Where reason is lively, and mixes itself with some propensity, it ought to be assented to. Where it does not, it never can have any title to operate upon us. (Treatise 22.214.171.124, SBN 270)
This comes from a discussion at the end of Book I of the Treatise, in which Hume gives the reasons why the skepticism he has come to is not crippling. THere is some dispute about how this should be understood.
I'm inclined to think that a lot of the dispute arises from considering it as a principle in the first place. It is not a general principle, and certainly not a principle in the sense of a rule; rather, I think it is a conclusion, a summation of a sentiment at the end of a reflection -- one might say a resolution. He had started out arguing that it is not possible to make any general rule about whether we should accept or reject highly refined kinds of reasoning that lead to skepticism:
For my part, I know not what ought to be done in the present case. I can only observe what is commonly done; which is, that this difficulty is seldom or never thought of; and even where it has once been present to the mind, is quickly forgot, and leaves but a small impression behind it. Very refined reflections have little or no influence upon us; and yet we do not, and cannot establish it for a rule, that they ought not to have any influence; which implies a manifest contradiction.
He then pulls back from the claim that "refined reflections have little or not influence upon us," pointing out how much confusion skepticism can plunge one into. We then have the famous backgammon passage:
Most fortunately it happens, that since reason is incapable of dispelling these clouds, nature herself suffices to that purpose, and cures me of this philosophical melancholy and delirium, either by relaxing this bent of mind, or by some avocation, and lively impression of my senses, which obliterate all these chimeras. I dine, I play a game of backgammon, I converse, and am merry with my friends; and when after three or four hours' amusement, I would return to these speculations, they appear so cold, and strained, and ridiculous, that I cannot find in my heart to enter into them any farther.
Here then I find myself absolutely and necessarily determined to live, and talk, and act like other people in the common affairs of life.
This doesn't completely address the issue, because the residue of the skeptical confusion remains. However, this residue does not eliminate the attractions of the sociable life; and it simply does not eliminate one of the key facts about skepticism, namely, that skepticism can give no reason why we should be particularly concerned about skeptical reasonings. Skeptical reasonings are hard work, and by their very nature they promise nothing to compensate for the pain and hardship of working one's way through all the insoluble problems raised by them. Thus in practical terms they can be set aside:
Under what obligation do I lie of making such an abuse of time? And to what end can it serve either for the service of mankind, or for my own private interest? No: If I must be a fool, as all those who reason or believe any thing certainly are, my follies shall at least be natural and agreeable. Where I strive against my inclination, I shall have a good reason for my resistance; and will no more be led a wandering into such dreary solitudes, and rough passages, as I have hitherto met with.
We cannot possibly have an obligation to waste our time in reasonings that by their very nature can never get anywhere, if we have no benefit, for ourselves or others, from engaging them; and what possible benefit could we expect to arise from abstract reasonings that put into question whether other minds exist or whether there is an external world? What use could such bizarrely remote philosophical questions be?
All this, however, is a line of reasoning that is founded on being faced with that "philosophical melancholy and delirium". There are other moods, however, and when we are in a better mood, these philosophical reasonings are not such obvious bugbears. In a better mood, a skeptical philosopher like Hume will be willing to face life more skeptically, living life according to inclination but still preserving skepticism. And this is where Hume gives us the Title Principle. It's not a rule for reasoning. It's not even an answer to the problem of skepticism as such: it is description of a sentiment arising in philosophical psychology. Rather, I think, it is part of a larger line of reasoning for the idea that the problem of skepticism (how does a skeptic live a life) is not as practically important as it might seem. Our minds are not stuck in one mood all the time; and how seriously we can take such problems will depend on our moods.
One of the difficulties of interpreting these two sentences is what is meant by 'ought' here. How strongly should it be taken? But one can also read it simply as an expression of a practical feeling. With the return of a good-humored disposition, one feels one can have both the skepticism and practical life by mingling both reason and sentiment. We go with what seems good, as the old Greek skeptics suggested, and thus, given that sentiment, that is our plan of action, what we ought to do. In different moods it might be different; but that does not change what seems to be the most natural thing to do in the times of good mood. And this is exactly what Hume goes on to describe in the next paragraph