The Ontological Argument proposes that if God is "that than which no greater can be conceived," then God must exist, because something that does exist is greater than something that does not, and so existence is necessarily bundled up into "that than which no greater can be conceived." Though Immanuel Kant's refutation, denying existence itself as a quality, goes to the heart of such a claim of existence being tautological, he is applying that, I think, to a purported conception which itself never exists in the first place. For, in fact, it is impossible for something approaching "perfection" in any capacity to actually be conceived.
The Ontological Argument requires us to first conceive something which is perfect, as a step towards requiring the actualisation of this perfection on the basis of existence itself being a higher state of perfection. A simple, devastating blow to this argument can be laid down by a confrontation with the liberties which the first requirement takes with the very nature of conception itself. As the first step in the argument is to define "God" as "that than which no greater can be conceived," we must consider: what exactly is it which we are capable of conceiving?
Picture, for a moment, an infinitely long piece of string. Try and get that image in your head. Well, really, whatever you've thought of, it is a certainty that you are not actually picturing something "infinite" -- perhaps you imagine infinity by picturing that string trailing off into the distance, to the point where we can no longer see it at all, but (we tell ourselves) it continues on forever outside of our view, or ability to picture. Or, you may picture a string running straight across a horizon, your image pulling back from it as your field of view expands by orders of magnitude.
We do these things in place of undertaking the impossible task of picturing such a string as it actually goes on, forever. To contemplate an actualisable infinite string, we would need to spend an infinite amount of time on the thought itself. And so it is this way, in which we imagine perfection, by modeling an actually imperfect mental construct that comes as close to perfection as our minds are able to contemplate, but does not in fact achieve the conceptual step prerequisite to actualisation. Seeking a more abstract conception, consider the greatest or most perfect piece of music composable. The phrase "the greatest piece of music composable" is not, itself, utterly devoid of meaning, as we can imagine that such a thing might be -- but there is no means to conceptualise the actual tune for which that description would be universally true. We can not hum a few bars and know our conceptualisation to be objectively correct.
Simply put, perfection -- being "the greatest conceivable" in any field -- is a form of infinity, a projection that is infinite along the lines of perfectness. And, since we really can't truly conceive of an infinite, no conception actually exists to require this illusory conceived infinite be perfected along some tautological additional dimension of actual existence. Not only can we not conceive the infinite, we are, in fact (indeed, by definition) unable to truly fully conceive of things that are merely incomprehensibly large. For example, we can look at a book's worth of pictures of Jupiter and descriptions of its characteristics, but we can no more construct a fully accurate mental image of the sheer vastness of that planet than we can circumnavigate it by crawling naked for the length of the Jovian equator.
Reflecting upon the limitations of the human mind to do anything more than model limited versions of abstract infinites, we can see the impossibility of actually conceiving "that than which no greater can be conceived." Where David Hume, in the previous node, says the ideal can exist only in the human mind, he has already gone a step too far, for it is only model of the ideal that can therein persist. And, anticipating one remaining possible challenge, if we remove this humanistic consideration, then the Ontological Argument itself ceases to exist, for it is only a construct of human thought. As an absolute premise, the argument requires the human reader giving it consideration to first conceive the perfection suggested -- to suppose that God must exist because God would be able to conceive God is to beg the question.