Philosopher, what is the meaning of the great mitzva of Hachnosas Orchim which is greater than the acceptance of the Shchina?
Actually Philosopher wins that point. Hachnosas Orchim means inviting travelers, people who have no home to go to. Inviting people who have a home at which they could eat is NOT hachnosas orchim. If the people are lonely then inviting them is surely a great mitzvah, but not that one. It falls under chessed, ve’ahavta lere’acha kamocha, and the Torah’s general concern for the stranger, orphan, widow, and Levi, a category which surely also includes the divorced and the single, but the Shulchan Aruch (Orach Chaim ch 308) defines hachnosas orchim and this does not fit the definition.