The most perfect happiness, surely, must arise from the contemplation of the most perfect object. But what more perfect than beauty and virtue? And where is beauty to be found equal to that of the universe? Or virtue, which can be compared to the benevolence and justice of the Deity? If aught can diminish the pleasure of this contemplation, it must be either the narrowness of our faculties, which conceals from us the greatest part of these beauties and perfections; or the shortness of our lives, which allows not time sufficient to instruct us in them. But it is our comfort, that, if we employ worthily the faculties here assigned us, they will be enlarged in another state of existence, so as to render us more suitable worshippers of our maker: And that the task, which can never be finished in time, will be the business of an eternity.[David Hume, "The Platonist," Essays Moral, Political, and Literary.]
Hume's "The Platonist" is one of a quartet, the other three essays being "The Epicurean," "The Stoic," and "The Sceptic." They are really masterworks, probably Hume's most brilliant essays, but it has always been somewhat difficult to pin down what Hume is doing in them. The genre is easy enough to figure out: they are each philosophical sketches, from a distinct philosophical point of view. It also seems clear enough that the fundamental object of each essay is to describe human happiness as it appears from that philosophical perspective. None of the four gives Hume's own view, in any straightforward way; comparing the essays to Hume's other works shows that each has affinities with some things Hume says elsewhere, and that each says things that are hard to square with things Hume says elsewhere. (You might, for instance, assume that the Sceptic's view is simply identical with Hume's, but on one point in the essay itself Hume actually criticizes a point in the Sceptic's argument in a footnote.) They aren't historical essays, since the viewpoint given in each has only a loose family resemblance to the historical schools of thought that give them their titles. We have to use a lot of guesswork to make sense of the four as a unit, but my suggestion, very rough and somewhat speculative, would be:
(1) Each of the essays describes a view of human happiness that Hume thinks naturally arises among human beings.
(2) The particular formulation given of each account of happiness seems to be one to which Hume is at least sympathetic. Obviously the sceptical account is the one with which Hume has the most sympathy (it is massively longer than any of the other three), and the 'platonic' account is the one with which he has the least (which is arguably why it is noticeably shorter than the others). But they are all formulated in such a way that any true Humean can see the force and appeal of each.
(3) Thus the essays together compose a sort of indirect argument. These are the best formulations of four natural tendencies in how we think of happiness. They are not completely consistent, but they are not wholly inconsistent, either. The best account of human happiness will be the one that does the most justice to each of these tendencies.
(4) All four essays circle around the question of how much of human happiness is due to nature and how much is due to human artifice, and this is where they diverge most sharply. The Epicurean insists that true happiness can only flow from nature; the Stoic insists that it depends on human art giving shape to nature; the Platonist insists that happiness is received from without, and that we attain to perfect happiness by rational of contemplation what is perfect; the Sceptic insists that it is experienced within and that we cannot therefore expect to attain to any perfect happiness, happiness owing at least as much to fortune as to reason. Closer study of this is what's really necessary to improve our understanding of the quartet.
(5) The footnote to "The Sceptic," mentioned above, seems also to be important, and its ending may well be the main thrust of the essays as a group:
Assist yourself by a frequent perusal of the entertaining moralists: Have recourse to the learning of PLUTARCH, the imagination of LUCIAN, the eloquence of CICERO, the wit of SENECA, the gaiety of MONTAIGNE, the sublimity of SHAFTESBURY. Moral precepts, so couched, strike deep, and fortify the mind against the illusions of passion. But trust not altogether to external aid: By habit and study acquire that philosophical temper which both gives force to reflection, and by rendering a great part of your happiness independent, takes off the edge from all disorderly passions, and tranquillizes the mind. Despise not these helps; but confide not too much in them neither; unless nature has been favourable in the temper, with which she has endowed you.
If we should take this, as is, to be Hume's point, then the essays are an argument for what might be called sceptical moral eclecticism: proceeding cautiously, nonetheless one should draw on the full panoply of moral authors (note that, for instance, Plutarch is a Platonist, and that Seneca is a Stoic), but without taking any of them to be the key to happiness. This is also something that would bear further study.
(6) Another point that needs to be studied more closely in the future: the Stoic answers the Epicurean, the Platonist responds to both (dismissing both of their ideals), and the Sceptic responds to all three. Is the quartet seen as a sort of progress toward skepticism? Or is there something else going on with this structure?
So do we find in Hume's Platonist? He gives one of Hume's several formulations of an argument from design; he puts considerable emphasis on beauty; and he insists on philosophical humility before the greatness of the universe. All three of these are things with which Hume has a provable sympathy. But the Platonist, of course, is not a skeptic, and Hume is, and this makes a big difference otherwise.