Here are two more arguments to add to the list.
In Spectres of False Divinity, Hume scholar Thomas Holden argues that Hume accepted moral atheism -- very roughly, the view that there is no god that has moral attributes. Holden distinguishes between weak and strong moral atheism. Weak moral atheism is the view that there is no god that is morally praiseworthy. By contrast, strong moral atheism is the view that there is no morally assessable god; that is, there is no god that is a proper object of moral evaluation one way or the other. Given this distinction, it follows that strong moral atheism entails weak moral atheism, but not vice-versa. In the book, Holden argues that Hume is a strong moral atheist.
Holden extracts from Hume's writings two arguments for moral atheism that are based on Hume's sentimentalist ethical theory: the argument from sentimentalism and the argument from moral motivation. In the conclusion of the book, Holden summarizes the two arguments as follows:
Hume has two distinct lines of argument for strong moral atheism. One appeals to his account of the natural ambit of our human passions along with his sentimentalist metaphysics of morals in order to conclude that the first cause or designer is beyond the projected, response- dependent world of moral properties. According to this argument from sentimentalism our natural feelings of approval and disapproval range only so far as the outer frontier of sense and imagination. The projected properties of virtue and vice are thus confined to the immanent world, and cannot characterize any transcendental order beyond this permanent horizon (see Chapters 3 and 4). (p. 209)
Hume’s second argument also turns on facts about sentimental psychology, though this time the emphasis is on the deity’s own sentiments and passions (if indeed it has any). This argument from motivation appeals to Hume’s account of the passions as the engines of action along with a form of probabilistic reasoning about the likely character of any first cause or ultimate organizing principle responsible for the ordered universe. According to Hume, even though we know nothing substantive about the distinctive intrinsic character of the original cause of all, we can judge it highly unlikely that this being or principle has anything like our own sentimental psychology. But if the deity lacks some sort of approximately anthropomorphic sentimental psychology, it will not be moved by moral concerns: weak moral atheism follows. Moreover, without an approximately human-like system of passions, the deity’s behavior will be unintelligible in human terms—and for Hume this is sufficient to place this being or principle beyond the sphere of moral assessable beings: strong moral atheism also follows (see Chapter 5). (Ibid.)
S1. The deity is not a natural object of any human passion.
S2. Moral sentiments are a species of human passion.
S3. If a being is not a natural object of the moral sentiments, then it cannot have moral attributes (either virtues or vices).
S4. The deity cannot have moral attributes (either virtues or vices). (p. 51)
Rico Vitz helpfully expresses the argument from moral motivation as follows:
(M1) In order to be morally assessable, a being must have a sentimental psychology sufficiently similar to that of human beings.
(M2) If the first cause lacks a sentimental psychology sufficiently similar to that of human beings, the first cause is not morally assessable.
(M3) The first cause does, most likely, lack a sentimental psychology sufficiently similar to that of human beings.
(M4) The first cause is, most likely, not morally assessable.