How we cite our quotes: (line number)
Quote #4
I'm afraid I must tell you I wanted the dog to live so that I could see what our new relationship might come to… Please understand, Peter; that sort of thing is important. You must believe me; it is important. We have to know the effect of our actions. (160)
Jerry's setting down a rule here: we must know the effect of our actions. It's not a rule you can really follow, though: how can you tell what effect your actions have? Jerry wants there to be meaning and order but there isn't. So he poisons dogs. It's not a good plan, really.
Quote #5
JERRY: I suppose you don't quite know what to make of me, eh?
PETER: (A joke) We get all kinds in publishing. (Chuckles) (178-179)
Jerry feels he can't be categorized; Peter responds by saying that Jerry is unusual in a familiar, categorizable way. Even uncategorizability can be categorized in Peter's world.
Quote #6
After all, stop, stop, hee, hee, hee, after all, the parakeets will be getting dinner ready soon. Hee, hee. And the cats are setting the table. (193)
This is Peter's great moment of spiritual release. Jerry tickles him, and he has a goofy little fantasy about parakeets setting the table and things going mildly and pleasantly out of rule and order. Awww. (And then everything goes to rat poison, of course.)