that.

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I guess the idea of greatness comes from numbers, but you might say something is great if it benefits yourself, or the majority, depending on your ethics

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