[Edit: I feel kind of like a doof. This post is basically a systematization of a conversation Mike and I had in comments on a similarly-themed post I made awhile ago. Thus I feel I owe him at least in part for the basic thing about the sets and the possibilities of members vs wholes having been planted in my head, in the specifics of persons, humanity and salvation.]
1. Let x be an arbitrary member of the set A.
2. Let it be the case that for any given x, with x being part of A, it is possible that x has property q.
3. Then it seems to be the case that, it must also be possible that all x in A have property q.
What's the relevance to theology? Let's let x be an arbitrary person, and let our set A be the set of all human persons, past, present, and future.
4. The Scriptures seem to teach us that we must not despair of the salvation of a given person.
5. This means we must hold out the possibility of the salvation of a given person x in the set of people.
6. So for any given x, where x is a person, it is possible that person x is saved.
7. Then it seems to be the case that it must also be possible that all persons x are saved.
It seems then that on an intellectual level, holding out hope for any arbitrary member of the human race does imply that we hold out the possibility (though not necessarily the probability) of universal salvation.
This doesn't need to be a probability; for instance, I am skeptical that I will see Adolf Hitler in heaven, and I am skeptical of universal salvation due to the weight of Biblical evidence being, in my mind, against its realization. But per Christian Tradition, when I am being reasonable, it seems I cannot eliminate either possibility.