what logic does jack use to assure the others that there are no large beats on the island?

This is an interesting question. Jack says that he has been all over the island and has seen no beast. Initially the bigger boys laugh at the prospect of a beast or monster. But when fear starts to creep into the "littluns", Jack watches many "bigguns" get scared too. Jack seizes the opportunity to plant the seeds of doubt, "There isn't a snake-thing. But if there was a snake we'd hunt it and kill it." Jack quickly learns that fear is a great way to control people. If he can offer protection against a perceived monster, he can leverage much more power than Ralph.