Objection 1: It would seem that one may hope for another's eternal happiness. For the Apostle says (Phil. 1:6): "Being confident of this very thing, that He Who hath begun a good work in you, will perfect it unto the day of Jesus Christ." Now the perfection of that day will be eternal happiness. Therefore one man may hope for another's eternal happiness.
Obj. 2: Further, whatever we ask of God, we hope to obtain from Him. But we ask God to bring others to eternal happiness, according to James 5:16: "Pray for one another that you may be saved." Therefore we can hope for another's eternal happiness.
Obj. 3: Further, hope and despair are about the same object. Now it is possible to despair of another's eternal happiness, else Augustine would have no reason for saying (De Verb. Dom., Serm. lxxi) that we should not despair of anyone so long as he lives. Therefore one can also hope for another's eternal salvation.
On the contrary, Augustine says (Enchiridion viii) that "hope is only of such things as belong to him who is supposed to hope for them."
I answer that, We can hope for something in two ways: first, absolutely, and thus the object of hope is always something arduous and pertaining to the person who hopes. Secondly, we can hope for something, through something else being presupposed, and in this way its object can be something pertaining to someone else. In order to explain this we must observe that love and hope differ in this, that love denotes union between lover and beloved, while hope denotes a movement or a stretching forth of the appetite towards an arduous good. Now union is of things that are distinct, wherefore love can directly regard the other whom a man unites to himself by love, looking upon him as his other self: whereas movement is always towards its own term which is proportionate to the subject moved. Therefore hope regards directly one's own good, and not that which pertains to another. Yet if we presuppose the union of love with another, a man can hope for and desire something for another man, as for himself; and, accordingly, he can hope for another's eternal life, inasmuch as he is united to him by love, and just as it is the same virtue of charity whereby a man loves God, himself, and his neighbor, so too it is the same virtue of hope, whereby a man hopes for himself and for another.
This suffices for the Replies to the Objections.