In Chapter 8, the aunt uses logos to convince Quoyle he should take the job at the Gammy Bird:
Of course you can do the job. We face up to awful things because we can't go around them, or forget them. The sooner you get it over with, the sooner you say 'Yes, it happened, and there's nothing I can do about it,' the sooner you can get on with your own life. You've got children to bring up. So you've got to get over it. What we have to get over, somehow we do. Even the worst things.
Though there may not appear to be a specific logic here, that's exactly the aunt's point. She is drawing on the tried-and-true logos of common sense. If one continues to avoid the hard things in life, they will fester. Rather than complaining about them, one should just do them, even if one doesn't feel entirely capable or qualified for the task at hand.
This logic is especially relevant for Quoyle. He is not just thinking for himself but his two young daughters who depend on him. If he can't find the willpower to do things for himself, then he should think about them: what kind of life does he want to give them?