One disastrously misleading trope in the study of Adam Smith is that his fundamental metaphysical and psychological commitments are basically Hume's. I attack it regularly in print. (See, e.g., here, here, here, here.) But I have overlooked a very important example of the way in which Smith deviates from Hume. Consider this passage:
Let us suppose that the great empire of China, with all its myriads of inhabitants, was suddenly swallowed up by an earthquake, and let us consider how a man of humanity in Europe, who had no sort of connexion with that part of the world, would be affected upon receiving intelligence of this dreadful calamity. He would, I imagine, first of all, express very strongly his sorrow for the misfortune of that unhappy people, he would make many melancholy reflections upon the precariousness of human life, and the vanity of all the labours of man, which could thus be annihilated in a moment. He would too, perhaps, if he was a man of speculation, enter into many reasonings concerning the effects which this disaster might produce upon the commerce of Europe, and the trade and business of the world in general. And when all this fine philosophy was over, when all these humane sentiments had been once fairly expressed, he would pursue his business or his pleasure, take his repose or his diversion, with the same ease and tranquillity, as if no such accident had happened. The most frivolous disaster which could befal himself would occasion a more real disturbance. If he was to lose his little finger to-morrow, he would not sleep to-night; but, provided he never saw them, he will snore with the most profound security over the ruin of a hundred millions of his brethren, and the destruction of that immense multitude seems plainly an object less interesting to him, than this paltry misfortune of his own. To prevent, therefore, this paltry misfortune to himself, would a man of humanity be willing to sacrifice the lives of a hundred millions of his brethren, provided he had never seen them? Human nature startles with horror at the thought, and the world, in its greatest depravity and corruption, never produced such a villain as could be capable of entertaining it. But what makes this difference? When our passive feelings are almost always so sordid and so selfish, how comes it that our active principles should often be so generous and so noble? When we are always so much more deeply affected by whatever concerns ourselves, than by whatever concerns other men; what is it which prompts the generous, upon all occasions, and the mean upon many, to sacrifice their own interests to the greater interests of others? It is not the soft power of humanity, it is not that feeble spark of benevolence which Nature has lighted up in the human heart, that is thus capable of counteracting the strongest impulses of self-love. It is a stronger power, a more forcible motive, which exerts itself upon such occasions. It is reason, principle, conscience, the inhabitant of the breast, the man within, the great judge and arbiter of our conduct. It is he who, whenever we are about to act so as to affect the happiness of others, calls to us, with a voice capable of astonishing the most presumptuous of our passions, that we are but one of the multitude, in no respect better than any other in it; and that when we prefer ourselves so shamefully and so blindly to others, we become the proper objects of resentment, abhorrence, and execration. It is from him only that we learn the real littleness of ourselves, and of whatever relates to ourselves, and the natural misrepresentations of self-love can be corrected only by the eye of this impartial spectator. (The Theory of Moral Sentiments (TMS), emphasis added)
Now this is not wholly anti-Humean. For example, Hume (see here) and Smith agree that commerce is a proper subject of speculation. Even so, among other things, Smith is criticizing (at least) four Humean doctrines here. First (and this has been noted by Samuel Fleischacker), Smith is targeting an infamous passage in Hume:
Where a passion is neither founded on false suppositions, nor chuses means insufficient for the end, the understanding can neither justify nor condemn it. ’Tis not contrary to reason to prefer the destruction of the whole world to the scratching of my finger. ’Tis not contrary to reason for me to chuse my total ruin, to prevent the least uneasiness of an Indian or person wholly unknown to me. (Treatise of Human Nature, 126.96.36.199)
Now, from context it is clear that Hume is not saying that it is reasonable (or rational) to prefer the destruction of the whole world to the scratching of one's finger. But as Fleischacker argues for Smith it is not from affect, but from reason that we resist the idea that we prefer the destruction of the whole world to the scratching of one's finger.
And this gets me to Smith's second criticism of Hume. Hume is notorious for claiming that "Reason is, and ought only to be the slave of the passions, and can never pretend to any other office than to serve and obey them." (188.8.131.52) Now behind this claim is the view that according to Hume reason is not a so-called active principle. (Hume cites 2.3.3 here.) By contrast "conscience" or a "sense of morals" are active principles according to Hume (184.108.40.206). An active principle is a "force or efficacy" (220.127.116.11). Interestingly enough, then, in Hume reason is not a mental cause, while conscience can motivate actions.
Now in the long quote above, according to Smith reason is a so-called "active principle." So, this is a second significant departure from Hume, and helps explain why for Smith reason can correct the sentiments even in the case of what our proper response to a very distant earthquake ought to be. Third, in Smith's system reason is a synonym for "conscience" (and also "the inhabitant of the breast, the man within, the great judge and arbiter of our conduct," etc), and this is a big departure from Hume. (Maria Carrasco has famously argued that in Smith this use of "reason" is an instance of practical reason.)
Neither Hume nor Smith discusses so-called active principles in their moral psychology very often. But an important treatment occurs in material that Smith added to the the final edition of TMS, where he explains that sympathy for one's children is much more efficacious than sympathy for parents. The affections founded on the former (such as tenderness) are active principles. Now for a proper understanding of Adam Smith this is very significant because it nicely illustrates the fact that for Smith sympathy is not just a judgment, but it can also be motivating. And this shows that Leon Montes was right to doubt the claim promoted by the editors of the Glasgow Edition of TMS that sympathy is "entirely different" from "the motive to action!" (Ryan Hanley's edition of TMS provides far more reliable guidance.) Some other time I explore the intellectual origins of this idea of sympathy as an active principle.
Finally, I conclude with a fourth difference: in the long quote above, Smith is targeting Hume's claim in the Enquiry Concerning the Principles of Morals that "humanity...alone is the foundation of morals, or any system of behavior." According to Smith humanity is too "soft" a power! So, while Smith does not deny that Humean humanity has the right kind of (let's call it) formal features (that is, it is in principle equally available in everyone and providing identical judgments), it does not have the motivational pull for a morality worth having.