[Sorry, but I don't see an online edition of this work, which is very disappointing. I have taken the liberty of repairing the noxious plural-neuter pronouns in this snippet, since St. Anselm surely would not have used them, and they are rather obviously an artifact of a misguided modernity.]
Of all the things that exist, there is one nature that is supreme. It alone is self-sufficient in its eternal happiness, yet through its all-powerful goodness it creates and gives to all other things their very existence and their goodness. Now, take someone who either has never heard of, or does not believe in, and so does not know, this—this, or indeed any of the numerous other things which we necessarily believe about God and his creation. I think that [he] can, even if of average ability, convince [himself], to a large extent, of the truth of these beliefs, simply by reason alone. [Monologion, 1; emphasis added]
St. Anselm suggests, then, that what he's going to present is an argument about God – his existence and nature – from reason alone. And so he does: there are no appeals to Scripture in this work. He also says that he thinks that this argument should be acceptable to the average man who knows nothing about God.
It seems to me that he begins admirably. I'm not sure how persuasive his argument would be for the modern man, but he begins by arguing that all things must derive their excellences from some supreme Excellence, and it seems to me that his meaning is that they enjoy it by way of participation in the excellence of the supreme essence. I've read very little Plato, and none in the last couple decades, but from what I gather this is supposed to be an approach influenced by Plato. And it's not really all that bad.
After several chapters, though, it seems (to this Thomist-in-training) that St. Anselm's course veers off in an unfortunate direction for his stated purpose. We'll come back to this in a little bit, because I think it's important, but for now let's see what he begins to do. After having established that the supreme essence must be the creator from nothing of all other things that exist (because existence is a good, and they must derive their existence from the One who has existence supremely – namely, the supreme essence), he writes:
But I seem to see something which demands that we distinguish carefully the sense in which it is possible to say that created things were nothing before being created. For a maker makes something rationally if, and only if, there is already something there in his reasoning—as a sort of exemplar. … The following then is clear: before all things existed, the manner, features, and fact of their future existence already existed, in the reasoning of the supreme nature. …
But what is this form that is already there…? Before a craftsman makes something by means of his craft, he first expresses it within himself by means of a mental conception. So, what is the form but this kind of verbalization of the things to be created in the maker's reason? [ibid., 9-10 passim; emphasis added]
From here, and again in several subsequent chapters, Anselm builds an argument that this "verbalization" may be described as "the Word," and later as "begotten," and finally as "the Son."
Do you see where this is going?
After pursuing the distinctions between and attributes of the Father and the Son (as he now frequently names them), he comes to this:
What delight to gaze upon what is proper to Father and Son and what they have in common! And nothing gives me more delight in contemplation than their mutual love. For the supreme spirit indeed loves itself, just as it is conscious of, and understands, itself. … Therefore, as it is conscious of, and understands itself, so the supreme spirit loves itself. [ibid., 49]
Lest we miss it: Anselm would have us understand the Father as "the consciousness" of the supreme spirit, and the Son as its self-understanding. He continues:
Now, it is quite clear to any rational mind that self-consciousness and self-understanding are not due to self-love. But rather self-love happens because of self-consciousness and self-understanding. Self-love is impossible without self-consciousness. It is impossible without self-understanding. Nothing is loved without being the object of consciousness and understanding. … Therefore it is clear that the supreme spirit's love proceeds from its being self-conscious and self-understanding. And given that it makes sense to think of the supreme spirit's consciousness as Father, and its understanding as Son, it is evident that the supreme spirit as love, proceeds equally from the Father and the Son. [50; emphasis added]
Hopefully it's obvious that St. Anselm hasn't merely attempted an argument for the existence of God using reason alone, but also for the Trinity!
Well, my reaction to this is unquestionably that of St. Thomas: that it's not possible to make a cogent argument for the Trinity from reason alone. With respect to how he argues for the Son: he moves from saying that God must be reasonable (which is unproblematic) to making declarations about the means by which God created: namely, by his verbalization or word. But this, it seems to me, is an unwarranted leap. Even if we conclude (reasonably enough) that God created all things ex nihilo, it's a big step to then make assertions about how he did so, and yet another huge jump to go from creation by means of his word to The-Word-As-Coequal-Person of the Godhead. And similarly for how he argues for God's self-love as a Third Coequal: there is simply no good reason for it, and if there is, there's simply no good reason to stop with his love. We ought to continue with his justice and goodness and so forth, it seems to me.
So as I say: I do not consider this to be a successful argument of the kind St. Anselm says that he was presenting: namely, one that draws on reason alone, for the sake of persuading the man who knows nothing about God.
However, this is not to say that I consider the argument to be a failure. I have pondered a little how it is that St. Anselm might have considered what he was doing to be a success, and I think that it is here that we have the beginning of an answer. He writes, in the prologue:
Some of my brethren have often and earnestly asked me to write down, as a kind of model meditation, some of the things I have said, in everyday language, on the subject of meditating upon the essence of the divine; and on some other subjects bound up with such meditation. They specified…the following form for this written meditation: nothing whatsoever to be argued on the basis of the authority of Scripture, but the constraints of reason concisely to prove, and the clarity of truth clearly to show, in the plain style, … the conclusions of distinct investigations.
The brethren in view were his fellow monks of the Abbey of Bec. So what St. Anselm has written was really for the purpose of satisfying the wishes of his fellow Catholics, not for the sake of apologetics. Secondly, and (so it seems to me) importantly, I think it's worth considering something famously said by St. Anselm elsewhere: "I believe, in order that I may understand." It seems to me, if we look at the Monologion as something written for believers, and written not as a means to draw them to the Faith but rather as something that helps them to understand it, then the work comes off looking much, much better. Then, we see, Anselm and his audience have something in common. They already believe; now they wish to understand (as far as possible). That being the case, it's not necessary for Anselm to justify to the unbeliever his case for the Word and Spirit as persons of the Trinity: he is merely explicating what the monks already believe. He is helping them to understand it. Seen this way, I'd say that the Proslogion looks pretty good. I'm not sure that I understand why it is that he proposed it as something that might persuade the unbeliever, but in view of his own prologue I think we're justified in granting more weight to his audience and intended purpose: to assist his fellow monks.