With the sort of exquisite courtesy one likes in a houseguest, our spider has politely taken down his web this morning and retired into cracks in the wall. (I flailed through the air madly with a stick for a few minutes before venturing outside, mind you, but no web.) If he decides to make a habit of this, I'll allow him to stay. As long as he's on the other side of glass, and the web is gone by ten, he's a beneficial little predator and I have no quarrel with him.
It's weird, but he's so big that he's almost less scary. Small spiders have that AGGH! Scurrying! thing, but provided he doesn't ever touch me, the fact that I can see all of his moving parts clearly makes him almost an honorary vertebrate. It's like having a web-spinning lobster rather than an evil bug.