On to business:
All of the secondary literature I’ve read about Anselm’s ontological argument indicates that the argument was not actually intended as a “proof” of the existence of God as against some sort of skepticism. For one thing, modern skepticism is rooted in empirical priorities (which I think was evident from the previous discussion), but this sort of skepticism wasn’t around in the middle ages when these original arguments were written. For another, the argument seems to rest on premises that sort of already presuppose the conclusion.
(Paul Vincent Spade, “Medieval Philosophy,” The Oxford Illustrated History of Philosophy 77-78)[Anselm] was not trying to prove the truths of theology as though they were otherwise subject to doubt. His purpose was not to shore up a faith that might otherwise falter, but rather simply to explore what he already firmly believed. His attitude is summed up near the beginning of the Proslogion in a famous statement: ‘I believe in order to understand’ (Credo ut intellegam).
(Hyman & Walsh, eds., Philosophy in the Middle Ages, 149)On the assumption that a Christian Platonism is integral to the proof, including an assumption of divine illumination and even perhaps a scriptural conception of God, it has been claimed that Anselm was not offering such a proof as would be intended to convince skeptics, but merely an elucidation of a belief already held, or perhaps even a kind of map of a mystical journey to the mind of God.
(Colin Brown, Philosophy & the Christian Faith, 22-24)Barth has argued...that Anselm’s point was not to prove the existence of God by reason alone without any appeal to experience and the Christian revelation. His argument was intended to show that we cannot rationally deny the living God once we know who he is — the most perfect being. ... If Barth’s interpretation of Anselm is correct, then...[Anselm’s] work was not a piece of natural theology at all. The object of the exercise was not to discover rational, objective proofs for the things we believe in by faith. God is known in experience through personal encounter. The aim of philosophy is to understand the nature of this experience in depth. ... It is not a case of proving first and then believing. We cannot believe theological truths for non-theological reasons. Rather, it is only when we encounter the living God in faith that we are in a position to grasp the truth of Christian faith. The task of philosophical theology is to examine the implications of this.
So when we look at Anselm’s ontological argument with a skeptical eye, when we try to apply it to our skepticism about God, we may be committing an anachronism. The argument seems to operate within an already faithful framework, perhaps more specifically Platonic or neo-Platonic, which empiricists obviously reject out of hand.
On the surface, then, it appears it would be a circular argument. But to me it seems like the validity of the argument is going to depend on your ontological priorities, your take on metaphysics. If Platonic realism seems plausible — if things like pure geometry, numbers, “perfection” etc., have some manner of real existence aside from the empirical, observable universe — or any other sort of transcendence — Anselm’s argument holds a lot more water than if the physical universe is all there is.
I’ve heard roughly the same be said of the Thomistic arguments - from contingency, teleology, etc.: at the end of those arguments he says things like “this everyone understands to be God,” not, “therefore God exists,” which seems to indicate that his audience is also already working within his framework, at least to some extent, so these arguments aren’t addressing “our” skepticism per se. (He also doesn’t go so far as to say that these arguments point to the One True Christian God, but just the concept of god that people seem naturally to have fits in here. He argued that divine revelation was needed in addition to this sort of natural intuition to get all the way there.) As far as I understand, Aquinas’ primary purpose was to fit Christian belief within an Aristotelian system of thought — or maybe the other way around — not apologetics. So these arguments are going to make more sense to you if you already subscribe to Aristotelian metaphysics and/or Christian belief than if you subscribe to neither. And skeptical empiricists subscribe to neither, obviously.
So I think these arguments don’t “work” — they fail to convince — in the sense that they don’t address, and therefore don’t stand up to, skeptical/empirical demands.
But I think they do “work” — they have relevance — in that they can be made to question in the first place those demands and/or their basis, if we drill down to the underlying assumptions.